Machine_Learning.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/github/dr-mushtaq/Machine-Learning/blob/master/Machine_Learning.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "source": [
        "#<p style=\"font-family:JetBrains Mono; font-weight:normal; letter-spacing: 1px; color:#207d06; font-size:100%; text-align:left;padding: 0px; border-bottom: 3px solid #207d06;\">**Section**</p>"
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      "metadata": {
        "id": "cv-fT4BB7JXs"
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    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "1.   Linear Regression with one Variable\n",
        "2.   Multivariate Linear Regression\n",
        "3.   Logistic Regression\n",
        "4.   Regularization\n",
        "\n"
      ],
      "metadata": {
        "id": "m-I2rd6T7REv"
      }
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    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "#<p style=\"font-family:JetBrains Mono; font-weight:normal; letter-spacing: 1px; color:#207d06; font-size:100%; text-align:left;padding: 0px; border-bottom: 3px solid #207d06;\">**⭐️Chapter: 1- Linear Regression with one Variable**</p>"
      ],
      "metadata": {
        "id": "vt0OvLLQwdLF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the first part of exercise 1, we're tasked with implementing simple linear regression to predict profits for a food truck. Suppose you are the CEO of a restaurant franchise and are considering different cities for opening a new outlet. The chain already has trucks in various cities and you have data for profits and populations from the cities. You'd like to figure out what the expected profit of a new food truck might be given only the population of the city that it would be placed in.\n",
        "\n",
        "Let's start by examining the data which is in a file called \"ex1data1.txt\" in the \"data\" directory of my repository above. First we need to import a few libraries.\n"
      ],
      "metadata": {
        "id": "2zUQhnqb9kfa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Import libraries**"
      ],
      "metadata": {
        "id": "LOSfypIpxfrn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import os\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "metadata": {
        "id": "acUJVC9xxooL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let's get things rolling. We can use pandas to load the data into a data frame and display the first few rows using the \"head\" function."
      ],
      "metadata": {
        "id": "YO53oSqD9wwB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Load dataseet**"
      ],
      "metadata": {
        "id": "jSPAg9YexrfA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
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        "colab": {
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        "id": "I3ZNc6OCx3R-",
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#path = os.getcwd() + '/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex1data1.txt'\n",
        "data = pd.read_csv('/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex1data1.txt', header=None, names=['Population', 'Profit'])\n",
        "data.head()"
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              "   Population   Profit\n",
              "0      6.1101  17.5920\n",
              "1      5.5277   9.1302\n",
              "2      8.5186  13.6620\n",
              "3      7.0032  11.8540\n",
              "4      5.8598   6.8233"
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      "source": [
        "Another useful function that pandas provides out-of-the-box is the \"describe\" function, which calculates some basic statistics on a data set. This is helpful to get a \"feel\" for the data during the exploratory analysis stage of a project."
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            "text/plain": [
              "       Population     Profit\n",
              "count   97.000000  97.000000\n",
              "mean     8.159800   5.839135\n",
              "std      3.869884   5.510262\n",
              "min      5.026900  -2.680700\n",
              "25%      5.707700   1.986900\n",
              "50%      6.589400   4.562300\n",
              "75%      8.578100   7.046700\n",
              "max     22.203000  24.147000"
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              "      <td>97.000000</td>\n",
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              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>8.159800</td>\n",
              "      <td>5.839135</td>\n",
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              "      <th>std</th>\n",
              "      <td>3.869884</td>\n",
              "      <td>5.510262</td>\n",
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              "      <th>min</th>\n",
              "      <td>5.026900</td>\n",
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              "    [theme=dark] .colab-df-convert {\n",
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              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-574debb3-8e2e-4e70-b240-33bb038ef957 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-574debb3-8e2e-4e70-b240-33bb038ef957');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-b3b4a732-619d-42aa-9e5a-ed0babf45f02\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-b3b4a732-619d-42aa-9e5a-ed0babf45f02')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-b3b4a732-619d-42aa-9e5a-ed0babf45f02 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Examining stats about your data can be helpful, but sometimes you need to find ways to visualize it too. Fortunately this data set only has one dependent variable, so we can toss it in a scatter plot to get a better idea of what it looks like. We can use the \"plot\" function provided by pandas for this, which is really just a wrapper for matplotlib."
      ],
      "metadata": {
        "id": "sEFYOylk99_h"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 733
        },
        "id": "Trw8oYBxyzWv",
        "outputId": "87a3010a-1194-4deb-b740-81f128a58b31"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Population', ylabel='Profit'>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "It really helps to actually look at what's going on, doesn't it? We can clearly see that there's a cluster of values around cities with smaller populations, and a somewhat linear trend of increasing profit as the size of the city increases. Now let's get to the fun part - implementing a linear regression algorithm in python from scratch!"
      ],
      "metadata": {
        "id": "AaHK9CYy-D33"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Implementing Simple Linear Regression**"
      ],
      "metadata": {
        "id": "HnRRYsy1y9gI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "If you're not familiar with linear regression, it's an approach to modeling the relationship between a dependent variable and one or more independent variables (if there's one independent variable then it's called simple linear regression, and if there's more than one independent variable then it's called multiple linear regression). There are lots of different types and variances of linear regression that are outside the scope of this discussion so I won't go into that here, but to put it simply - we're trying to create a linear model of the data X, using some number of parameters theta, that describes the variance of the data such that given a new data point that's not in X, we could accurately predict what the outcome y would be without actually knowing what y is.\n",
        "\n",
        "In this implementation we're going to use an optimization technique called gradient descent to find the parameters theta. If you're familiar with linear algebra, you may be aware that there's another way to find the optimal parameters for a linear model called the \"normal equation\" which basically solves the problem at once using a series of matrix calculations. However, the issue with this approach is that it doesn't scale very well for large data sets. In contrast, we can use variants of gradient descent and other optimization methods to scale to data sets of unlimited size, so for machine learning problems this approach is more practical.\n",
        "\n",
        "Okay, that's enough theory. Let's write some code. The first thing we need is a cost function. The cost function evaluates the quality of our model by calculating the error between our model's prediction for a data point, using the model parameters, and the actual data point. For example, if the population for a given city is 4 and we predicted that it was 7, our error is (7-4)^2 = 3^2 = 9 (assuming an L2 or \"least squares\" loss function). We do this for each data point in X and sum the result to get the cost. Here's the function:"
      ],
      "metadata": {
        "id": "ZCj_EP4e-nVy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def computeCost(X, y, theta):\n",
        "    inner = np.power(((X * theta.T) - y), 2)\n",
        "    return np.sum(inner) / (2 * len(X))"
      ],
      "metadata": {
        "id": "s_Xw5FmMzDlv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notice that there are no loops. We're taking advantage of numpy's linear algrebra capabilities to compute the result as a series of matrix operations. This is far more computationally efficient than an unoptimizted \"for\" loop.\n",
        "\n",
        "In order to make this cost function work seamlessly with the pandas data frame we created above, we need to do some manipulating. First, we need to insert a column of 1s at the beginning of the data frame in order to make the matrix operations work correctly (I won't go into detail on why this is needed, but it's in the exercise text if you're interested - basically it accounts for the intercept term in the linear equation). Second, we need to separate our data into independent variables X and our dependent variable y."
      ],
      "metadata": {
        "id": "I98NALTt-vQx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# append a ones column to the front of the data set\n",
        "data.insert(0, 'Ones', 1)"
      ],
      "metadata": {
        "id": "ilxkKaqszIiu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# set X (training data) and y (target variable)\n",
        "cols = data.shape[1]\n",
        "X = data.iloc[:,0:cols-1]\n",
        "y = data.iloc[:,cols-1:cols]"
      ],
      "metadata": {
        "id": "g4Btq9SxzL-E"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, we're going to convert our data frames to numpy matrices and instantiate a parameter matirx."
      ],
      "metadata": {
        "id": "K5FmpL4_-4vS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# convert from data frames to numpy matrices\n",
        "X = np.matrix(X.values)\n",
        "y = np.matrix(y.values)\n",
        "theta = np.matrix(np.array([0,0]))"
      ],
      "metadata": {
        "id": "TymPlVeEzRLQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "One useful trick to remember when debugging matrix operations is to look at the shape of the matrices you're dealing with. It's also helpful to remember when walking through the steps in your head that matrix multiplications look like (i x j) * (j x k) = (i x k), where i, j, and k are the shapes of the relative dimensions of the matrix."
      ],
      "metadata": {
        "id": "fA08sDYx-_mL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X.shape, theta.shape, y.shape\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7tp-QZDDzUbU",
        "outputId": "3d71dc13-dc48-4634-cbb5-a5722b56bafe"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((97, 2), (1, 2), (97, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Okay, so now we can try out our cost function. Remember the parameters were initialized to 0 so the solution isn't optimal yet, but we can see if it works."
      ],
      "metadata": {
        "id": "IAF3xy_q_LBH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "computeCost(X, y, theta)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "btX6ofwczY3T",
        "outputId": "5a1b6b8e-40f4-4316-a35c-7f4814292756"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "32.072733877455676"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So far so good. Now we need to define a function to perform gradient descent on the parameters theta using the update rules defined in the exercise text. Here's the function for gradient descent:"
      ],
      "metadata": {
        "id": "Yw_igC0hX1UU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gradientDescent(X, y, theta, alpha, iters):\n",
        "    temp = np.matrix(np.zeros(theta.shape))\n",
        "    parameters = int(theta.ravel().shape[1])\n",
        "    cost = np.zeros(iters)\n",
        "\n",
        "    for i in range(iters):\n",
        "        error = (X * theta.T) - y\n",
        "\n",
        "        for j in range(parameters):\n",
        "            term = np.multiply(error, X[:,j])\n",
        "            temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))\n",
        "\n",
        "        theta = temp\n",
        "        cost[i] = computeCost(X, y, theta)\n",
        "\n",
        "    return theta, cost"
      ],
      "metadata": {
        "id": "TbJQn9V9zfBR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The idea with gradient descent is that for each iteration, we compute the gradient of the error term in order to figure out the appropriate direction to move our parameter vector. In other words, we're calculating the changes to make to our parameters in order to reduce the error, thus bringing our solution closer to the optimal solution (i.e best fit).\n",
        "\n",
        "This is a fairly complex topic and I could easily devote a whole blog post just to discussing gradient descent. If you're interested in learning more, I would recommend starting with this article and branching out from there.\n",
        "\n",
        "Once again we're relying on numpy and linear algebra for our solution. You may notice that my implementation is not 100% optimal. In particular, there's a way to get rid of that inner loop and update all of the parameters at once. I'll leave it up to the reader to figure it out for now (I'll cover it in a later post).\n",
        "\n",
        "Now that we've got a way to evaluate solutions, and a way to find a good solution, it's time to apply this to our data set."
      ],
      "metadata": {
        "id": "1XmR6tq7X9Yf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# initialize variables for learning rate and iterations\n",
        "alpha = 0.01\n",
        "iters = 1000\n",
        "\n",
        "# perform gradient descent to \"fit\" the model parameters\n",
        "g, cost = gradientDescent(X, y, theta, alpha, iters)"
      ],
      "metadata": {
        "id": "AFR9sVYfzj9L"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "g"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aDbKifKUzoRC",
        "outputId": "bfc618f1-4d67-4607-9815-df49c0a76de2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[-3.24140214,  1.1272942 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "matrix([[-3.24140214, 1.1272942 ]])\n",
        "\n",
        "Note that we've initialized a few new variables here. If you look closely at the gradient descent function, it has parameters called alpha and iters. Alpha is the learning rate - it's a factor in the update rule for the parameters that helps determine how quickly the algorithm will converge to the optimal solution. Iters is just the number of iterations. There is no hard and fast rule for how to initialize these parameters and typically some trial-and-error is involved.\n",
        "\n",
        "We now have a parameter vector descibing what we believe is the optimal linear model for our data set. One quick way to evaluate just how good our regression model is might be to look at the total error of our new solution on the data set:"
      ],
      "metadata": {
        "id": "VR_9h8BXYGV2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "computeCost(X, y, g)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rkq1XTU_zslk",
        "outputId": "bf494e2d-facd-4579-d99e-02282b16d9d6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4.515955503078914"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Viewing The Results**"
      ],
      "metadata": {
        "id": "PRhmIexHzx2y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We're now going to use matplotlib to visualize our solution. Remember the scatter plot from before? Let's overlay a line representing our model on top of a scatter plot of the data to see how well it fits. We can use numpy's \"linspace\" function to create an evenly-spaced series of points within the range of our data, and then \"evaluate\" those points using our model to see what the expected profit would be. We can then turn it into a line graph and plot it."
      ],
      "metadata": {
        "id": "Ltj5RX0PYO0f"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.linspace(data.Population.min(), data.Population.max(), 100)\n",
        "f = g[0, 0] + (g[0, 1] * x)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.plot(x, f, 'r', label='Prediction')\n",
        "ax.scatter(data.Population, data.Profit, label='Traning Data')\n",
        "ax.legend(loc=2)\n",
        "ax.set_xlabel('Population')\n",
        "ax.set_ylabel('Profit')\n",
        "ax.set_title('Predicted Profit vs. Population Size')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 755
        },
        "id": "5R2_N2nyz2eB",
        "outputId": "9c432acf-c5ab-4537-f136-e26cf8ac8c40"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Predicted Profit vs. Population Size')"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Not bad! Our solution looks like and optimal linear model of the data set. Since the gradient decent function also outputs a vector with the cost at each training iteration, we can plot that as well."
      ],
      "metadata": {
        "id": "EvdGuBqMYUfv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.plot(np.arange(iters), cost, 'r')\n",
        "ax.set_xlabel('Iterations')\n",
        "ax.set_ylabel('Cost')\n",
        "ax.set_title('Error vs. Training Epoch')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 689
        },
        "id": "8ew9B1yHz735",
        "outputId": "3db95b31-bd28-495a-a758-28e3332abc9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs. Training Epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notice that the cost always decreases - this is an example of what's called a convex optimization problem. If you were to plot the entire solution space for the problem (i.e. plot the cost as a function of the model parameters for every possible value of the parameters) you would see that it looks like a \"bowl\" shape with a \"basin\" representing the optimal solution.\n",
        "\n",
        "That's all for now! In part 2 we'll finish off the first exercise by extending this example to more than 1 variable. I'll also show how the above solution can be reached by using a popular machine learning library called scikit-learn."
      ],
      "metadata": {
        "id": "mnnOFJCfYa7R"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#<p style=\"font-family:JetBrains Mono; font-weight:normal; letter-spacing: 1px; color:#207d06; font-size:100%; text-align:left;padding: 0px; border-bottom: 3px solid #207d06;\">**⭐️Chapter: 2-Multivariate Linear Regression**</p>"
      ],
      "metadata": {
        "id": "-d0YIYebDPKQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        " For part 2 we've got a new task - predict the price that a house will sell for. The difference this time around is we have more than one dependent variable. We're given both the size of the house in square feet, and the number of bedrooms in the house. Can we easily extend our previous code to handle multiple linear regression? Let's find out!"
      ],
      "metadata": {
        "id": "yhGPFXCdZnmv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Import libraries**"
      ],
      "metadata": {
        "id": "Su4-HDd6GGjZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import os\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "metadata": {
        "id": "PNBYdE8SGJ5E"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Load Dataset**"
      ],
      "metadata": {
        "id": "pr4hUM4MDxNK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3EiGk4I0DriD",
        "outputId": "798556ad-85b3-4011-9b32-63455d9c317c"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "data2 = pd.read_csv('/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex1data2.txt', header=None, names=['Size', 'Bedrooms', 'Price'])\n",
        "data2.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "WEoMp1L9EXfq",
        "outputId": "b89e221b-d475-4a5b-d849-d1de44837afd"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Size  Bedrooms   Price\n",
              "0  2104         3  399900\n",
              "1  1600         3  329900\n",
              "2  2400         3  369000\n",
              "3  1416         2  232000\n",
              "4  3000         4  539900"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-af03e290-1ebc-4a48-b401-ecb9a93de8f8\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Size</th>\n",
              "      <th>Bedrooms</th>\n",
              "      <th>Price</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2104</td>\n",
              "      <td>3</td>\n",
              "      <td>399900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1600</td>\n",
              "      <td>3</td>\n",
              "      <td>329900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2400</td>\n",
              "      <td>3</td>\n",
              "      <td>369000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1416</td>\n",
              "      <td>2</td>\n",
              "      <td>232000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>3000</td>\n",
              "      <td>4</td>\n",
              "      <td>539900</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-af03e290-1ebc-4a48-b401-ecb9a93de8f8')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-af03e290-1ebc-4a48-b401-ecb9a93de8f8 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-af03e290-1ebc-4a48-b401-ecb9a93de8f8');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-46dbd951-ca59-4c59-8062-c701edaa09b8\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-46dbd951-ca59-4c59-8062-c701edaa09b8')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-46dbd951-ca59-4c59-8062-c701edaa09b8 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data2",
              "summary": "{\n  \"name\": \"data2\",\n  \"rows\": 47,\n  \"fields\": [\n    {\n      \"column\": \"Size\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 794,\n        \"min\": 852,\n        \"max\": 4478,\n        \"num_unique_values\": 47,\n        \"samples\": [\n          2526,\n          2162,\n          1458\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Bedrooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 1,\n        \"max\": 5,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          2,\n          1,\n          4\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Price\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 125039,\n        \"min\": 169900,\n        \"max\": 699900,\n        \"num_unique_values\": 40,\n        \"samples\": [\n          252900,\n          199900,\n          449900\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notice that the scale of the values for each variable is vastly different. A house will typically have 2-5 bedrooms but may have anywhere from hundreds to thousands of square feet. If we were to run our regression algorithm on this data as-is, the \"size\" variable would be weighted too heavily and would end up dwarfing any contributions from the \"number of bedrooms\" feature. To fix this, we need to do something called \"feature normalization\". That is, we need to adjust the scale of the features to level the playing field. One way to do this is by subtracting from each value in a feature the mean of that feature, and then dividing by the standard deviation. Fortunately this is one line of code using pandas."
      ],
      "metadata": {
        "id": "juT46B1MZ5t0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Feature normalization**"
      ],
      "metadata": {
        "id": "ENrEJXx4GXuz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data2 = (data2 - data2.mean()) / data2.std()\n",
        "data2.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "9zZ15ghHGfvW",
        "outputId": "669b382e-46c5-42a3-93fe-3c4e8cc5ad0a"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Size  Bedrooms     Price\n",
              "0  0.130010 -0.223675  0.475747\n",
              "1 -0.504190 -0.223675 -0.084074\n",
              "2  0.502476 -0.223675  0.228626\n",
              "3 -0.735723 -1.537767 -0.867025\n",
              "4  1.257476  1.090417  1.595389"
            ],
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              "      <td>-0.223675</td>\n",
              "      <td>-0.084074</td>\n",
              "    </tr>\n",
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              "      <th>2</th>\n",
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              "      <td>-0.223675</td>\n",
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              "    </tr>\n",
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              "      <th>4</th>\n",
              "      <td>1.257476</td>\n",
              "      <td>1.090417</td>\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
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              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
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              "        const element = document.querySelector('#df-77c6deec-8708-4d24-82bb-11084a2648bb');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
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              "      --disabled-fill-color: #666;\n",
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              "\n",
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              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-b081bbbb-8b5c-4474-a152-69aa5abe3f19 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data2",
              "summary": "{\n  \"name\": \"data2\",\n  \"rows\": 47,\n  \"fields\": [\n    {\n      \"column\": \"Size\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0000000000000002,\n        \"min\": -1.4454227371491544,\n        \"max\": 3.117291823687202,\n        \"num_unique_values\": 47,\n        \"samples\": [\n          0.6610262906611214,\n          0.20299316872388104,\n          -0.6828730890888036\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Bedrooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.9999999999999994,\n        \"min\": -2.8518586363995424,\n        \"max\": 2.4045082620623597,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          -1.5377669117840669,\n          -2.8518586363995424,\n          1.0904165374468842\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Price\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.9999999999999999,\n        \"min\": -1.3636659989209765,\n        \"max\": 2.874981038969331,\n        \"num_unique_values\": 40,\n        \"samples\": [\n          -0.6998778778928718,\n          -1.1237425816819027,\n          0.8756192286437142\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we need to modify our implementation of linear regression from part 1 to handle more than 1 dependent variable. Or do we? Let's take a look at the code for the gradient descent function again."
      ],
      "metadata": {
        "id": "Gs7bJxIOaHtz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Model Training**"
      ],
      "metadata": {
        "id": "g1m8Ar-SGx92"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Gradient descent function"
      ],
      "metadata": {
        "id": "s8jcHK-NG8hH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gradientDescent(X, y, theta, alpha, iters):\n",
        "    temp = np.matrix(np.zeros(theta.shape))\n",
        "    parameters = int(theta.ravel().shape[1])\n",
        "    cost = np.zeros(iters)\n",
        "\n",
        "    for i in range(iters):\n",
        "        error = (X * theta.T) - y\n",
        "\n",
        "        for j in range(parameters):\n",
        "            term = np.multiply(error, X[:,j])\n",
        "            temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))\n",
        "\n",
        "        theta = temp\n",
        "        cost[i] = computeCost(X, y, theta)\n",
        "\n",
        "    return theta, cost"
      ],
      "metadata": {
        "id": "ZxuVIGvpHCL4"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def computeCost(X, y, theta):\n",
        "    inner = np.power(((X * theta.T) - y), 2)\n",
        "    return np.sum(inner) / (2 * len(X))"
      ],
      "metadata": {
        "id": "AStx394LIfbv"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Look closely at the line of code calculating the error term: error = (X * theta.T) - y. It might not be obvious at first but we're using all matrix operations! This is the power of linear algebra at work. This code will work correctly no matter how many variables (columns) are in X, as long as the number of parameters in theta agree. Similarly, it will compute the error term for every row in X as long as the number of rows in y agree. On top of that, it's a very efficient calculation. This is a powerful way to apply ANY expression to a large number of instances at once.\n",
        "\n",
        "Since both our gradient descent and cost function are using matrix operations, there is in fact no change to the code necessary to handle multiple linear regression. Let's test it out. We first need to perform a few initializations to create the appropriate matrices to pass to our functions."
      ],
      "metadata": {
        "id": "HPr8Hzi_aPsD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Parameter initializations"
      ],
      "metadata": {
        "id": "421EVaNyHir3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# add ones column\n",
        "data2.insert(0, 'Ones', 1)\n",
        "\n",
        "# set X (training data) and y (target variable)\n",
        "cols = data2.shape[1]\n",
        "X2 = data2.iloc[:,0:cols-1]\n",
        "y2 = data2.iloc[:,cols-1:cols]\n",
        "\n",
        "# convert to matrices and initialize theta\n",
        "X2 = np.matrix(X2.values)\n",
        "y2 = np.matrix(y2.values)\n",
        "theta2 = np.matrix(np.array([0,0,0]))\n"
      ],
      "metadata": {
        "id": "GzPlPD2uHnnH"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 0.01\n",
        "iters = 1000"
      ],
      "metadata": {
        "id": "jWKKZoiBIGqG"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now we're ready to give it a try. Let's see what happens.\n",
        "\n"
      ],
      "metadata": {
        "id": "rSbk_iflbS-U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# perform linear regression on the data set\n",
        "g2, cost2 = gradientDescent(X2, y2, theta2, alpha, iters)"
      ],
      "metadata": {
        "id": "PW45nP4fH0LP"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# get the cost (error) of the model\n",
        "computeCost(X2, y2, g2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HKiivAIFIl8_",
        "outputId": "52668edb-9419-46f0-f2f3-22da63ff71c0"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.13070336960771892"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Plot the training progress**"
      ],
      "metadata": {
        "id": "-LxkLXlvIsVO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Looks promising! We can also plot the training progress to confirm that the error was in fact decreasing with each iteration of gradient descent."
      ],
      "metadata": {
        "id": "hY2PBvWcbgyY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.plot(np.arange(iters), cost2, 'r')\n",
        "ax.set_xlabel('Iterations')\n",
        "ax.set_ylabel('Cost')\n",
        "ax.set_title('Error vs. Training Epoch')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 755
        },
        "id": "myOB7Z22Irwf",
        "outputId": "c29af1a5-8ee1-42cf-f9d1-bbd4ccb60438"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs. Training Epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The cost, or error of the solution, dropped with each sucessive iteration until it bottomed out. This is exactly what we would expect to happen. It looks like our algorithm worked.\n",
        "\n",
        "It's worth noting that we don't HAVE to implement any algorithms from scratch to solve this problem. The great thing about Python is its huge developer community and abundance of open-source software. In the machine learning realm, the top Python library is scikit-learn. Let's see how we could have handled our simple linear regression task from part 1 using scikit-learn's linear regression class."
      ],
      "metadata": {
        "id": "rsEW9N3mbpPo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Normal Equation**"
      ],
      "metadata": {
        "id": "vU_v_doQKSjg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "def normal_equation(X, y):\n",
        " theta = np.linalg.inv(X.T @ X) @ X.T @ y\n",
        " return theta\n",
        "# Example usage:\n",
        "X = np.array([[1, 2], [1, 3], [1, 4]]) # Features\n",
        "y = np.array([2, 5, 7]) # Target values\n",
        "theta = normal_equation(X, y)\n",
        "print(\"Optimal parameters:\", theta)"
      ],
      "metadata": {
        "id": "1TyddO_4Kfut",
        "outputId": "31fc2c56-cb5e-4cd7-e629-895c6f78e2a4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimal parameters: [-2.83333333  2.5       ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import linear_model\n",
        "model = linear_model.LinearRegression()\n",
        "model.fit(X, y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "id": "RsGnoha0cINP",
        "outputId": "02303eeb-4e7e-49fb-c543-9a6e792b9183"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-1 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-1 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-1 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-1 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-1 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "It doesn't get much easier than that. There are lots of parameters to the \"fit\" method that we could have tweaked depending on how we want the algorithm to function, but the defaults are sensible enough for our problem that I left them alone. Let's try plotting the fitted parameters to see how it compares to our earlier results."
      ],
      "metadata": {
        "id": "WJAJ7yg-cSjN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.array(X[:, 1].A1)\n",
        "f = model.predict(X).flatten()\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.plot(x, f, 'r', label='Prediction')\n",
        "ax.scatter(data.Population, data.Profit, label='Traning Data')\n",
        "ax.legend(loc=2)\n",
        "ax.set_xlabel('Population')\n",
        "ax.set_ylabel('Profit')\n",
        "ax.set_title('Predicted Profit vs. Population Size')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 211
        },
        "id": "uUEkqmcmcQvT",
        "outputId": "2b2b2e5a-9288-4e12-b630-87aeba56c186"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "'numpy.ndarray' object has no attribute 'A1'",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-15-236548e6f66e>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mA1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Prediction'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'A1'"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notice I'm using the \"predict\" function to get the predicted y values in order to draw the line. This is much easier than trying to do it manually. Scikit-learn has a great API with lots of convenience functions for typical machine learning workflows. We'll explore some of these in more detail in future posts.\n",
        "\n",
        "That's it for today. In part 3, we'll take a look at exercise 2 and dive into some classification tasks using logistic regression."
      ],
      "metadata": {
        "id": "-agjluCAcfc_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "#<p style=\"font-family:JetBrains Mono; font-weight:normal; letter-spacing: 1px; color:#207d06; font-size:100%; text-align:left;padding: 0px; border-bottom: 3px solid #207d06;\">**Chapter 3:Logistic Regression**</p>"
      ],
      "metadata": {
        "id": "ST3EnvDS9ZY0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **4.1-Logistic Regression with sample Example**"
      ],
      "metadata": {
        "id": "dYMjweho9ofC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n"
      ],
      "metadata": {
        "id": "kV8oCxAG92eW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate a small dataset for illustration\n",
        "np.random.seed(42)\n",
        "X = 2 * np.random.rand(100, 1)\n",
        "y = (4 + 3 * X + np.random.randn(100, 1) > 5).astype(int)\n",
        "\n",
        "# Add a bias term to the feature matrix\n",
        "X_b = np.c_[np.ones((100, 1)), X]"
      ],
      "metadata": {
        "id": "lu1ZAkXz98He"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Sigmoid (logistic) function\n",
        "def sigmoid(z):\n",
        "    return 1 / (1 + np.exp(-z))"
      ],
      "metadata": {
        "id": "4f7KhtCJ9_98"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Cost function for logistic regression\n",
        "def cost_function(theta, X, y):\n",
        "    m = len(y)\n",
        "    h = sigmoid(X.dot(theta))\n",
        "    cost = -1/m * (y.T.dot(np.log(h)) + (1 - y).T.dot(np.log(1 - h)))\n",
        "    return cost.item()"
      ],
      "metadata": {
        "id": "IKIf2b7C-Dps"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Gradient descent to update parameters\n",
        "def gradient_descent(theta, X, y, learning_rate, n_iterations):\n",
        "    m = len(y)\n",
        "    costs = []\n",
        "\n",
        "    for iteration in range(n_iterations):\n",
        "        h = sigmoid(X.dot(theta))\n",
        "        gradient = 1/m * X.T.dot(h - y)\n",
        "        theta -= learning_rate * gradient\n",
        "        cost = cost_function(theta, X, y)\n",
        "        costs.append(cost)\n",
        "\n",
        "    return theta, costs"
      ],
      "metadata": {
        "id": "KYlz9BO_-HpM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Initialize parameters\n",
        "theta_initial = np.random.randn(2, 1)\n"
      ],
      "metadata": {
        "id": "S-3JZ-cO-MEP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Set hyperparameters\n",
        "learning_rate = 0.01\n",
        "n_iterations = 1000"
      ],
      "metadata": {
        "id": "rCL05BHI-Pyk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Run gradient descent\n",
        "theta_final, costs = gradient_descent(theta_initial, X_b, y, learning_rate, n_iterations)"
      ],
      "metadata": {
        "id": "iEnG6die-TOT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the data points and decision boundary\n",
        "plt.scatter(X, y)\n",
        "plt.xlabel(\"Feature\")\n",
        "plt.ylabel(\"Label\")\n",
        "plt.title(\"Logistic Regression Example\")\n",
        "x_values = np.array([np.min(X), np.max(X)])\n",
        "#y_values = -(theta_final[0] + theta_final[1] * x_values) / theta_final[2]\n",
        "y_values = -(theta_final[0] + theta_final[1] * x_values)\n",
        "\n",
        "plt.plot(x_values, y_values, label=\"Decision Boundary\", color='red')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "T3FUCx6q-Xzf",
        "outputId": "1077042f-a4a8-44ce-95c4-5e7d7097ab44"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the cost over iterations\n",
        "plt.plot(range(n_iterations), costs)\n",
        "plt.xlabel(\"Iterations\")\n",
        "plt.ylabel(\"Cost\")\n",
        "plt.title(\"Cost Function Over Iterations\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "JSyVCk4i_I3m",
        "outputId": "a8ef62ec-e06c-4639-c57f-0d93b90c1677"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **4.2-Logistic Regression**"
      ],
      "metadata": {
        "id": "m5eZO3avMtJi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "You may be wondering – why are we using a “regression” algorithm on a classification problem? Although the name seems to indicate otherwise, logistic regression is actually a classification algorithm. I suspect it’s named as such because it’s very similar to linear regression in its learning approach, but the cost and gradient functions are formulated differently. In particular, logistic regression uses a sigmoid or “logit” activation function instead of the continuous output in linear regression (hence the name). We’ll see more later on when we dive into the implementation.\n",
        "\n",
        "To get started, let’s import and examine the data set we’ll be working with."
      ],
      "metadata": {
        "id": "V9FXJI6hO_UV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Load dataseet**"
      ],
      "metadata": {
        "id": "P6B028nVNIyr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HOksrl_SNOFi",
        "outputId": "10708bfb-c665-40ea-9169-c419e85ebfaa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Import libraries**"
      ],
      "metadata": {
        "id": "rMIgjBYPNe9t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import os\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "metadata": {
        "id": "L2wKm3nhNlyD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Load dataseet**"
      ],
      "metadata": {
        "id": "Y7yf8wjbNvgz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#path = os.getcwd() + '/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex1data1.txt'\n",
        "data = pd.read_csv('/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex2data1.txt', header=None, names=['Exam 1', 'Exam 2', 'Admitted'])\n",
        "data.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "n-qIfHK2Nt7s",
        "outputId": "c4144b78-e63e-4bcf-9a0c-1ff32e28361a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Exam 1     Exam 2  Admitted\n",
              "0  34.623660  78.024693         0\n",
              "1  30.286711  43.894998         0\n",
              "2  35.847409  72.902198         0\n",
              "3  60.182599  86.308552         1\n",
              "4  79.032736  75.344376         1"
            ],
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            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data",
              "summary": "{\n  \"name\": \"data\",\n  \"rows\": 100,\n  \"fields\": [\n    {\n      \"column\": \"Exam 1\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 19.458222275425072,\n        \"min\": 30.05882244669796,\n        \"max\": 99.82785779692128,\n        \"num_unique_values\": 100,\n        \"samples\": [\n          57.23870631569862,\n          34.52451385320009,\n          32.72283304060323\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Exam 2\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 18.582783039307344,\n        \"min\": 30.60326323428011,\n        \"max\": 98.86943574220612,\n        \"num_unique_values\": 100,\n        \"samples\": [\n          59.51428198012956,\n          60.39634245837173,\n          43.30717306430063\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Admitted\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 0,\n        \"max\": 1,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          1,\n          0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "There are two continuous independent variables in the data - “Exam 1” and “Exam 2”. Our prediction target is the “Admitted” label, which is binary-valued. A value of 1 means the student was admitted and a value of 0 means the student was not admitted. Let’s see this graphically with a scatter plot of the two scores and use color coding to visualize if the example is positive or negative."
      ],
      "metadata": {
        "id": "5am88ooFPO-L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "positive = data[data['Admitted'].isin([1])]\n",
        "negative = data[data['Admitted'].isin([0])]\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.scatter(positive['Exam 1'], positive['Exam 2'], s=50, c='b', marker='o', label='Admitted')\n",
        "ax.scatter(negative['Exam 1'], negative['Exam 2'], s=50, c='r', marker='x', label='Not Admitted')\n",
        "ax.legend()\n",
        "ax.set_xlabel('Exam 1 Score')\n",
        "ax.set_ylabel('Exam 2 Score')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 733
        },
        "id": "Hd3aonz4PT7E",
        "outputId": "4facb756-3387-4404-85b3-76a1f4b5e238"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Exam 2 Score')"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "From this plot we can see that there’s a nearly linear decision boundary. It curves a bit so we can’t classify all of the examples correctly using a straight line, but we should be able to get pretty close. Now we need to implement logistic regression so we can train a model to find the optimal decision boundary and make class predictions. The first step is to implement the sigmoid function.\n",
        "\n",
        "def sigmoid(z):"
      ],
      "metadata": {
        "id": "TV8ii6gvPftQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sigmoid(z):\n",
        "    return 1 / (1 + np.exp(-z))"
      ],
      "metadata": {
        "id": "vRf1Otv6P4Qa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "This function is the “activation” function for the output of logistic regression. It converts a continuous input into a value between zero and one. This value can be interpreted as the class probability, or the likelihood that the input example should be classified positively. Using this probability along with a threshold value, we can obtain a discrete label prediction. It helps to visualize the function’s output to see what it’s really doing."
      ],
      "metadata": {
        "id": "O303jfvNQDRJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "nums = np.arange(-10, 10, step=1)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.plot(nums, sigmoid(nums), 'r')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 713
        },
        "id": "ElUlIItwQJfD",
        "outputId": "17a2782e-d4de-46f4-b896-c51a88f5b869"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7e493ad91300>]"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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P48Yl8+cne+2V7Lln2WkAaCVKNQBAW3v00eTyy4tx08rfAHQISjUAQFs75ZSkUkkOOSQZPLjsNAC0IqUaAKAt3XdfctNNxUrfZ51VdhoAWplSDQDQViqVZMyYYnzMMclmm5WbB4BWp1QDALSVW29N7r036dkzOf30stMA0AaUagCAttDYmIwdW4xPOCFZb71y8wDQJpRqAIC2cOWVxarfffosmgIOQIejVAMAtLZ585LTTivG3/52stZa5eYBoM0o1QAAre2//zt57rmkf//kxBPLTgNAG1KqAQBa05w5iy6dddppyWqrlZsHgDalVAMAtKYf/ziZPj3ZaKPk2GPLTgNAG1OqAQBayxtvJOedV4zPOivp0aPcPAC0OaUaAKC1nHdeMmtWsu22yWGHlZ0GgHagVAMAtIZp04qp30lyzjlJF39mAXQG/m8PANAazjwzef/9ZNddk332KTsNAO1EqQYAWFlPP51cfHExPvfcpK6u3DwAtBulGgBgZZ12WtLQkOy7b7LbbmWnAaAdKdUAACvjoYeSiROLs9PnnFN2GgDamVINALAyvvvd4v7ww4tVvwHoVFpUqidMmJANN9wwPXv2zJAhQ/Lggw8ud/8LL7wwm2++eVZZZZUMGjQo3/zmN/P++++3KDAAQNW4667k9tuTbt2KhcoA6HSaXaonTpyY0aNHZ9y4cXnooYey3XbbZfjw4XnttdeWuv8VV1yRMWPGZNy4cXn88cdz8cUXZ+LEiflu07/qAgDUokolGTu2GH/1q8nHP15uHgBKUVepVCrNOWDIkCHZaaed8pOf/CRJ0tjYmEGDBuWEE07ImDFjltj/G9/4Rh5//PFMmjRp4baTTz45DzzwQO69994V+p6zZ89Onz59MmvWrPTu3bs5cQEA2sYNNyQjRiSrrpo880yyzjplJwKgFa1oD23Wmep58+ZlypQpGTZs2KIv0KVLhg0blsmTJy/1mF122SVTpkxZOEX8ueeeyy233JJ9lnP9xrlz52b27NmL3QAAqkZDw6LPUp90kkIN0Il1a87OM2fOTENDQ/r377/Y9v79++eJJ55Y6jGHH354Zs6cmd122y2VSiULFizIcccdt9zp3+PHj88ZZ5zRnGgAAO3nV79KHnssWXPN5FvfKjsNACVq89W/77777pxzzjn5f//v/+Whhx7Kddddl5tvvjlnnXXWMo8ZO3ZsZs2atfD20ksvtXVMAIAVM3ducvrpxXjs2GSNNUqNA0C5mnWmum/fvunatWtmzJix2PYZM2ZkwIABSz3mtNNOy5FHHpmvfOUrSZJtttkmc+bMyVe/+tWccsop6dJlyV5fX1+f+vr65kQDAGgfF12UTJ2aDByYfOMbZacBoGTNOlPdo0ePDB48eLFFxxobGzNp0qQMHTp0qce8++67SxTnrl27JkmauUYaAEC53n47OfvsYjxuXLLKKuXmAaB0zTpTnSSjR4/OUUcdlR133DE777xzLrzwwsyZMydHH310kmTUqFFZd911M378+CTJfvvtlx/96Ef55Cc/mSFDhuSZZ57Jaaedlv32229huQYAqAkXXJDMnJlsumnyv3/7ANC5NbtUjxw5Mq+//npOP/30TJ8+Pdtvv31uu+22hYuXTZ06dbEz06eeemrq6upy6qmnZtq0aVl77bWz33775fvf/37r/RQAAG3t9deT888vxmefnXTvXm4eAKpCs69TXQbXqQYASjd6dHGmeocdkj//OVnKujAAdBxtcp1qAIBOaerUZMKEYjx+vEINwEJ+IwAAfJTvfS+ZNy/Zc8/kc58rOw0AVUSpBgBYnsceSy67rBifc05SV1duHgCqilINALA8p52WNDYmI0Ykn/pU2WkAqDJKNQDAsjz4YHLddcVnqJuuTw0AH6BUAwAsTaWSjBlTjEeNSrbaqtw8AFQlpRoAYGnuvDO5666kR49ioTIAWAqlGgDgwxobk7Fji/HXv55ssEG5eQCoWko1AMCHXXttMmVK0qtX8t3vlp0GgCqmVAMAfNCCBcmppxbjk09O1l673DwAVDWlGgDggy69NHnqqaRv32T06LLTAFDllGoAgCbvvbdoUbJTTkl69y41DgDVT6kGAGgyYUIybVqy/vrJcceVnQaAGqBUAwAkyVtvJeecU4zPOCPp2bPUOADUBqUaACBJzj8/efPNZIstkiOPLDsNADVCqQYAmDEjueCCYvz97yddu5abB4CaoVQDAJx9dvLuu8nOOycjRpSdBoAaolQDAJ3bc88lP/1pMT733KSurtw8ANQUpRoA6NzGjUvmz0/22ivZc8+y0wBQY5RqAKDzevTR5PLLi3HTyt8A0AxKNQDQeZ1ySlKpJAcfnAweXHYaAGqQUg0AdE733ZfcdFOx0vdZZ5WdBoAapVQDAJ1PpZKMGVOMjzkm2XzzcvMAULOUagCg87n11uTee5OePZPTTy87DQA1TKkGADqXxsZk7NhifMIJyXrrlZsHgJqmVAMAncuVVxarfvfunXznO2WnAaDGKdUAQOcxb15y2mnF+NvfTj72sXLzAFDzlGoAoPO4+OLkueeS/v2TE08sOw0AHYBSDQB0DnPmJGeeWYxPOy3p1avcPAB0CEo1ANA5/PjHyfTpyUYbJcceW3YaADoIpRoA6PjeeCM577xifNZZSY8e5eYBoMNQqgGAju/HP05mzUq22SY57LCy0wDQgSjVAEDHVqkkv/pVMR4zJunizx8AWo/fKgBAxzZlSvLss8mqqyYHHFB2GgA6GKUaAOjYrryyuN9//2S11crNAkCHo1QDAB1XY2MycWIxPvTQcrMA0CEp1QBAx3X//cnLLyd9+iSf/3zZaQDogJRqAKDjapr6/cUvJvX15WYBoENSqgGAjmnBguTqq4uxqd8AtBGlGgDomO6+O3nttaRv3+Qznyk7DQAdlFINAHRMTVO/Dzoo6d693CwAdFhKNQDQ8cybl1x7bTE29RuANqRUAwAdz+9+l7z1VjJwYLLbbmWnAaADU6oBgI7n178u7g85JOnatdwsAHRoSjUA0LG8+25yww3F2NRvANqYUg0AdCw335zMmZNsuGGy885lpwGgg1OqAYCOpWnV70MPTerqys0CQIenVAMAHcfs2cWZ6sTUbwDahVINAHQcN9yQzJ2bfOITybbblp0GgE5AqQYAOg5TvwFoZ0o1ANAx/POfxfWpk2TkyHKzANBpKNUAQMdw3XXJggXJ9tsX078BoB0o1QBAx/DBqd8A0E6UagCg9r36anLXXcXY1G8A2pFSDQDUvmuuSSqV5FOfSjbcsOw0AHQiSjUAUPtM/QagJEo1AFDbXnwxuf/+4hJaBx9cdhoAOhmlGgCobVddVdzvsUcycGC5WQDodJRqAKC2mfoNQImUagCgdj31VPLQQ0nXrsmXvlR2GgA6IaUaAKhdEycW95/7XNK3b7lZAOiUlGoAoDZVKsmvf12MTf0GoCRKNQBQm/7+9+Txx5MePZIRI8pOA0AnpVQDALWpaYGyffZJ+vQpNwsAnZZSDQDUnkrFqt8AVAWlGgCoPX/5S/Lcc8mqqyZf+ELZaQDoxJRqAKD2NJ2l3n//ZLXVys0CQKemVAMAtaWxcdGltEz9BqBkSjUAUFvuuy+ZNq1YnOzzny87DQCdnFINANSWpqnfBx6Y1NeXmwWATk+pBgBqx4IFydVXF2NTvwGoAko1AFA77roref31pG/f5DOfKTsNACjVAEANaZr6ffDBSbdu5WYBgCjVAECtmDs3ue66YmzqNwBVQqkGAGrD736XvPVWMnBgsttuZacBgCRKNQBQK5qmfo8cmXTxJwwA1cFvJACg+r37bnLDDcXY1G8AqohSDQBUv5tvTubMSTbaKNlpp7LTAMBCSjUAUP2apn4femhSV1duFgD4AKUaAKhus2cXZ6oTU78BqDpKNQBQ3a6/vric1hZbJNtsU3YaAFiMUg0AVDdTvwGoYko1AFC9Zs5M7rijGI8cWW4WAFgKpRoAqF7XXZcsWJB88pPJ5puXnQYAlqBUAwDV64NTvwGgCinVAEB1evXV5O67i/Ehh5QaBQCWRakGAKrT1VcnlUoydGiy4YZlpwGApVKqAYDqZOo3ADVAqQYAqs8LLySTJxeX0Dr44LLTAMAyKdUAQPW56qri/tOfTtZZp9QoALA8SjUAUH1M/QagRijVAEB1efLJ5OGHk27dkgMPLDsNACyXUg0AVJeJE4v7z30u6du33CwA8BGUagCgelQqya9/XYxN/QagBijVAED1+NvfkieeSOrrkwMOKDsNAHwkpRoAqB5NC5Tts0/Sp0+5WQBgBSjVAEB1qFSs+g1AzVGqAYDq8Oc/J88/n6y2WrLvvmWnAYAVolQDANWh6Sz1/vsXxRoAaoBSDQCUr7Fx0aW0TP0GoIYo1QBA+e69N3nllWJxsuHDy04DACusRaV6woQJ2XDDDdOzZ88MGTIkDz744HL3f+utt3L88cdnnXXWSX19fTbbbLPccsstLQoMAHRATVO/DzywuJwWANSIbs09YOLEiRk9enQuuuiiDBkyJBdeeGGGDx+eJ598Mv369Vti/3nz5uVzn/tc+vXrl2uuuSbrrrtuXnzxxayxxhqtkR8AqHULFiRXX12MTf0GoMbUVSqVSnMOGDJkSHbaaaf85Cc/SZI0NjZm0KBBOeGEEzJmzJgl9r/ooovy7//+73niiSfSvXv3FoWcPXt2+vTpk1mzZqV3794t+hoAQJX63e+KKd99+yavvpp0a/a/+QNAq1vRHtqs6d/z5s3LlClTMmzYsEVfoEuXDBs2LJMnT17qMb/97W8zdOjQHH/88enfv3+23nrrnHPOOWloaFjm95k7d25mz5692A0A6KCapn4ffLBCDUDNaVapnjlzZhoaGtK/f//Ftvfv3z/Tp09f6jHPPfdcrrnmmjQ0NOSWW27Jaaedlh/+8Ic5++yzl/l9xo8fnz59+iy8DRo0qDkxAYBaMXduct11xdjUbwBqUJuv/t3Y2Jh+/frlZz/7WQYPHpyRI0fmlFNOyUUXXbTMY8aOHZtZs2YtvL300kttHRMAKMPttyezZiUDBya77VZ2GgBotmbNserbt2+6du2aGTNmLLZ9xowZGTBgwFKPWWedddK9e/d07dp14bYtttgi06dPz7x589KjR48ljqmvr0+9lT8BoONrmvo9cmTSxZU+Aag9zfrt1aNHjwwePDiTJk1auK2xsTGTJk3K0KFDl3rMrrvummeeeSaNjY0Ltz311FNZZ511llqoAYBOYs6c5IYbirGp3wDUqGb/k/Do0aPz85//PJdddlkef/zxfO1rX8ucOXNy9NFHJ0lGjRqVsWPHLtz/a1/7Wt54442ceOKJeeqpp3LzzTfnnHPOyfHHH996PwUAUHtuvjl5991ko42SnXYqOw0AtEizl9gcOXJkXn/99Zx++umZPn16tt9++9x2220LFy+bOnVqunxg+tagQYNy++2355vf/Ga23XbbrLvuujnxxBPzne98p/V+CgCg9jRN/T700KSurtwsANBCzb5OdRlcpxoAOphZs5L+/YvVv//612TbbctOBACLaZPrVAMAtIobbigK9RZbJNtsU3YaAGgxpRoAaH+mfgPQQSjVAED7mjkzueOOYjxyZLlZAGAlKdUAQPu67rpkwYLkk59MNt+87DQAsFKUagCgff3618W9a1MD0AEo1QBA+3nlleSee4rxIYeUmwUAWoFSDQC0n6uvTiqVZOjQZMMNy04DACtNqQYA2s8HV/0GgA5AqQYA2sfzzyd/+lNxCa2DDy47DQC0CqUaAGgfV11V3H/608k665QaBQBai1INALSPpqnfhx1Wbg4AaEVKNQDQ9p54InnkkaRbt+TAA8tOAwCtRqkGANrexInF/V57JR/7WLlZAKAVKdUAQNuqVKz6DUCHpVQDAG3r0UeL6d/19ckBB5SdBgBalVINALStprPU++6b9O5dbhYAaGVKNQDQdkz9BqCDU6oBgLbz4IPJCy8kq61WnKkGgA5GqQYA2k7TWeoDDkhWXbXcLADQBpRqAKBtNDQsupSWqd8AdFBKNQDQNu69N3n11WSNNYrrUwNAB6RUAwBto2nq94EHFpfTAoAOSKkGAFrf/PnJNdcUY1O/AejAlGoAoPX9/vfJzJnJ2msne+5ZdhoAaDNKNQDQ+pqmfh98cNKtW7lZAKANKdUAQOuaOze57rpibOo3AB2cUg0AtK7bbktmz07WXTfZddey0wBAm1KqAYDW1TT1e+TIpIs/NQDo2PymAwBaz5w5yW9/W4xN/QagE1CqAYDWc9NNybvvJh//eLLjjmWnAYA2p1QDAK2naer3oYcmdXXlZgGAdqBUAwCtY9as5JZbirGp3wB0Eko1ANA6rr8+mTcv2XLLZOuty04DAO1CqQYAWoep3wB0Qko1ALDyZs5M7rijGI8cWW4WAGhHSjUAsPKuvTZpaEh22CHZbLOy0wBAu1GqAYCV98Gp3wDQiSjVAMDKeeWV5J57ivEhh5SbBQDamVINAKycq69OKpVkl12SDTYoOw0AtCulGgBYOaZ+A9CJKdUAQMs9/3zypz8lXbokBx9cdhoAaHdKNQDQchMnFvef/nQyYECpUQCgDEo1ANBypn4D0Mkp1QBAyzz+ePLXvybduiUHHlh2GgAohVINALRM09TvvfZKPvaxcrMAQEmUagCg+SoVU78BIEo1ANASf/1r8uSTSX19csABZacBgNIo1QBA8zWdpd5336R373KzAECJlGoAoHkqlUWfpzb1G4BOTqkGAJrngQeSF15IVlutOFMNAJ2YUg0ANE/T1O8DDkhWXbXcLABQMqUaAFhxDQ3JVVcVY1O/AUCpBgCa4Y9/TF59NVljjeL61ADQySnVAMCKa5r6feCBxeW0AKCTU6oBgBUzf35yzTXF2NRvAEiiVAMAK2rSpOSf/0zWXjvZc8+y0wBAVVCqAYAV0zT1++CDk27dys0CAFVCqQYAPtr77ye/+U0xNvUbABZSqgGAj3bbbcns2cl66yW77lp2GgCoGko1APDRmqZ+jxyZdPHnAwA08VsRAFi+OXOSG28sxqZ+A8BilGoAYPluvDF5991k442TwYPLTgMAVUWpBgCWr2nq96GHJnV15WYBgCqjVAMAy/bWW8mttxZjU78BYAlKNQCwbNdfn8ybl2y1VbL11mWnAYCqo1QDAMv2wanfAMASlGoAYOlefz25885iPHJkuVkAoEop1QDA0l17bdLQUKz4vemmZacBgKqkVAMAS2fqNwB8JKUaAFjStGnJH/5QjA85pNwsAFDFlGoAYElXX51UKsmuuybrr192GgCoWko1ALAkU78BYIUo1QDA4p5/PnnggaRLl+Sgg8pOAwBVTakGABY3cWJxv+eeyYAB5WYBgCqnVAMAizP1GwBWmFINACzy+OPJX/+adOuWHHhg2WkAoOop1QDAIk1Tv4cPT9Zaq9wsAFADlGoAoFCpmPoNAM2kVAMAhb/+NXnyyaRnz2T//ctOAwA1QakGAApNZ6n33Tfp3bvcLABQI5RqAMDUbwBoIaUaAEgeeCB58cWkV69kn33KTgMANUOpBgAWnaU+4IBk1VXLzQIANUSpBoDOrqEhueqqYmzqNwA0i1INAJ3dH/+YvPpqssYayV57lZ0GAGqKUg0AnV3T1O8vfSnp0aPcLABQY5RqAOjM5s9PrrmmGJv6DQDNplQDQGc2aVLyz38m/foln/502WkAoOYo1QDQmTVN/T744KRbt3KzAEANUqoBoLN6//3kN78pxqZ+A0CLKNUA0Fndemsye3ay3nrJLruUnQYAapJSDQCdVdPU75Ejky7+JACAlvAbFAA6o3feSW68sRib+g0ALaZUA0BndOONyXvvJRtvnAweXHYaAKhZSjUAdEZNU78PPTSpqys3CwDUMKUaADqbN98sFilLTP0GgJWkVANAZ3P99cn8+cnWWxc3AKDFlGoA6Gw+OPUbAFgpSjUAdCavvZZMmlSMR44sNwsAdABKNQB0JtdemzQ0JDvumGyySdlpAKDmKdUA0JmY+g0ArapFpXrChAnZcMMN07NnzwwZMiQPPvjgCh135ZVXpq6uLiNGjGjJtwUAVsbLLyd//GMxPuSQcrMAQAfR7FI9ceLEjB49OuPGjctDDz2U7bbbLsOHD89rr7223ONeeOGF/N//+3+z++67tzgsALASrr46qVSS3XZLBg0qOw0AdAjNLtU/+tGPcuyxx+boo4/OlltumYsuuiirrrpq/ud//meZxzQ0NOSII47IGWeckY9//OMrFRgAaCFTvwGg1TWrVM+bNy9TpkzJsGHDFn2BLl0ybNiwTJ48eZnHnXnmmenXr1++/OUvr9D3mTt3bmbPnr3YDQBYCc89lzz4YNKlS3LQQWWnAYAOo1mleubMmWloaEj//v0X296/f/9Mnz59qcfce++9ufjii/Pzn/98hb/P+PHj06dPn4W3QaaoAcDKmTixuP/MZ5IP/R4HAFquTVf/fvvtt3PkkUfm5z//efr27bvCx40dOzazZs1aeHvppZfaMCUAdAKmfgNAm+jWnJ379u2brl27ZsaMGYttnzFjRgYMGLDE/s8++2xeeOGF7Lfffgu3NTY2Ft+4W7c8+eST2XjjjZc4rr6+PvX19c2JBgAsy2OPJY8+mnTvnnzxi2WnAYAOpVlnqnv06JHBgwdn0qRJC7c1NjZm0qRJGTp06BL7f+ITn8jf/va3PPLIIwtv+++/f/bcc8888sgjpnUDQHtomvo9fHiy1lrlZgGADqZZZ6qTZPTo0TnqqKOy4447Zuedd86FF16YOXPm5Oijj06SjBo1Kuuuu27Gjx+fnj17Zuutt17s+DXWWCNJltgOALSBSsXUbwBoQ80u1SNHjszrr7+e008/PdOnT8/222+f2267beHiZVOnTk2XLm36UW0AYEU98kjy1FNJz57J/vuXnQYAOpy6SqVSKTvER5k9e3b69OmTWbNmpXfv3mXHAYDa8Z3vJD/4QXEZrauvLjsNANSMFe2hTikDQEdl6jcAtDmlGgA6qj/9KZk6NenVK9lnn7LTAECHpFQDQEfVdJZ6xIhklVVKjQIAHZVSDQAdUUNDctVVxdjUbwBoM0o1AHREf/hDMn16suaayec+V3YaAOiwlGoA6Iiapn5/6UtJjx7lZgGADkypBoCOZv785JprirGp3wDQppRqAOho7rwzeeONpH//5NOfLjsNAHRoSjUAdDRNU78PPjjp2rXcLADQwSnVANCRvP9+8pvfFGNTvwGgzSnVANCR3Hpr8vbbyaBBydChZacBgA5PqQaAjqRp6vfIkUkXv+YBoK35bQsAHcU77yQ33liMTf0GgHahVANAR3Hjjcl77yWbbJLssEPZaQCgU1CqAaCjaJr6feihSV1duVkAoJNQqgGgI3jzzWKRssTUbwBoR0o1AHQE11+fzJ+fbL11stVWZacBgE5DqQaAjuCDU78BgHajVANArXvttWTSpGI8cmS5WQCgk1GqAaDWXXtt0tCQ7LhjsfI3ANBulGoAqHVNU78PO6zcHADQCSnVAFDLXn45+eMfi/Ehh5SbBQA6IaUaAGrZ1VcnlUqy++7JeuuVnQYAOh2lGgBqmVW/AaBUSjUA1KrnnksefDDp0iU56KCy0wBAp6RUA0CtmjixuP/sZ5N+/crNAgCdlFINALXK1G8AKJ1SDQC16LHHkkcfTbp3T774xbLTAECnpVQDQC1qmvr9+c8na65ZbhYA6MSUagCoNZWKqd8AUCWUagCoNY88kjz1VLLKKsn++5edBgA6NaUaAGrNr39d3H/hC0mvXuVmAYBOTqkGgFrS2Ljo89SmfgNA6ZRqAKglf/pTMnVqsvrqyd57l50GADo9pRoAaknTAmUjRhSfqQYASqVUA0CtaGhIrrqqGJv6DQBVQakGgFpxzz3JjBnJWmslw4aVnQYAiFINALWjaer3l76U9OhRbhYAIIlSDQC1Yd685Npri7Gp3wBQNZRqAKgFd96ZvPFG0r9/ssceZacBAP6XUg0AtaBp6vchhyRdu5abBQBYSKkGgGr33nvJ9dcXY1O/AaCqKNUAUO1uvTV5++1k/fWTT32q7DQAwAco1QBQ7Zqmfo8cmXTxqxsAqonfzABQzd5+O7nppmJs6jcAVB2lGgCq2Y03Fp+p3nTT5JOfLDsNAPAhSjUAVLOmqd+HHprU1ZWbBQBYglINANXqzTeT224rxqZ+A0BVUqoBoFr95jfJ/PnJNtskW25ZdhoAYCmUagCoVh+c+g0AVCWlGgCq0WuvJZMmFeORI8vNAgAsk1INANXommuSxsZkp52SjTcuOw0AsAxKNQBUI1O/AaAmKNUAUG1efjn54x+L8SGHlJsFAFgupRoAqs1VVxX3u++erLdeuVkAgOVSqgGg2pj6DQA1Q6kGgGry7LPJn/+cdO2aHHRQ2WkAgI+gVANANZk4sbj/7GeTfv3KzQIAfCSlGgCqianfAFBTlGoAqBb/+Efyt78l3bsnX/xi2WkAgBWgVANAtWia+r333skaa5QaBQBYMUo1AFSDSsXUbwCoQUo1AFSDhx9Onn46WWWVZL/9yk4DAKwgpRoAqkHTWer99kt69So3CwCwwpRqAChbY+Oiz1Ob+g0ANUWpBoCy/elPydSpyeqrF4uUAQA1Q6kGgLL97GfF/Re/mPTsWW4WAKBZlGoAKNNjjyW//GUx/vrXy80CADSbUg0AZTr11OIz1SNGJEOGlJ0GAGgmpRoAyvLAA8lvfpN06ZKcfXbZaQCAFlCqAaAMlUoydmwxHjUq2WqrcvMAAC2iVANAGe68M7nrrqRHj+R73ys7DQDQQko1ALS3xsZFZ6m//vVkgw3KzQMAtJhSDQDt7dprkylTkl69ku9+t+w0AMBKUKoBoD0tWFCs+J0kJ5+crL12uXkAgJWiVANAe7r00uSpp5K+fZPRo8tOAwCsJKUaANrLe+8tWpTslFOS3r1LjQMArDylGgDay4QJybRpyfrrJ8cdV3YaAKAVKNUA0B7eeis555xifMYZSc+epcYBAFqHUg0A7eH885M330y23DI58siy0wAArUSpBoC2Nn16csEFxfjss5OuXcvNAwC0GqUaANra97+fvPtusvPOyYgRZacBAFqRUg0Abem555Kf/rQYn3tuUldXbh4AoFUp1QDQlsaNS+bPT/baK9lzz7LTAACtTKkGgLby6KPJ5ZcX46aVvwGADkWpBoC2csopSaWSHHJIMnhw2WkAgDagVANAW7jvvuSmm4qVvs86q+w0AEAbUaoBoLVVKsmYMcX4mGOSzTYrNw8A0GaUagBobbfemtx7b9KzZ3L66WWnAQDakFINAK2psTEZO7YYn3BCst565eYBANqUUg0ArenKK4tVv/v0WTQFHADosJRqAGgt8+Ylp51WjL/97WSttcrNAwC0OaUaAFrLf/938txzSf/+yYknlp0GAGgHSjUAtIY5cxZdOuu005LVVis3DwDQLpRqAGgNP/5xMn16stFGybHHlp0GAGgnSjUArKw33kjOO68Yn3VW0qNHuXkAgHajVAPAyjrvvGTWrGTbbZPDDis7DQDQjpRqAFgZ06YVU7+T5Jxzki5+tQJAZ+I3PwCsjDPPTN5/P9l112SffcpOAwC0M6UaAFrq6aeTiy8uxueem9TVlZsHAGh3SjUAtNRppyUNDcm++ya77VZ2GgCgBEo1ALTEQw8lEycWZ6fPOafsNABASVpUqidMmJANN9wwPXv2zJAhQ/Lggw8uc9+f//zn2X333bPmmmtmzTXXzLBhw5a7PwDUhO9+t7g//PBi1W8AoFNqdqmeOHFiRo8enXHjxuWhhx7Kdtttl+HDh+e1115b6v533313DjvssNx1112ZPHlyBg0alL322ivTpk1b6fAAUIq77kpuvz3p1q1YqAwA6LTqKpVKpTkHDBkyJDvttFN+8pOfJEkaGxszaNCgnHDCCRkzZsxHHt/Q0JA111wzP/nJTzJq1Kil7jN37tzMnTt34ePZs2dn0KBBmTVrVnr37t2cuADQuiqVZOjQ5IEHkq9/PZkwoexEAEAbmD17dvr06fORPbRZZ6rnzZuXKVOmZNiwYYu+QJcuGTZsWCZPnrxCX+Pdd9/N/Pnzs9Zaay1zn/Hjx6dPnz4Lb4MGDWpOTABoO7/9bVGoV101OfXUstMAACVrVqmeOXNmGhoa0r9//8W29+/fP9OnT1+hr/Gd73wnAwcOXKyYf9jYsWMza9ashbeXXnqpOTEBoG00NCz6LPVJJyXrrFNqHACgfN3a85ude+65ufLKK3P33XenZ8+ey9yvvr4+9fX17ZgMAFbAr36VPPZYsuaaybe+VXYaAKAKNKtU9+3bN127ds2MGTMW2z5jxowMGDBguceef/75Offcc3PnnXdmW6ukAlBr5s5NTj+9GI8dm6yxRqlxAIDq0Kzp3z169MjgwYMzadKkhdsaGxszadKkDB06dJnH/eAHP8hZZ52V2267LTvuuGPL0wJAWS66KJk6NRk4MPnGN8pOAwBUiWZP/x49enSOOuqo7Ljjjtl5551z4YUXZs6cOTn66KOTJKNGjcq6666b8ePHJ0nOO++8nH766bniiiuy4YYbLvzsda9evdKrV69W/FEAoI28/XZy9tnFeNy4ZJVVys0DAFSNZpfqkSNH5vXXX8/pp5+e6dOnZ/vtt89tt922cPGyqVOnpkuXRSfA/+u//ivz5s3LQQcdtNjXGTduXL73ve+tXHoAaA8XXJDMnJlsumnyv/+IDACQtOA61WVY0euDAUCre/31ZOONi7PVEycmhxxSdiIAoB20yXWqAaDTGT++KNQ77JB8aNYVAIBSDQDLMnVqMmFCMR4/Puni1yYAsDh/HQDAsnzve8m8ecmeeyaf+1zZaQCAKqRUA8DSPPZYctllxficc5K6unLzAABVSakGgKU57bSksTEZMSL51KfKTgMAVCmlGgA+7MEHk+uuKz5D3XR9agCApVCqAeCDKpVkzJhiPGpUstVW5eYBAKqaUg0AH3TnnclddyU9ehQLlQEALIdSDQBNGhuTsWOL8de/nmywQbl5AICqp1QDQJNrr02mTEl69Uq++92y0wAANUCpBoAkWbAgOfXUYnzyycnaa5ebBwCoCUo1ACTJpZcmTz2V9O2bjB5ddhoAoEYo1QDw3nuLFiU75ZSkd+9S4wAAtUOpBoAJE5Jp05L110+OO67sNABADVGqAejc3norOeecYnzGGUnPnqXGAQBqi1INQOd2/vnJm28mW2yRHHlk2WkAgBqjVAPQec2YkVxwQTH+/veTrl3LzQMA1BylGoDO6+yzk3ffTXbeORkxouw0AEANUqoB6Jyeey756U+L8bnnJnV15eYBAGqSUg1A5zRuXDJ/frLXXsmee5adBgCoUUo1AJ3Po48ml19ejJtW/gYAaAGlGoDO55RTkkolOfjgZPDgstMAADVMqQagc7nvvuSmm4qVvs86q+w0AECNU6oB6DwqlWTMmGJ8zDHJ5puXmwcAqHlKNQCdx623Jvfem/TsmZx+etlpAIAOQKkGoHNobEzGji3GJ5yQrLdeuXkAgA5BqQagc7jyymLV7z59Fk0BBwBYSUo1AB3fvHnJaacV4299K1lrrXLzAAAdhlINQMd38cXJc88l/fsnJ55YdhoAoANRqgHo2ObMSc48sxifdlrSq1e5eQCADkWpBqBj+/GPk+nTk402So49tuw0AEAHo1QD0HG98UZy3nnF+Kyzkh49ys0DAHQ4SjUAHdd55yWzZiXbbpscdljZaQCADkipBqBjmjatmPqdJN//ftLFrzwAoPX5CwOAjumss5L330923TXZd9+y0wAAHZRSDUDH8/TTyX//dzE+99ykrq7cPABAh6VUA9DxnHpq0tBQnKHebbey0wAAHZhSDUDH0diYfPvbyVVXFWenzzmn7EQAQAfXrewAANAq5s9Pvvzl5Je/LB6fd16x6jcAQBtSqgGofe+8kxx8cHLbbUnXrsXnqf/1X8tOBQB0Ako1ALVt5szis9MPPpisskpy9dVW+wYA2o1SDUDteuGFZPjw5KmnkrXWSm66KRk6tOxUAEAnolQDUJsefTT5/OeTV19NBg1Kbr892WKLslMBAJ2M1b8BqD333JPsvntRqLfaKrn/foUaACiFUg1AbbnuumLK9+zZxTWo//jHZL31yk4FAHRSSjUAteO//is56KBk7txkxIjkd79L1lyz7FQAQCemVANQ/SqVZNy45OtfL8Zf/Wqxyvcqq5SdDADo5JRqAKrbggXJccclZ55ZPD799OSii5Ju1toEAMrnLxIAqtd77yWHH55cf31SV5f8v/9XFGwAgCqhVANQnd58M9l//+Tee5P6+uSKK5IDDyw7FQDAYpRqAKrPtGnFNaj//vekd+/kt79N9tij7FQAAEtQqgGoLo8/Xlwy66WXknXWSW67Ldl227JTAQAslYXKAKgekycX155+6aVks82S++9XqAGAqqZUA1Adbr45+exnkzfeSHbeObnvvmTDDctOBQCwXEo1AOW75JLkgAOK1b733jv5/e+Tvn3LTgUA8JGUagDKU6kk556bHHNM0tCQjBqV3HBDstpqZScDAFghSjUA5WhsTE46KRk7tnj87W8nl16adO9eZioAgGax+jcA7W/u3OSoo5KJE4vHP/pR8s1vlpsJAKAFlGoA2tfs2cmBByaTJhVnpS+9NDn88LJTAQC0iFINQPuZMaNYiOzhh4vPTV93XbLXXmWnAgBoMaUagPbxzDPJ8OHJc88la6+d3HJLsuOOZacCAFgpSjUAbe+hh4oz1K+9lmy0UXL77cmmm5adCgBgpVn9G4C2deedyR57FIV6++2T++9XqAGADkOpBqDtXHllss8+yTvvJJ/5THLPPcmAAWWnAgBoNUo1AG3jP/4jOeywZP785JBDis9Q9+5ddioAgFalVAPQuiqVZOzY5KSTiscnnJD8+tdJfX2psQAA2oKFygBoPfPnJ8cem1x2WfH4nHOSMWOSurpycwEAtBGlGoDWMWfOomneXbsmP/95cvTRZacCAGhTSjUAK++f/0z23Td54IFklVWSq65KvvCFslMBALQ5pRqAlfPii8nw4cmTTyZrrpncfHMydGjZqQAA2oVSDUDL/e1vyec/n7zySjJoUHL77ckWW5SdCgCg3Vj9G4CW+eMfk913Lwr1Vlsl99+vUAMAnY5SDUDzXX998rnPJbNmJbvtVhTs9dYrOxUAQLtTqgFonp/+NPnSl5K5c5MDDkh+97vis9QAAJ2QUg3AiqlUkjPPTI47LmlsLK5Hfc01xWrfAACdlFINwEdraEi+/vVk3Lji8WmnFWesu1nvEgDo3Pw1BMDyzZ6dHH10ct11SV1dMmFC8rWvlZ0KAKAqKNUALKmhIZk0KbnssuQ3v0neey/p0SO5/PLkoIPKTgcAUDWUagAWefzxokj/6lfJtGmLtn/iE8lFFyV77FFeNgCAKqRUA3R2//xncuWVRZn+858XbV9zzeTQQ5Ojjkp23rmY+g0AwGKUaoDOaP785JZbiiJ9003F4yTp2jXZZ5+iSH/hC0l9fbk5AQCqnFIN0FlUKsnDDxdF+oorkpkzFz23/fZFkT788KRfv9IiAgDUGqUaoKN79dVigbHLLkv+/vdF2/v3T444oijT225bXj4AgBqmVAN0RO+9l9xwQ/KLXyS33540Nhbb6+uTAw4oivRee7nONADASvLXFEBHUakk999fnJG+6qpk1qxFzw0dWhTpQw4pFiADAKBVKNUAte6FF5Jf/rI4K/3MM4u2r79+MmpUcuSRyWablRYPAKAjU6oBatHbbyfXXFOclb7nnkXbV1stOeig4qz0HnskXbqUlxEAoBNQqgFqRUNDctddRZG+7rrk3XeL7XV1yZ57FkX6wAOTXr3KzQkA0Iko1QDV7skniyL9y18mL7+8aPummxZF+sgji6neAAC0O6UaoBq98UZy5ZVFmX7wwUXb11gjOfTQokwPGVKcpQYAoDRKNUC1mD8/ue22okjfeGMyb16xvWvX5POfL4r0fvslPXuWmxMAgIWUaoCyPfJIUaQvvzx5/fVF27fbrijShx+e9O9fWjwAAJZNqQYow/TpRYn+xS+SRx9dtL1fv+SII4oyvd125eUDAGCFKNUAbentt5Nnny2uH/3008X9k08mf/pTsZp3kvTokRxwQFGk99or6d693MwAAKwwpRpgZc2eXRTnptLcdP/MM8UZ6WX51KeKIj1yZLLmmu2XFwCAVqNUA6yIWbMWFeUPluann05ee235x/btm2yySXEJrE02KW477VQ8BgCgpinVAE3eemvppfmZZxZfQGxp1l578dL8wfEaa7RHegAASqBUA53Lm28uvTQ//XTyz38u/9h+/RaV5Q+W5k02Sfr0aZ/8AABUFaUa6Hj++c9lT9V+443lHztgwJKledNNk403Tnr3bp/8AADUDKUaqG4LFhQraM+eXdyaxh/c9sYbyXPPLSrQb765/K+5zjqLF+em+403TlZfvX1+LgAAOgSlGmh9DQ3JO+98dBle3ram8XvvtSzDwIFL/4zzxhsnvXq17s8LAECn1aJSPWHChPz7v/97pk+fnu222y7/+Z//mZ133nmZ+1999dU57bTT8sILL2TTTTfNeeedl3322afFoYFWUKkUZ4Hnz1/y9t57H112l7ftnXdaP299fTH9evXVF7/v3bv4PPNGGy0q0BtvnKy2WutnAACAD2l2qZ44cWJGjx6diy66KEOGDMmFF16Y4cOH58knn0y/fv2W2P/+++/PYYcdlvHjx+cLX/hCrrjiiowYMSIPPfRQtt5661b5IWCpKpWksXHJ27K2r8xzH/X80oprW9zmzVvxfRcsaPvXoFu3RcX3gyV4acX4o7b16NH2eQEAoJnqKpVKpTkHDBkyJDvttFN+8pOfJEkaGxszaNCgnHDCCRkzZswS+48cOTJz5szJTTfdtHDbpz71qWy//fa56KKLlvo95s6dm7lz5y58PHv27AwaNCizZs1K72pdKOjdd5O99lr0+MP/WZvzeGWObcnXatpWC+MP3j6q3NJ8dXVJ9+7JKqssKrYtLcG9exdnl+vqyv6pAACg2WbPnp0+ffp8ZA9t1pnqefPmZcqUKRk7duzCbV26dMmwYcMyefLkpR4zefLkjB49erFtw4cPz/XXX7/M7zN+/PicccYZzYlWvsbG5L77yk7ByqirS7p0KW4fHH/wtqztH3VM9+4tv/XosXLHN+fWtWvZrwIAANSUZpXqmTNnpqGhIf37919se//+/fPEE08s9Zjp06cvdf/p06cv8/uMHTt2sSLedKa6qvXsmVx33ZLbP3yWrq0ft/RrNG37qPGK7teSY5qzX3NL7UcV4Q9+HwAAgBVUlat/19fXp76+vuwYzdOtW/LFL5adAgAAgHbUpTk79+3bN127ds2MGTMW2z5jxowMGDBgqccMGDCgWfsDAABArWhWqe7Ro0cGDx6cSZMmLdzW2NiYSZMmZejQoUs9ZujQoYvtnyR33HHHMvcHAACAWtHs6d+jR4/OUUcdlR133DE777xzLrzwwsyZMydHH310kmTUqFFZd911M378+CTJiSeemD322CM//OEPs+++++bKK6/MX/7yl/zsZz9r3Z8EAAAA2lmzS/XIkSPz+uuv5/TTT8/06dOz/fbb57bbblu4GNnUqVPTpcuiE+C77LJLrrjiipx66qn57ne/m0033TTXX3+9a1QDAABQ85p9neoyrOj1wQAAAKA1rGgPbdZnqgEAAIBFlGoAAABoIaUaAAAAWkipBgAAgBZSqgEAAKCFlGoAAABoIaUaAAAAWkipBgAAgBZSqgEAAKCFlGoAAABoIaUaAAAAWkipBgAAgBZSqgEAAKCFlGoAAABoIaUaAAAAWkipBgAAgBZSqgEAAKCFlGoAAABoIaUaAAAAWqhb2QFWRKVSSZLMnj275CQAAAB0Bk39s6mPLktNlOq33347STJo0KCSkwAAANCZvP322+nTp88yn6+rfFTtrgKNjY155ZVXsvrqq6eurq7sOMs0e/bsDBo0KC+99FJ69+5ddhyawWtXu7x2tc3rV7u8drXLa1e7vHa1zetXeyqVSt5+++0MHDgwXbos+5PTNXGmukuXLllvvfXKjrHCevfu7Y1So7x2tctrV9u8frXLa1e7vHa1y2tX27x+tWV5Z6ibWKgMAAAAWkipBgAAgBZSqltRfX19xo0bl/r6+rKj0Exeu9rltattXr/a5bWrXV672uW1q21ev46rJhYqAwAAgGrkTDUAAAC0kFINAAAALaRUAwAAQAsp1QAAANBCSjUAAAC0kFLdDN///vezyy67ZNVVV80aa6yx1H2mTp2afffdN6uuumr69euXb33rW1mwYMFyv+4bb7yRI444Ir17984aa6yRL3/5y3nnnXfa4Cegyd133526urql3v785z8v87hPf/rTS+x/3HHHtWNykmTDDTdc4nU499xzl3vM+++/n+OPPz4f+9jH0qtXr3zpS1/KjBkz2ikxSfLCCy/ky1/+cjbaaKOsssoq2XjjjTNu3LjMmzdvucd535VnwoQJ2XDDDdOzZ88MGTIkDz744HL3v/rqq/OJT3wiPXv2zDbbbJNbbrmlnZLSZPz48dlpp52y+uqrp1+/fhkxYkSefPLJ5R5z6aWXLvEe69mzZzsl5oO+973vLfFafOITn1juMd531WFpf5vU1dXl+OOPX+r+3ncdi1LdDPPmzcvBBx+cr33ta0t9vqGhIfvuu2/mzZuX+++/P5dddlkuvfTSnH766cv9ukcccUT+8Y9/5I477shNN92UP/zhD/nqV7/aFj8C/2uXXXbJq6++utjtK1/5SjbaaKPsuOOOyz322GOPXey4H/zgB+2Umg8688wzF3sdTjjhhOXu/81vfjM33nhjrr766txzzz155ZVXcuCBB7ZTWpLkiSeeSGNjY37605/mH//4Ry644IJcdNFF+e53v/uRx3rftb+JEydm9OjRGTduXB566KFst912GT58eF577bWl7n///ffnsMMOy5e//OU8/PDDGTFiREaMGJG///3v7Zy8c7vnnnty/PHH509/+lPuuOOOzJ8/P3vttVfmzJmz3ON69+692HvsxRdfbKfEfNhWW2212Gtx7733LnNf77vq8ec//3mx1+2OO+5Ikhx88MHLPMb7rgOp0GyXXHJJpU+fPktsv+WWWypdunSpTJ8+feG2//qv/6r07t27Mnfu3KV+rccee6ySpPLnP/954bZbb721UldXV5k2bVqrZ2fp5s2bV1l77bUrZ5555nL322OPPSonnnhi+4RimTbYYIPKBRdcsML7v/XWW5Xu3btXrr766oXbHn/88UqSyuTJk9sgISvqBz/4QWWjjTZa7j7ed+XYeeedK8cff/zCxw0NDZWBAwdWxo8fv9T9DznkkMq+++672LYhQ4ZU/u3f/q1Nc7J8r732WiVJ5Z577lnmPsv6u4b2N27cuMp22223wvt731WvE088sbLxxhtXGhsbl/q8913H4kx1K5o8eXK22Wab9O/ff+G24cOHZ/bs2fnHP/6xzGPWWGONxc6ODhs2LF26dMkDDzzQ5pkp/Pa3v80///nPHH300R+57+WXX56+fftm6623ztixY/Puu++2Q0I+7Nxzz83HPvaxfPKTn8y///u/L/djFlOmTMn8+fMzbNiwhds+8YlPZP3118/kyZPbIy7LMGvWrKy11lofuZ/3XfuaN29epkyZsth7pkuXLhk2bNgy3zOTJ09ebP+k+B3oPVauWbNmJclHvs/eeeedbLDBBhk0aFAOOOCAZf7dQtt7+umnM3DgwHz84x/PEUcckalTpy5zX++76jRv3rz86le/yjHHHJO6urpl7ud913F0KztARzJ9+vTFCnWShY+nT5++zGP69eu32LZu3bplrbXWWuYxtL6LL744w4cPz3rrrbfc/Q4//PBssMEGGThwYB599NF85zvfyZNPPpnrrruunZKSJP/n//yf7LDDDllrrbVy//33Z+zYsXn11Vfzox/9aKn7T58+PT169FhiLYT+/ft7n5XomWeeyX/+53/m/PPPX+5+3nftb+bMmWloaFjq77Qnnnhiqccs63eg91h5Ghsbc9JJJ2XXXXfN1ltvvcz9Nt988/zP//xPtt1228yaNSvnn39+dtlll/zjH//4yN+LtK4hQ4bk0ksvzeabb55XX301Z5xxRnbffff8/e9/z+qrr77E/t531en666/PW2+9lX/9139d5j7edx1Lpy/VY8aMyXnnnbfcfR5//PGPXCSC6tCS1/Pll1/O7bffnquuuuojv/4HP+u+zTbbZJ111slnP/vZPPvss9l4441bHpxmvXajR49euG3bbbdNjx498m//9m8ZP3586uvr2zoqH9KS9920adPy+c9/PgcffHCOPfbY5R7rfQctc/zxx+fvf//7cj+TmyRDhw7N0KFDFz7eZZddssUWW+SnP/1pzjrrrLaOyQfsvffeC8fbbrtthgwZkg022CBXXXVVvvzlL5eYjOa4+OKLs/fee2fgwIHL3Mf7rmPp9KX65JNPXu6/IiXJxz/+8RX6WgMGDFhiZdSm1YUHDBiwzGM+vOjLggUL8sYbbyzzGJatJa/nJZdcko997GPZf//9m/39hgwZkqQ44+aP+5WzMu/FIUOGZMGCBXnhhRey+eabL/H8gAEDMm/evLz11luLna2eMWOG91kraO5r98orr2TPPffMLrvskp/97GfN/n7ed22vb9++6dq16xIr5C/vPTNgwIBm7U/b+sY3vrFw8dPmnvXq3r17PvnJT+aZZ55po3SsqDXWWCObbbbZMl8L77vq8+KLL+bOO+9s9mwq77va1ulL9dprr5211167Vb7W0KFD8/3vfz+vvfbawindd9xxR3r37p0tt9xymce89dZbmTJlSgYPHpwk+f3vf5/GxsaFfziy4pr7elYqlVxyySUZNWpUunfv3uzv98gjjyRJ1llnnWYfy+JW5r34yCOPpEuXLkt8lKLJ4MGD071790yaNClf+tKXkiRPPvlkpk6duti/EtMyzXntpk2blj333DODBw/OJZdcki5dmr+0h/dd2+vRo0cGDx6cSZMmZcSIEUmKqcSTJk3KN77xjaUeM3To0EyaNCknnXTSwm133HGH91g7q1QqOeGEE/Kb3/wmd999dzbaaKNmf42Ghob87W9/yz777NMGCWmOd955J88++2yOPPLIpT7vfVd9LrnkkvTr1y/77rtvs47zvqtxZa+UVktefPHFysMPP1w544wzKr169ao8/PDDlYcffrjy9ttvVyqVSmXBggWVrbfeurLXXntVHnnkkcptt91WWXvttStjx45d+DUeeOCByuabb155+eWXF277/Oc/X/nkJz9ZeeCBByr33ntvZdNNN60cdthh7f7zdUZ33nlnJUnl8ccfX+K5l19+ubL55ptXHnjggUqlUqk888wzlTPPPLPyl7/8pfL8889XbrjhhsrHP/7xyr/8y7+0d+xO7f77769ccMEFlUceeaTy7LPPVn71q19V1l577cqoUaMW7vPh165SqVSOO+64yvrrr1/5/e9/X/nLX/5SGTp0aGXo0KFl/Aid1ssvv1zZZJNNKp/97GcrL7/8cuXVV19dePvgPt531eHKK6+s1NfXVy699NLKY489VvnqV79aWWONNRZe4eLII4+sjBkzZuH+9913X6Vbt26V888/v/L4449Xxo0bV+nevXvlb3/7W1k/Qqf0ta99rdKnT5/K3Xffvdh77N133124z4dfuzPOOKNy++23V5599tnKlClTKoceemilZ8+elX/84x9l/Aid2sknn1y5++67K88//3zlvvvuqwwbNqzSt2/fymuvvVapVLzvql1DQ0Nl/fXXr3znO99Z4jnvu45NqW6Go446qpJkidtdd921cJ8XXnihsvfee1dWWWWVSt++fSsnn3xyZf78+Qufv+uuuypJKs8///zCbf/85z8rhx12WKVXr16V3r17V44++uiFRZ22ddhhh1V22WWXpT73/PPPL/b6Tp06tfIv//IvlbXWWqtSX19f2WSTTSrf+ta3KrNmzWrHxEyZMqUyZMiQSp8+fSo9e/asbLHFFpVzzjmn8v777y/c58OvXaVSqbz33nuVr3/965U111yzsuqqq1a++MUvLlbmaHuXXHLJUv8f+sF/3/W+qy7/+Z//WVl//fUrPXr0qOy8886VP/3pTwuf22OPPSpHHXXUYvtfddVVlc0226zSo0ePylZbbVW5+eab2zkxy3qPXXLJJQv3+fBrd9JJJy18nfv371/ZZ599Kg899FD7h6cycuTIyjrrrFPp0aNHZd11162MHDmy8swzzyx83vuuut1+++2VJJUnn3xyiee87zq2ukqlUmnHE+MAAADQYbhONQAAALSQUg0AAAAtpFQDAABACynVAAAA0EJKNQAAALSQUg0AAAAtpFQDAABACynVAAAA0EJKNQAAALSQUg0AAAAtpFQDAABAC/3/8fj0puE0EQAAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Cost Function**"
      ],
      "metadata": {
        "id": "ip2Jv28aQSjR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Our next step is to write the cost function. Remember that the cost function evaluates the performance of the model on the training data given a set of model parameters. Here’s the cost function for logistic regression."
      ],
      "metadata": {
        "id": "vFhDEHi1QWdL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def cost(theta, X, y):\n",
        "    theta = np.matrix(theta)\n",
        "    X = np.matrix(X)\n",
        "    y = np.matrix(y)\n",
        "    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))\n",
        "    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))\n",
        "    return np.sum(first - second) / (len(X))"
      ],
      "metadata": {
        "id": "WYxm5fxnQb0_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that we reduce the output down to a single scalar value, which is the sum of the “error” quantified as a function of the difference between the class probability assigned by the model and the true label of the example. The implementation is completely vectorized – it’s computing the model’s predictions for the whole data set in one statement (sigmoid(X * theta.T)). If the math here isn’t making sense, refer to the exercise text I linked to above for a more detailed explanation.\n",
        "\n",
        "We can test the cost function to make sure it’s working, but first we need to do some setup."
      ],
      "metadata": {
        "id": "KewRDTpEQn8S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# add a ones column - this makes the matrix multiplication work out easier\n",
        "data.insert(0, 'Ones', 1)\n"
      ],
      "metadata": {
        "id": "47KU86n5Q8wh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# set X (training data) and y (target variable)\n",
        "cols = data.shape[1]\n",
        "X = data.iloc[:,0:cols-1]\n",
        "y = data.iloc[:,cols-1:cols]"
      ],
      "metadata": {
        "id": "yXvp0GzjRBkJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# convert to numpy arrays and initalize the parameter array theta\n",
        "X = np.array(X.values)\n",
        "y = np.array(y.values)\n",
        "theta = np.zeros(3)"
      ],
      "metadata": {
        "id": "pE8Vcb_TRHdJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "I like to check the shape of the data structures I’m working with fairly often to convince myself that their values are sensible. This technique if very useful when implementing matrix multiplication."
      ],
      "metadata": {
        "id": "J0ajS-9eRTfC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X.shape, theta.shape, y.shape\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qL7SSvNmRW_C",
        "outputId": "8c3119b1-8a37-426e-dd83-939a4b8fc527"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((100, 3), (3,), (100, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let’s compute the cost for our initial solution given zeros for the model parameters, here represented as “theta”."
      ],
      "metadata": {
        "id": "mssL8cLkRdWx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cost(theta, X, y)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-2ioozJTRgaR",
        "outputId": "aa6ca07b-d63d-440a-cb5e-1c530718dce1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6931471805599453"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now that we have a working cost function, the next step is to write a function that computes the gradient of the model parameters to figure out how to change the parameters to improve the outcome of the model on the training data. Recall that with gradient descent we don’t just randomly jigger around the parameter values and see what works best. At each training iteration we update the parameters in a way that’s guaranteed to move them in a direction that reduces the training error (i.e. the “cost”). We can do this because the cost function is differentiable. The calculus involved in deriving the equation is well beyond the scope of this blog post, but the full equation is in the exercise text. Here’s the function."
      ],
      "metadata": {
        "id": "-u8uNOGvRxhF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gradient(theta, X, y):\n",
        "    theta = np.matrix(theta)\n",
        "    X = np.matrix(X)\n",
        "    y = np.matrix(y)\n",
        "\n",
        "    parameters = int(theta.ravel().shape[1])\n",
        "    grad = np.zeros(parameters)\n",
        "\n",
        "    error = sigmoid(X * theta.T) - y\n",
        "\n",
        "    for i in range(parameters):\n",
        "        term = np.multiply(error, X[:,i])\n",
        "        grad[i] = np.sum(term) / len(X)\n",
        "\n",
        "    return grad"
      ],
      "metadata": {
        "id": "HhipZA3ER2GO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that we don't actually perform gradient descent in this function - we just compute a single gradient step. In the exercise, an Octave function called \"fminunc\" is used to optimize the parameters given functions to compute the cost and the gradients. Since we're using Python, we can use SciPy's optimization API to do the same thing."
      ],
      "metadata": {
        "id": "2vG7LR_6R90A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.optimize as opt\n",
        "result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y))\n",
        "cost(result[0], X, y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x-mzyEN1SBAO",
        "outputId": "014eb8d1-1cbb-4866-8c5e-6a1b359805f5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.20349770158947447"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We now have the optimal model parameters for our data set. Next we need to write a function that will output predictions for a dataset X using our learned parameters theta. We can then use this function to score the training accuracy of our classifier."
      ],
      "metadata": {
        "id": "4-28sH4hSKI4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def predict(theta, X):\n",
        "    probability = sigmoid(X * theta.T)\n",
        "    return [1 if x >= 0.5 else 0 for x in probability]\n",
        "\n",
        "theta_min = np.matrix(result[0])\n",
        "predictions = predict(theta_min, X)\n",
        "correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]\n",
        "accuracy = (sum(map(int, correct)) % len(correct))\n",
        "print('accuracy = {0}%'.format(accuracy))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "myYa07XYSOth",
        "outputId": "f10034e5-272c-472c-ca05-c3011a9f1393"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy = 89%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Our logistic regression classifer correctly predicted if a student was admitted or not 89% of the time. Not bad! Keep in mind that this is training set accuracy though. We didn't keep a hold-out set or use cross-validation to get a true approximation of the accuracy so this number is likely higher than its true performance (this topic is covered in a later exercise)."
      ],
      "metadata": {
        "id": "khvRyOw4SgGm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Regularized Logistic Regression**\n"
      ],
      "metadata": {
        "id": "hFTdHkj2Sv6h"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now that we have a working implementation of logistic regression, we'll going to improve the algorithm by adding regularization. Regularization is a term in the cost function that causes the algorithm to prefer \"simpler\" models (in this case, models will smaller coefficients). The theory is that this helps to minimize overfitting and improve the model's ability to generalize. We’ll apply our regularized version of logistic regression to a slightly more challenging problem. Suppose you are the product manager of the factory and you have the test results for some microchips on two different tests. From these two tests, you would like to determine whether the microchips should be accepted or rejected. To help you make the decision, you have a data set of test results on past microchips, from which you can build a logistic regression model.\n",
        "\n",
        "Let's start by visualizing the data."
      ],
      "metadata": {
        "id": "SEAsHKZkTKIO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#path = os.getcwd() + '/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex1data1.txt'\n",
        "data2 = pd.read_csv('/content/drive/MyDrive/Courses /Data Science /Machine Learning/Theory /ML andrew/Dataset/ex2data2.txt', header=None, names=['Test 1', 'Test 2', 'Accepted'])\n",
        "data2.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "oymarG4eTYIo",
        "outputId": "02047d13-18e2-4cc3-c8ce-b00b43257e86"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     Test 1   Test 2  Accepted\n",
              "0  0.051267  0.69956         1\n",
              "1 -0.092742  0.68494         1\n",
              "2 -0.213710  0.69225         1\n",
              "3 -0.375000  0.50219         1\n",
              "4 -0.513250  0.46564         1"
            ],
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              "        const element = document.querySelector('#df-948461dc-c13e-4d9e-b6d9-1d317c1051aa');\n",
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              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
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              "  }\n",
              "\n",
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              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    }\n",
              "  }\n",
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              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
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              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
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              "\n",
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            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data2",
              "summary": "{\n  \"name\": \"data2\",\n  \"rows\": 118,\n  \"fields\": [\n    {\n      \"column\": \"Test 1\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.496653790573339,\n        \"min\": -0.83007,\n        \"max\": 1.0709,\n        \"num_unique_values\": 102,\n        \"samples\": [\n          -0.26555,\n          0.79435,\n          0.93836\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Test 2\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.5197429100518889,\n        \"min\": -0.76974,\n        \"max\": 1.1089,\n        \"num_unique_values\": 92,\n        \"samples\": [\n          0.15863,\n          -0.27266,\n          0.7288\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Accepted\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 0,\n        \"max\": 1,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          0,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "positive = data2[data2['Accepted'].isin([1])]\n",
        "negative = data2[data2['Accepted'].isin([0])]\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.scatter(positive['Test 1'], positive['Test 2'], s=50, c='b', marker='o', label='Accepted')\n",
        "ax.scatter(negative['Test 1'], negative['Test 2'], s=50, c='r', marker='x', label='Rejected')\n",
        "ax.legend()\n",
        "ax.set_xlabel('Test 1 Score')\n",
        "ax.set_ylabel('Test 2 Score')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 733
        },
        "id": "9okCJ5nRTOwx",
        "outputId": "54f9d135-3fbc-484f-8d5f-a134e06ba829"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Test 2 Score')"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This data looks a bit more complicated than the previous example. In particular, you'll notice that there is no linear decision boundary that will perform well on this data. One way to deal with this using a linear technique like logistic regression is to construct features that are derived from polynomials of the original features. We can try creating a bunch of polynomial features to feed into the classifier."
      ],
      "metadata": {
        "id": "czMa2gXzT26L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "degree = 5\n",
        "x1 = data2['Test 1']\n",
        "x2 = data2['Test 2']\n",
        "\n",
        "data2.insert(3, 'Ones', 1)\n",
        "\n",
        "for i in range(1, degree):\n",
        "    for j in range(0, i):\n",
        "        data2['F' + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j)\n",
        "\n",
        "data2.drop('Test 1', axis=1, inplace=True)\n",
        "data2.drop('Test 2', axis=1, inplace=True)\n",
        "\n",
        "data2.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 226
        },
        "id": "2O8dXmL2UElP",
        "outputId": "6963cdab-0a07-486e-9372-1354302d6a72"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Accepted  Ones       F10       F20       F21       F30       F31       F32  \\\n",
              "0         1     1  0.051267  0.002628  0.035864  0.000135  0.001839  0.025089   \n",
              "1         1     1 -0.092742  0.008601 -0.063523 -0.000798  0.005891 -0.043509   \n",
              "2         1     1 -0.213710  0.045672 -0.147941 -0.009761  0.031616 -0.102412   \n",
              "3         1     1 -0.375000  0.140625 -0.188321 -0.052734  0.070620 -0.094573   \n",
              "4         1     1 -0.513250  0.263426 -0.238990 -0.135203  0.122661 -0.111283   \n",
              "\n",
              "        F40       F41       F42       F43  \n",
              "0  0.000007  0.000094  0.001286  0.017551  \n",
              "1  0.000074 -0.000546  0.004035 -0.029801  \n",
              "2  0.002086 -0.006757  0.021886 -0.070895  \n",
              "3  0.019775 -0.026483  0.035465 -0.047494  \n",
              "4  0.069393 -0.062956  0.057116 -0.051818  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-0e2128c3-1b83-46f2-b7af-976364385a35\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Accepted</th>\n",
              "      <th>Ones</th>\n",
              "      <th>F10</th>\n",
              "      <th>F20</th>\n",
              "      <th>F21</th>\n",
              "      <th>F30</th>\n",
              "      <th>F31</th>\n",
              "      <th>F32</th>\n",
              "      <th>F40</th>\n",
              "      <th>F41</th>\n",
              "      <th>F42</th>\n",
              "      <th>F43</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0.051267</td>\n",
              "      <td>0.002628</td>\n",
              "      <td>0.035864</td>\n",
              "      <td>0.000135</td>\n",
              "      <td>0.001839</td>\n",
              "      <td>0.025089</td>\n",
              "      <td>0.000007</td>\n",
              "      <td>0.000094</td>\n",
              "      <td>0.001286</td>\n",
              "      <td>0.017551</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>-0.092742</td>\n",
              "      <td>0.008601</td>\n",
              "      <td>-0.063523</td>\n",
              "      <td>-0.000798</td>\n",
              "      <td>0.005891</td>\n",
              "      <td>-0.043509</td>\n",
              "      <td>0.000074</td>\n",
              "      <td>-0.000546</td>\n",
              "      <td>0.004035</td>\n",
              "      <td>-0.029801</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>-0.213710</td>\n",
              "      <td>0.045672</td>\n",
              "      <td>-0.147941</td>\n",
              "      <td>-0.009761</td>\n",
              "      <td>0.031616</td>\n",
              "      <td>-0.102412</td>\n",
              "      <td>0.002086</td>\n",
              "      <td>-0.006757</td>\n",
              "      <td>0.021886</td>\n",
              "      <td>-0.070895</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>-0.375000</td>\n",
              "      <td>0.140625</td>\n",
              "      <td>-0.188321</td>\n",
              "      <td>-0.052734</td>\n",
              "      <td>0.070620</td>\n",
              "      <td>-0.094573</td>\n",
              "      <td>0.019775</td>\n",
              "      <td>-0.026483</td>\n",
              "      <td>0.035465</td>\n",
              "      <td>-0.047494</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>-0.513250</td>\n",
              "      <td>0.263426</td>\n",
              "      <td>-0.238990</td>\n",
              "      <td>-0.135203</td>\n",
              "      <td>0.122661</td>\n",
              "      <td>-0.111283</td>\n",
              "      <td>0.069393</td>\n",
              "      <td>-0.062956</td>\n",
              "      <td>0.057116</td>\n",
              "      <td>-0.051818</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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            }
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now we need to modify the cost and gradient functions to include the regularization term. In each case, the regularizer is added on to the previous calculation. Here’s the updated cost function."
      ],
      "metadata": {
        "id": "lWMlh8LaUN4W"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def costReg(theta, X, y, learningRate):\n",
        "    theta = np.matrix(theta)\n",
        "    X = np.matrix(X)\n",
        "    y = np.matrix(y)\n",
        "    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))\n",
        "    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))\n",
        "    reg = (learningRate / 2 * len(X)) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))\n",
        "    return np.sum(first - second) / (len(X)) + reg"
      ],
      "metadata": {
        "id": "waU0Dbf8UWwh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notice that we’ve added a new variable called “reg” that is a function of the parameter values. As the parameters get larger, the penalization added to the cost function increases. Also note that we’ve added a new “learning rate” parameter to the function. This is also part of the regularization term in the equation. The learning rate gives us a new hyper-parameter that we can use to tune how much weight the regularization holds in the cost function.\n",
        "\n",
        "Next we’ll add regularization to the gradient function."
      ],
      "metadata": {
        "id": "4rutVg0TUm1g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gradientReg(theta, X, y, learningRate):\n",
        "    theta = np.matrix(theta)\n",
        "    X = np.matrix(X)\n",
        "    y = np.matrix(y)\n",
        "\n",
        "    parameters = int(theta.ravel().shape[1])\n",
        "    grad = np.zeros(parameters)\n",
        "\n",
        "    error = sigmoid(X * theta.T) - y\n",
        "\n",
        "    for i in range(parameters):\n",
        "        term = np.multiply(error, X[:,i])\n",
        "\n",
        "        if (i == 0):\n",
        "            grad[i] = np.sum(term) / len(X)\n",
        "        else:\n",
        "            grad[i] = (np.sum(term) / len(X)) + ((learningRate / len(X)) * theta[:,i])\n",
        "\n",
        "    return grad"
      ],
      "metadata": {
        "id": "E0BwEXf9Uq5F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Just as with the cost function, the regularization term is added on to the original calculation. However, unlike the cost function, we included logic to make sure that the first parameter is not regularized. The intuition behind this decision is that the first parameter is considered the “bias” or “intercept” of the model and shouldn’t be penalized.\n",
        "\n",
        "We can test out the new functions just as we did before."
      ],
      "metadata": {
        "id": "ZkOHoOLhVJJZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# set X and y (remember from above that we moved the label to column 0)\n",
        "cols = data2.shape[1]\n",
        "X2 = data2.iloc[:,1:cols]\n",
        "y2 = data2.iloc[:,0:1]\n",
        "\n",
        "# convert to numpy arrays and initalize the parameter array theta\n",
        "X2 = np.array(X2.values)\n",
        "y2 = np.array(y2.values)\n",
        "theta2 = np.zeros(11)\n",
        "\n",
        "learningRate = 1\n",
        "\n",
        "costReg(theta2, X2, y2, learningRate)"
      ],
      "metadata": {
        "id": "92sXt25PVOIH",
        "outputId": "7160f6ea-9db6-4e2c-de47-021e04da6f00",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6931471805599454"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can also re-use the optimization code from earlier to find the optimal model parameters."
      ],
      "metadata": {
        "id": "8UCxG_n5VUBG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "result2 = opt.fmin_tnc(func=costReg, x0=theta2, fprime=gradientReg, args=(X2, y2, learningRate))\n",
        "result2"
      ],
      "metadata": {
        "id": "Bhivn7UbVYCm",
        "outputId": "683c9a57-3778-4398-8026-5b534483a053",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-23-92e983cee313>:17: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
            "  grad[i] = (np.sum(term) / len(X)) + ((learningRate / len(X)) * theta[:,i])\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 1.22702480e-04,  7.19893533e-05, -3.74156020e-04, -1.44256518e-04,\n",
              "         2.93168594e-05, -5.64160697e-05, -1.02826715e-04, -2.83150640e-04,\n",
              "         6.47460472e-07, -1.99697745e-04, -1.68479401e-05]),\n",
              " 97,\n",
              " 1)"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, we can use the same method we applied earlier to create label predictions for the training data and evaluate the performance of the model.\n",
        "\n",
        "theta_min = np.matrix(result2[0])"
      ],
      "metadata": {
        "id": "Yv-SjzS3VeH4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "theta_min = np.matrix(result2[0])\n",
        "predictions = predict(theta_min, X2)\n",
        "correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y2)]\n",
        "accuracy = (sum(map(int, correct)) % len(correct))\n",
        "print('accuracy = {0}%'.format(accuracy))"
      ],
      "metadata": {
        "id": "NNvR4XEZVhoP",
        "outputId": "7a6e57c4-166d-44ba-ae6c-c83b078df634",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy = 77%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "That's all for part 3! In the next post in the series we'll expand on our implementation of logistic regression to tackle multi-class image classification."
      ],
      "metadata": {
        "id": "wIcKCHkVVovu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2**"
      ],
      "metadata": {
        "id": "1s9wsSGHqw-0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('default')"
      ],
      "metadata": {
        "id": "Uk0kATVsq4Hi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X = 2 * np.random.rand(100, 1)\n",
        "y = 4 + 3 * X + np.random.randn(100, 1)"
      ],
      "metadata": {
        "id": "Sa096EAyq74z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(x=X, y=y)\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "rpEicen5rA6M",
        "outputId": "d102d52f-0817-4df1-a929-35dbd19c15b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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tu3QnC9OvgSwUuKuTwl/0bF8LxBbJnjKdziGHVIYIN+dh6vBKKttVs2OPZix7LepxK2d/OyP2V2Idma8RZIDwTL0QZItUrcliai+FW27CnSQjF+VL9Vo+a+o+1bWr6qIe958XjtK0UUfF/X1M4fb6zdASkKVSsWcN3Itl9lgsd9c273bsdujEcRzjhlfSMexDfVt4BBkgi9l80bMds8e6cxvuehJvAExUqoLpoahvC49ZSwDgAe6uu0tmaOv6WqledyUdwZRZY+HRIwMAHuDuurtkhrZDXysd9WDpCqbpmjVmE4IMAHggnVOmbeE23DmOo8+a21wFwEgFuIF1V5JVGJzOYEp9WyiGlgDAI4G762J/6F16sb8gK6fAux06ufl7w6Iek5vjS+u+Yuke9gnUt00bdZSqhg7I2hAjMf0aADxn+5TpZEvWOjJerLvCsgbJw/RrALAEs8dCuRk6cXOMFzPDGPZJP4IMAMA4bsJdtGO8mhkWazC1tUfOlHYTZAAAGcmGmWG2DkWZ1G6KfQEAGcn0dVds3cnatHYTZAAAGcvUmWHpnFGVTCa2m6ElAEBGM7EANx1bGqSCie0myAAAYmJKkWcsTJsZZuteWya2myADAHDNpCJPm9m615aJ7aZGBgDgimlFnjYLzKiK1I/lU2dANG2vLRPbTZABgCznZmdoE4s8bWb6jKpITGw3Q0sAkMXcDhWZWORpO1t3sjat3QQZAPCYV8WzsewMbWKRZyYwcUaVGya1myADAB4K1yPSr3cvXXbaEF1z5nFJuzB0DUvfGty/x6EinzqHiiZWFCs3x2dkkWemMG1GlVumtJsgAwAeidQj8sWXB3XX+u166NUPddsPhifcVR8uLBX16aW9+w9GfE7XoSIblvv3io3T0TMJQQYAPNBT8WzAFwcOdhviiVWksNRTiDlUYKgoUOQ5Z0WtfFLI65lcnJpqTEf3HrOWAMAD0YpnAxzFPxvITViK5tChIlOX+/cK09HNQI8MAHgglqLYeGcDuQ1L4UQaKjKpyNNL0aajd60xQuoQZADAA7EWxcYzGyjeGUTRhopMKfL0EtPRzcHQEgC45GbhOLcCxbNuxTMbyO1zivrkhXyerUNFsWA6ujnokQEAF5Jd1Bkonv3Ritoej0tkNpDbmUYv/mKC3vro86weKooV09HNQY8M4LFk3uUjVLJ+tqkq6pxcWaJ7Z45Wv8N7hf16orOB3C4nn3dYjqqGDtC0UUepaugAQowLJu45lK18juNk9L+azc3N8vv9ampqUmFhodfNAUIwdTN1kvWzbe9wNG7xhoj1EIFejZfnnxl3AGjvcPRfGz7QQ6/U64sv/zEtOlm/C/yepUYg4Erhp6MzPJcYt9dvggzgkUjre/CPYOKS+bOt2bFHM5a9FvW4lbO/nXBRZyoXVmPRttQgJKaO2+u30TUy7e3tuvnmm7VixQo1NjaqtLRUl156qW644Qb5fPwBwl5M3UydZP9s01nUmcrZQMw0Sg2mo3vP6CCzePFiLV26VMuXL9ewYcP05ptv6rLLLpPf79dPfvITr5sHxI2pm6mT7J8tRZ2IhpDoLaODzKuvvqpp06ZpypQpkqQhQ4Zo5cqV2rRpk8ctAxLD1M3USfbPlj2GYINsHjo0Osiceuqpuv/++/X+++/r+OOP19tvv62XX35Zd955Z8TntLW1qa2tLfh5c3NzOpoKxIS7/NRJ9s+WPYbSI5svxInK9jodo4PMddddp+bmZp144onKzc1Ve3u7fvWrX+miiy6K+JxFixZp4cKFaWwlEDvu8lMnFT/bwB5DXS8WxXFeLLhoh8r2C3EiIhW2B5YGyIZJA0bPWlq1apV+8Ytf6De/+Y2GDRumuro6zZ07V3feeadmzZoV9jnhemTKysqYtQTjMHUzdVL1s01GAMnWi3aknx2z9+KXjqUBvJQR06/Lysp03XXX6eqrrw4+duutt2rFihV69913Xb0G069hsmSudcIdfigTA0O2XrQjvRc3TqnQLX/clrEX4lRL59IAXsiI6dcHDhxQTk7o4sO5ubnq6OjwqEVAciVj6qaJF2wTmDYtNlun3Pc09PHj3/e8PQOz93rGpIFORgeZqVOn6le/+pWOOeYYDRs2TJs3b9add96pH/7wh143DUiaRKZuMj7eM5OmxWbjlPto4c2tTL8Qx4tJA52MDjK//e1vdeONN+rHP/6xdu/erdLSUl111VW66aabvG4a4LlsvcOPlSnDbtl49xwtvLmV6RfieDFpoJPRQaZv3766++67dffdd3vdFMA42XiHHyuTht2y8e450VCWLRfieLE0QCd2vwYslY13+LFI1Y7V8crG3ZJjCWU97c6d6RfiRASWBij2h/6si/0FWTO0bHSPDIDIsvEO3y0Th92y8e7Z7dDHjVNO0i1//EtS1ujJRqYVtqcbQQawFOPjkZk67JbshfVM5za8Ta4s0aTKkqy9ECeDSYXt6UaQASyVjXf4bpk87JZtd89uw1s2X4iRGIIMYDG3FwlTZu6ki+nDbtl20c628Ib0IsggLbLtQppO0S4SJs3cSReG3cyTbeEN6WP0FgXJwBYF3svGC6kpsnVJfIm9rADbub1+M/0aKWXaFNhs4mZV1YVPbVN7R2L3Mu0djmp27NGauk9Vs2NPwq+XLExLBbIDQ0tIGROnwGaTdMzcMb23jdoMIPMRZJAypk6BzRapnrlj0j5PPdVgpaM2gxowwDsEGaSMyVNgs0EqZ+60dzi6+Ukzetu87hXy+vsD2Y4aGaSM6VNgM10ql8T/rw3b1djsrrctlbyuwfL6+wOII8jMmjVLL730UiraggyTjXvLmCSwYJ6U3H1s1m5t0F3rt7s6NpW9bekqZjb1+wPoFHOQaWpqUnV1tY477jj9+te/1qeffpqKdiEDpOpCCveSPXMncPF2K5W9bbHUYGXi9wfQKeYamdWrV+v//u//9Mgjj2j58uVasGCBqqurdfnll2vatGnq1atXKtoJS2Xb3jImSubMnWgX70OlurfN6xosr78/gE5xFfseeeSRmjdvnubNm6fa2lo99NBDuvjii/WNb3xDM2fO1I9//GMdd9xxyW4rLMUUWO8la+ZOLBflVPe2JasGK94ZR9SAAWZIaNZSQ0OD1q1bp3Xr1ik3N1fnnnuutmzZooqKCt1+++366U9/mqx2wnIsT54Z3F6Uf1p9fMp725KxDUEiM47YBgEwQ8w1MgcPHtRjjz2m7373uxo8eLD+8Ic/aO7cudq1a5eWL1+u9evX69FHH9V//Md/pKK9ADwUrYBbkooL83XNmd9MeVsSrcFKdMYRNWCAGWIOMiUlJZo9e7YGDx6sTZs26c0339SPfvSjkH0QJkyYoH79+iWznQAMEO3i7ZN08/eGpe3iHW8xc6wzjiJtw8A2CID3Yt408pFHHtF5552nggI7xn3ZNBJIPtMWgYu1zqVmxx7NWPZa1NddOfvbavryq6jnysq+QPK5vX6z+zWAuNh88V5T96muXVUX9bgfnjZED73yYcQaGHpdgNRxe/1miwIAcempgNv0kOO2aHl13a6wIUbqHIL62R/eZtNTwGMEGQBJZdqwUzhuZhz179NLe/d/1ePr7G9r19xVtfrtv3wrJe0EEB17LWW4SEWKQCrYsveQmxlH3x91lKvXevrPjfrq7x3JaxyAmNAjk8FsuDOGPaINF0WbCZTIjtipGKqKtuq0v3eeHnjlw6iv40h6pOZDXX76sQm1B0B8CDIZKnBn3PWiErgzpkgRsXATimPZeyiWxRFTGch7WnW6vcPR4Xm5OvBVe9TX+WjvgYTaASB+DC1lIHblRTK5HS5Kxd5D6RiqChQtTxt1lKqGDgj29OTm+HRuZbGr1xhcdHjC7QAQH4JMBmJXXiRLLKHY7UygI76Rn/TvnSq//sGIHlcxlqQcn3Rx1ZCUtQFAzwgyGYhdeZEssYRiN9sXSNLPHq1z1ZNiQiDPOyxHV36nvMdjZp9errzD+KcU8Ap/fRmIXXmRLG7DbmPTlz3OBDrUZ81troaFvAjk4Wb5XX9uha76Trm61hbn+KSrvlOu68+tSNr3BxA7in0zELvyIlncht1b/vgX9c7LDc4EuvnJbWpsDh8w3M5gSncg76mo+PpzK/Szs0/UIzUf6qO9BzS46HBdXDWEnhjAAPwVZiB25UWyuB0u+nz/V8FelsmVJfp/543s8Xg3w0LRvrdPnUEjGYHcTVFx3mE5uvz0Y/Uf0yp1+enHEmIAQ/CXmKHYlRfJcGgo7knX4tu/7W9z9fo9DQulK5CbUFQMIH4MLWWwntbIQGqYvsdQPAKh+N+e2KK9+w9GPO7QXpZkDQtFW7QuGYE8VevfAEgPgkyG62ljPyRXJq+kPLmyRF8e7NBP/6cu6rG7W1r13RGlSavTSnUgZ5YfAjLxRiQbEGSAJMiGlZQ/3rPf1XED+xYEh4XmrKiVTwr5ucQzLJTKQM4sP0iZfSOS6aiRARKUjBoL0zf3XLu1QXet397jMV2Lb22p00pnUTHMZMtmpwiPHhkgQYnWWJh+JxgIam507WWxoU4r2b1HpmLYJLxUbnaK9CDIAAlKpMbChiGpaEEtYG718WHbakOdVjqKir1kelj2EsXe9iPIAAmKt8bCljtBt0FtyBF2b5xoQ+9RPGwIy16i2Nt+1MgACYq3xsKEvYTcyKZi2Eg7YduKNXKiy6bf70xFkAESFO/CbbbcCVIMay9bwrKX+P22H0EGSIJ4ZujYcifIlhf2siUse4nfb/tRIwMkSaw1FjZt7pnpxbCZypaw7DV+v+3mcxwnowdHm5ub5ff71dTUpMLCQq+bA4QIFGJK4af9mlaIyRReu7R3OBq3eEPUsPzy/DN5H8Xvt2ncXr8JMoDHmBqLVLItLAMBBJmvEWRgA+4EkUqEZdiIIPM1ggwAEJZhH7fXb4p9ASAL2LDCMhAPpl8DAABrEWQAAIC1CDIAAMBaBBkAAGAtin0BII2YPQQkF0EGANKE9VyA5GNoCUBWaO9wVLNjj9bUfaqaHXvU3pHeJbQCK+x23Y26salVc1bUau3WhrS2B8gU9MgAyHhe94S0dzha+NS2sPsdOercLmDhU9s0saKYYSYgRvTIAMhoJvSEbKrf2+37H8qR1NDUqk31e1PeFiDTEGQAZKxoPSFSZ09IqoeZdrdEDjHxHAfgHwgyADKWKT0hA/sWJPU4AP9AjQyQYZje+w+m9ISMKS9Sib9AjU2tYXuHfJKK/Z3vFYDYEGSADOJ1UatpTOkJyc3xacHUCs1ZUSufFBJmAhFzwdSKrA2cQCIYWoLRvJ4yaxMTilpNE+gJiRQPfOoMeunoCZlcWaKlM0er2B8amor9BVo6c3RWBk0gGeiRgbHoXXCP6b3hmdYTMrmyRBMrihn6A5LI+B6ZTz/9VDNnztSAAQPUu3dvDR8+XG+++abXzUKK0bsQG1OKWk1kWk9Ibo5PVUMHaNqoo1Q1dAAhBkiQ0T0yn3/+uU477TRNmDBBf/rTn3TkkUdq+/bt6t+/v9dNQwrRuxA7t8Wq67c1qmrogBS3xjz0hACZy+ggs3jxYpWVlemhhx4KPlZeXu5hi5AOsfQuZONFORy3xapP1H2qf5uSnUWlgZ4QAJnF6KGlJ598UqeccorOO+88DRw4UCeffLKWLVvW43Pa2trU3Nwc8gG7mDJl1iZjyotU1Ccv6nF79x/MyuElAJnL6CDz17/+VUuXLtVxxx2nZ599VnPmzNFPfvITLV++POJzFi1aJL/fH/woKytLY4uRDKZMmbVJbo5P00eVujqWAAggkxgdZDo6OjR69Gj9+te/1sknn6wrr7xSs2fP1r333hvxOddff72ampqCHzt37kxji5EMJk2ZtcnEimJXxxEAAWQSo4NMSUmJKioqQh476aST9PHHH0d8Tn5+vgoLC0M+YJfAlFlJ3cIMi4dFFgiAkRAAAWQio4PMaaedpvfeey/ksffff1+DBw/2qEVIF9OmzNogEAB9IgACyB4+x3GMXSr1jTfe0KmnnqqFCxfq/PPP16ZNmzR79mzdf//9uuiii1y9RnNzs/x+v5qamuidsRD7BsXO5oUEeb8BBLi9fhsdZCTp6aef1vXXX6/t27ervLxc8+bN0+zZs10/nyCDbGRjILA5gAFIvowJMokiyADmC6zk3PUfo0D0YjgRyD5ur99G18gAiJ1tG21GW8lZ6lzJ2fTzAOANo1f2BbJZPMNDNg7PsJIzgEQQZAADxRNIIg3PBDbadDs8k+76GlZyBpAIggxgmHgCSbI22vSiR4eVnAEkghoZwCDx1ovEMjwTSSBAdX2dQIBau7XB5VnEhpWcASSCIAMYJN5AkujwjJcFt6zkDCARBBnAIPEGkkSHZ5LRo5MIVnIGEC9qZACDxBtIAsMzjU2tYXtVfOoMBZGGZ0wouJ1cWaKJFcXWLeQHwFv0yAAGibdeJNHhGVMKbnNzfKoaOkDTRh2lqqEDCDEAoiLIIC62Lbpmi0QCSSLDMxTcArAVWxQgZvFO0bVx/x+vJDINOt6fc2DWkqSQ4Sm2CQDgBfZa+hpBJrni3RPHxhVnveZF8LPlfSIUu8PPCTYjyHyNIJM87R2Oxi3eEHF2S6Cg9OX5Z4b8Y8mGgHYJd/GTZMwF8Zk/N+iGNVu1d/9XwcdMDFtesyWUApEQZL5GkEmemh17NGPZa1GPWzn728E9ceINPzCHSRfERc9s030v1Yf9mk+E4gBuHpAJ2P0aSRfPFF2v1ydBYrxa7TecZ/68K2KIkTp/l9glm93EkX0IMnAtnim6JqxPgviYdEFs73B0w5qtUY8jFHPzgOxDkIFr0aboSlJRn1761uD+wc9NWZ8EsTPpgripfq/27j/o6thsD8XcPCDbEGTgWk9rnATs3X9QZ/zmheCQA+uT2MukC2Is3yPbQzE3D8g2BBnEJNKia4c6tH6CDQHtZdIF0e33GNAnL+tDMTcPyDYEGcRscmWJXvzFBBX1yQv79a71E2wIaCeTLoiBtkRzy7TKrA/F3Dwg27BpJOLy1kefh6zj0dWh9RNVQwewIaCFAhfEOStq5VP41X7TdUE8tC2RSouv+k65zh1BKJb+0XPaddp8MevIIAMRZBCXeOonAhsCwh4mXRAjtaWoTy/dOq1S544oTVtbbMDNA7IFQQZxMal+Aqll0gXRpLbYgJsHZAOCDCTFvidLoGahsak1bFd/YMVeCgozg0kXRJPaAsB7BBnEtQS9SfUTAIDsxaylLJfIEvTMRgIAeI0emSwWbQl6nzqnUE+sKI7Ys0LNAgDASwSZLBbLEvQ91SRQswAA8ApDS1nMpCXoAQCIB0EmizGFGgBgO4JMFjNpCXoAAOJBkMlitu/J0t7hqGbHHq2p+1Q1O/aovSPS4vUAgExFsW+WM2kJ+ljEs/ZNKsW6oCAAIDl8juNk9G1sc3Oz/H6/mpqaVFhY6HVzjGXThTiw9k3XX9xAa9O9ho1poQoAMoHb6zdBBlZp73A0bvGGiNPGA1sjvDz/TElKeTgzLVQBQKZwe/1maAlWcbv2zX9t+ECr3vg4pb0kyVhQEACQGIp9kVSpLsB1u6bNXevfj2vbhVjEsqAgACA16JFB0qSjViSRNW2S3UvCgoIA4D16ZJAUiWw+GYtoa99Ek8xeEhYUBADvEWSQsGi1IlJnL0gyhpncrH3jRjJ6SVhQEAC8R5BBwtJdKxJY+6bYH9rTUewv0E+rj3P1GsnoJbF9QUEAyATUyCBhXtSKTK4s0cSK4m7TqyVp1Rs71djUGraHKDA9O1m9JLYuKAgAmYIgYzFTFrHzqlYkN8enqqEDuj2+YGqF5qyolU8KCTOp6iWJFKroiQGA1CPIWMqk1WQDtSLp6gWJxotekkihCgCQWqzsayETV5MNtEkK3wviRZtM6bECAMTO7fWbYl/LpHOGUCwmVhRrbvVx8vfuFfJ4sb/As2X6A70k00YdpaqhAwgxAJCBGFqyTCwzhNI11BFumKtf71667LRyXXPmNwkQAICUoUfGMqatJhtpIbymLw/q7vXva922xrS0AwCQnQgyljFpNVlTh7kAANmDIGOZWFaTTfUGjmyaCADwGjUyaZKsGTSB1WSjrZOybltjyqdnmzbMBQDIPgSZNEj2mi/R1kmRFHZ6dmADx2TNInI7fPXh3w4k/L0AAAiHdWTi5LaHJZVrvoRrgySNW7wh4pBPYHG6l+efmfBsovYOR+MWb4i4EN6h39OrKdgAADu5vX7TIxMHtz0s0Yphfeoshp1YURz3MFPXKdY1O/akbXp2YJjrR18vhNeTRM4TAIBIKPaNUaTpxoFhm7VbG4KPeVEMm+66lcmVJVF3nKboFwCQKgSZGMQ63diLYlgvpmcPOaKPq+Mo+gUAJBtBJgax9rB4ESpimZ6dLCatbQMAyC4EmRjE2sPiRagI1K0EXr/r95M6p2cns1bFi/MEAEAiyMQk1p4HL0KF9I/p2cX+0PamagNHr84TAABmLcUg0PMQabpxYGrzoT0P0dZ8SdWU5MmVJZpYUZyURfiiae9w5O+dp8tOG6LVdbu0d/9Xwa+l+jwBANmNdWRiFJi1JIVfVTdSj0eyVvY1Tbip6EV9eun7o45SdUVxxpwnACC93F6/GVqKUTzDNpkcYsJNRf98/0E9+MqHavryq4w4TwCAuRhaikMswzbJ3p7AFKle7A8AADfokYlTYFXdaaOOUtXQAT1uT+Bm8TzbsPM1AMAEVgWZ2267TT6fT3PnzvW6KVHFuniebdj5GgBgAmuCzBtvvKH77rtPI0aM8LoprmR6jwWL4AEATGBFkNm3b58uuugiLVu2TP379/e6Oa5keo8Fi+ABAExgRZC5+uqrNWXKFFVXV0c9tq2tTc3NzSEfXsj0HgsWwQMAmMD4ILNq1SrV1tZq0aJFro5ftGiR/H5/8KOsrCzFLQwvG3os0r2CMAAAXRm9IN7OnTt1yimnaN26dcHamPHjx2vUqFG6++67wz6nra1NbW1twc+bm5tVVlaWtAXxYhHv4nm2ydR1cgAA3nG7IJ7RQWb16tX6/ve/r9zc3OBj7e3t8vl8ysnJUVtbW8jXwkn2yr6xytR1ZAAASCW312+jF8Q766yztGXLlpDHLrvsMp144omaP39+1BBjgnTueQQAQLYxOsj07dtXlZWVIY/16dNHAwYM6Pa4yQKL5wEAgOQyvtgXAAAgEqN7ZMLZuHGj100AAACGoEcGAABYiyADAACsRZABAADWIsgAAABrEWQAAIC1CDIAAMBaBBkAAGAtggwAALAWQQYAAFiLIAMAAKxl3RYF8EZ7h8MO3gAA4xBkENXarQ1a+NQ2NTS1Bh8r8RdowdQKTa4s6XY8oQcAkC4EGfRo7dYGzVlRK6fL441NrZqzolZLZ44OCTOxhh4AABJBjQwiau9wtPCpbd1CjKTgYwuf2qb2js7PAqHn0BAj/SP0rN3akNoGAwCyDkEmBdo7HNXs2KM1dZ+qZsee4IXeNpvq93YLJYdyJDU0tWpT/d6YQw8AAMnA0FKSZdLQyu6WyCGm63GxhJ6qoQOS1EIAQLajRyaJMm1oZWDfAtfHxRJ6AABIFoJMkmTi0MqY8iKV+AsUab6RT529TWPKi2IKPQAAJAtBJkliGVqxRW6OTwumVkhStzAT+HzB1Arl5vhiCj0AACQLQSZJMnVoZXJliZbOHK1if2hPSrG/IGTqdSyhBwCAZKHYN0niGVqxZeG4yZUlmlhRHLWtgdDTtdi52NJiZwCA+QgySRIYWmlsag1bJ+NT5wU9MLRi2+ym3Byfq9lGbkMPAADJwNBSksQytJJps5u6CoSeaaOOUtXQAYQYAEDKEGSSyE09SSbObgIAwCsMLSVZtKEVFo4DACB5CDIp0FM9SabObgIAwAsEmRQKNyuJheMAAEgegkwc3EybjjQr6cYpJ8U0uwkAAERGkImRm2nTgVlJXYNKY1Orrv79Zl35nXLd/1K9fFLIMSwcBwBAbJi1FAM306bdzEp68u0GLfmX6KvlAgCAntEj41K0gOJT57Tpvvm9XM1K6t8nTy/PP5OF4wAASABBxiW306Zr/vo3V6+3u6XV9Wq5AAAgPIaWXHI/HdpdjwqzkgAASBxBxiW3waNq6ACV+AsixhmfOouDmZUEAEDiCDIuBTaFjBZQvn3sANd7LgEAgMQQZFyKZVNIN3suAQCAxPkcx8no3Qmbm5vl9/vV1NSkwsLChF/PzToyAW4WzgMAAN25vX4TZOJAQAEAILXcXr+Zfh0Hpk0DAGAGamQAAIC1CDIAAMBaBBkAAGAtggwAALAWQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUyfmXfwA4Mzc3NHrcEAAC4FbhuR9tJKeODTEtLiySprKzM45YAAIBYtbS0yO/3R/x6xm8a2dHRoV27dqlv377y+RLf2LG5uVllZWXauXNn0jahNA3naL9MPz+Jc8wUnGNmSMU5Oo6jlpYWlZaWKicnciVMxvfI5OTk6Oijj0766xYWFmbsL2QA52i/TD8/iXPMFJxjZkj2OfbUExNAsS8AALAWQQYAAFiLIBOj/Px8LViwQPn5+V43JWU4R/tl+vlJnGOm4Bwzg5fnmPHFvgAAIHPRIwMAAKxFkAEAANYiyAAAAGsRZAAAgLWyPsgsWbJEQ4YMUUFBgcaOHatNmzb1ePwf/vAHnXjiiSooKNDw4cP1zDPPhHzdcRzddNNNKikpUe/evVVdXa3t27en8hSiiuUcly1bptNPP139+/dX//79VV1d3e34Sy+9VD6fL+Rj8uTJqT6NHsVyjg8//HC39hcUFIQcY/v7OH78+G7n6PP5NGXKlOAxpr2PL730kqZOnarS0lL5fD6tXr066nM2btyo0aNHKz8/X9/85jf18MMPdzsm1r/xVIr1HB9//HFNnDhRRx55pAoLC1VVVaVnn3025Jibb7652/t44oknpvAsIov1/DZu3Bj297SxsTHkOJvfw3B/Zz6fT8OGDQseY9J7KEmLFi3SP/3TP6lv374aOHCgpk+frvfeey/q87y6PmZ1kPmf//kfzZs3TwsWLFBtba1GjhypSZMmaffu3WGPf/XVVzVjxgxdfvnl2rx5s6ZPn67p06dr69atwWNuv/123XPPPbr33nv1+uuvq0+fPpo0aZJaW1vTdVohYj3HjRs3asaMGXrhhRdUU1OjsrIynX322fr0009Djps8ebIaGhqCHytXrkzH6YQV6zlKnatPHtr+jz76KOTrtr+Pjz/+eMj5bd26Vbm5uTrvvPNCjjPpfdy/f79GjhypJUuWuDq+vr5eU6ZM0YQJE1RXV6e5c+fqiiuuCLnQx/O7kUqxnuNLL72kiRMn6plnntFbb72lCRMmaOrUqdq8eXPIccOGDQt5H19++eVUND+qWM8v4L333gtp/8CBA4Nfs/09/M///M+Qc9u5c6eKioq6/S2a8h5K0osvvqirr75ar732mtatW6eDBw/q7LPP1v79+yM+x9Pro5PFxowZ41x99dXBz9vb253S0lJn0aJFYY8///zznSlTpoQ8NnbsWOeqq65yHMdxOjo6nOLiYuc3v/lN8OtffPGFk5+f76xcuTIFZxBdrOfY1d///nenb9++zvLly4OPzZo1y5k2bVqymxq3WM/xoYcecvx+f8TXy8T38a677nL69u3r7Nu3L/iYae/joSQ5TzzxRI/H/PKXv3SGDRsW8tgFF1zgTJo0Kfh5oj+3VHJzjuFUVFQ4CxcuDH6+YMECZ+TIkclrWJK4Ob8XXnjBkeR8/vnnEY/JtPfwiSeecHw+n/Phhx8GHzP1PQzYvXu3I8l58cUXIx7j5fUxa3tkvvrqK7311luqrq4OPpaTk6Pq6mrV1NSEfU5NTU3I8ZI0adKk4PH19fVqbGwMOcbv92vs2LERXzOV4jnHrg4cOKCDBw+qqKgo5PGNGzdq4MCBOuGEEzRnzhzt2bMnqW13K95z3LdvnwYPHqyysjJNmzZN77zzTvBrmfg+PvDAA7rwwgvVp0+fkMdNeR/jEe3vMRk/N9N0dHSopaWl29/j9u3bVVpaqmOPPVYXXXSRPv74Y49aGJ9Ro0appKREEydO1CuvvBJ8PBPfwwceeEDV1dUaPHhwyOMmv4dNTU2S1O337lBeXh+zNsj87W9/U3t7uwYNGhTy+KBBg7qNzwY0Njb2eHzgv7G8ZirFc45dzZ8/X6WlpSG/fJMnT9bvfvc7Pf/881q8eLFefPFFnXPOOWpvb09q+92I5xxPOOEEPfjgg1qzZo1WrFihjo4OnXrqqfrkk08kZd77uGnTJm3dulVXXHFFyOMmvY/xiPT32NzcrC+//DIpv/+mueOOO7Rv3z6df/75wcfGjh2rhx9+WGvXrtXSpUtVX1+v008/XS0tLR621J2SkhLde++9euyxx/TYY4+prKxM48ePV21traTk/Btmkl27dulPf/pTt79Fk9/Djo4OzZ07V6eddpoqKysjHufl9THjd79G/G677TatWrVKGzduDCmGvfDCC4P/P3z4cI0YMUJDhw7Vxo0bddZZZ3nR1JhUVVWpqqoq+Pmpp56qk046Sffdd59uueUWD1uWGg888ICGDx+uMWPGhDxu+/uYbX7/+99r4cKFWrNmTUgNyTnnnBP8/xEjRmjs2LEaPHiwHn30UV1++eVeNNW1E044QSeccELw81NPPVU7duzQXXfdpUceecTDlqXG8uXL1a9fP02fPj3kcZPfw6uvvlpbt271tGYnmqztkTniiCOUm5urzz77LOTxzz77TMXFxWGfU1xc3OPxgf/G8pqpFM85Btxxxx267bbb9Nxzz2nEiBE9HnvsscfqiCOO0AcffJBwm2OVyDkG9OrVSyeffHKw/Zn0Pu7fv1+rVq1y9Y+hl+9jPCL9PRYWFqp3795J+d0wxapVq3TFFVfo0Ucf7dZ931W/fv10/PHHW/M+djVmzJhg2zPpPXQcRw8++KAuvvhi5eXl9XisKe/hNddco6efflovvPCCjj766B6P9fL6mLVBJi8vT9/61rf0/PPPBx/r6OjQ888/H3K3fqiqqqqQ4yVp3bp1wePLy8tVXFwcckxzc7Nef/31iK+ZSvGco9RZWX7LLbdo7dq1OuWUU6J+n08++UR79uxRSUlJUtodi3jP8VDt7e3asmVLsP2Z8j5KndMh29raNHPmzKjfx8v3MR7R/h6T8bthgpUrV+qyyy7TypUrQ6bPR7Jv3z7t2LHDmvexq7q6umDbM+U9lDpnAn3wwQeubiq8fg8dx9E111yjJ554Qhs2bFB5eXnU53h6fUyoVNhyq1atcvLz852HH37Y2bZtm3PllVc6/fr1cxobGx3HcZyLL77Yue6664LHv/LKK85hhx3m3HHHHc5f/vIXZ8GCBU6vXr2cLVu2BI+57bbbnH79+jlr1qxx/vznPzvTpk1zysvLnS+//DLt5+c4sZ/jbbfd5uTl5Tn/+7//6zQ0NAQ/WlpaHMdxnJaWFufnP/+5U1NT49TX1zvr1693Ro8e7Rx33HFOa2urFee4cOFC59lnn3V27NjhvPXWW86FF17oFBQUOO+8807wGNvfx4Bx48Y5F1xwQbfHTXwfW1panM2bNzubN292JDl33nmns3nzZuejjz5yHMdxrrvuOufiiy8OHv/Xv/7VOfzww51f/OIXzl/+8hdnyZIlTm5urrN27drgMdF+bukW6zn+93//t3PYYYc5S5YsCfl7/OKLL4LH/OxnP3M2btzo1NfXO6+88opTXV3tHHHEEc7u3buNP7+77rrLWb16tbN9+3Zny5YtzrXXXuvk5OQ469evDx5j+3sYMHPmTGfs2LFhX9Ok99BxHGfOnDmO3+93Nm7cGPJ7d+DAgeAxJl0fszrIOI7j/Pa3v3WOOeYYJy8vzxkzZozz2muvBb92xhlnOLNmzQo5/tFHH3WOP/54Jy8vzxk2bJjzxz/+MeTrHR0dzo033ugMGjTIyc/Pd8466yznvffeS8epRBTLOQ4ePNiR1O1jwYIFjuM4zoEDB5yzzz7bOfLII51evXo5gwcPdmbPnu3ZPyoBsZzj3Llzg8cOGjTIOffcc53a2tqQ17P9fXQcx3n33XcdSc5zzz3X7bVMfB8DU3G7fgTOa9asWc4ZZ5zR7TmjRo1y8vLynGOPPdZ56KGHur1uTz+3dIv1HM8444wej3eczinnJSUlTl5ennPUUUc5F1xwgfPBBx+k98S+Fuv5LV682Bk6dKhTUFDgFBUVOePHj3c2bNjQ7XVtfg8dp3Oace/evZ37778/7Gua9B46jhP2/CSF/H2ZdH30fd1oAAAA62RtjQwAALAfQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBoBV2tvbdeqpp+oHP/hByONNTU0qKyvTv//7v3vUMgBeYIsCANZ5//33NWrUKC1btkwXXXSRJOmSSy7R22+/rTfeeEN5eXketxBAuhBkAFjpnnvu0c0336x33nlHmzZt0nnnnac33nhDI0eO9LppANKIIAPASo7j6Mwzz1Rubq62bNmif/3Xf9UNN9zgdbMApBlBBoC13n33XZ100kkaPny4amtrddhhh3ndJABpRrEvAGs9+OCDOvzww1VfX69PPvnE6+YA8AA9MgCs9Oqrr+qMM87Qc889p1tvvVWStH79evl8Po9bBiCd6JEBYJ0DBw7o0ksv1Zw5czRhwgQ98MAD2rRpk+69916vmwYgzeiRAWCda6+9Vs8884zefvttHX744ZKk++67Tz//+c+1ZcsWDRkyxNsGAkgbggwAq7z44os666yztHHjRo0bNy7ka5MmTdLf//53hpiALEKQAQAA1qJGBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtQgyAADAWgQZAABgLYIMAACwFkEGAABYiyADAACsRZABAADW+v8ZFCRjcvcf/QAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let's compute using the normal equation:"
      ],
      "metadata": {
        "id": "qmbC2ja-rHn7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X_b = np.c_[np.ones_like(X), X]"
      ],
      "metadata": {
        "id": "DczUbgfRrOXZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n",
        "theta_best"
      ],
      "metadata": {
        "id": "IfyWjDxZrR5x",
        "outputId": "5dad98ed-f47f-4136-a26d-2822941009e6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3.97201277],\n",
              "       [3.08131953]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The parameters that we used to generate the data (with some noise) are\n",
        " and\n",
        ". The noise was responsible for not making it possible to recover the initial parameters\n",
        " &\n",
        "."
      ],
      "metadata": {
        "id": "cnSU_fhfrbOh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now we can make predictions using our optimal parameters:\n",
        "\n"
      ],
      "metadata": {
        "id": "0wJEPujCrf06"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X_ = np.array([[0], [2]])\n",
        "X_ = np.c_[np.ones_like(X_), X_].T\n",
        "X_.shape"
      ],
      "metadata": {
        "id": "X3x0tiJtrnqh",
        "outputId": "2a8ea56b-5cf9-48c6-cdb9-759cb69baa53",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_hat = np.matmul(theta_best.T, X_)"
      ],
      "metadata": {
        "id": "54G6qm3crskJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(x=X, y=y)\n",
        "plt.plot([0,2], y_hat.flatten(), color='red', label='Predictions')\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('y')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "QUDuGjrjrwWg",
        "outputId": "7a96f0a0-e9d7-4b85-b8fb-cbe11102258a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Performing Linear Regression using scikit-learn is also simple:"
      ],
      "metadata": {
        "id": "acvAY00Dr5ch"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LinearRegression\n"
      ],
      "metadata": {
        "id": "ibUc4YqEr8no"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#<p style=\"font-family:JetBrains Mono; font-weight:normal; letter-spacing: 1px; color:#207d06; font-size:100%; text-align:left;padding: 0px; border-bottom: 3px solid #207d06;\">**Chapter 4: Regularization**</p>"
      ],
      "metadata": {
        "id": "HHOEvTvdrHgJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Logistic Regression**"
      ],
      "metadata": {
        "id": "hfnFOFn1raKG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.datasets import load_breast_cancer\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import accuracy_score"
      ],
      "metadata": {
        "id": "CjR81zogrhp1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Load dataset\n",
        "data = load_breast_cancer()\n",
        "X = data.data\n",
        "y = data.target\n",
        "\n",
        "# Standardize the data\n",
        "scaler = StandardScaler()\n",
        "X_scaled = scaler.fit_transform(X)\n",
        "\n",
        "# Split the data into training and testing sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.3, random_state=42)\n"
      ],
      "metadata": {
        "id": "JJ41koakrplC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Train logistic regression models with and without regularization:"
      ],
      "metadata": {
        "id": "NHe5NQ2Hru77"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Logistic Regression without regularization (C is a large value)\n",
        "model_no_reg = LogisticRegression(penalty='none', max_iter=10000)\n",
        "model_no_reg.fit(X_train, y_train)\n",
        "y_pred_no_reg = model_no_reg.predict(X_test)\n",
        "accuracy_no_reg = accuracy_score(y_test, y_pred_no_reg)\n",
        "\n",
        "# Logistic Regression with L2 regularization (default)\n",
        "model_l2_reg = LogisticRegression(penalty='l2', C=1.0, max_iter=10000)\n",
        "model_l2_reg.fit(X_train, y_train)\n",
        "y_pred_l2_reg = model_l2_reg.predict(X_test)\n",
        "accuracy_l2_reg = accuracy_score(y_test, y_pred_l2_reg)\n",
        "\n",
        "# Logistic Regression with L1 regularization\n",
        "model_l1_reg = LogisticRegression(penalty='l1', solver='liblinear', C=1.0, max_iter=10000)\n",
        "model_l1_reg.fit(X_train, y_train)\n",
        "y_pred_l1_reg = model_l1_reg.predict(X_test)\n",
        "accuracy_l1_reg = accuracy_score(y_test, y_pred_l1_reg)\n"
      ],
      "metadata": {
        "id": "8C83EA28rwRM",
        "outputId": "6433f3a9-c59f-4664-ac17-b556c8954a5b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/linear_model/_logistic.py:1173: FutureWarning: `penalty='none'`has been deprecated in 1.2 and will be removed in 1.4. To keep the past behaviour, set `penalty=None`.\n",
            "  warnings.warn(\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'Accuracy without regularization: {accuracy_no_reg:.2f}')\n",
        "print(f'Accuracy with L2 regularization: {accuracy_l2_reg:.2f}')\n",
        "print(f'Accuracy with L1 regularization: {accuracy_l1_reg:.2f}')"
      ],
      "metadata": {
        "id": "KqBBxw-Qr7G5",
        "outputId": "30235a04-f666-4318-edde-aedb47d8f07b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy without regularization: 0.95\n",
            "Accuracy with L2 regularization: 0.98\n",
            "Accuracy with L1 regularization: 0.98\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **linear Regression**"
      ],
      "metadata": {
        "id": "iVPWtpBMsZo_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
        "from sklearn.datasets import fetch_california_housing # Use fetch_california_housing\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import mean_squared_error\n"
      ],
      "metadata": {
        "id": "C9KA_qFPsgX5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Load dataset\n",
        "data = fetch_california_housing()\n",
        "X = data.data\n",
        "y = data.target\n",
        "\n",
        "# Standardize the data\n",
        "scaler = StandardScaler()\n",
        "X_scaled = scaler.fit_transform(X)\n",
        "\n",
        "# Split the data into training and testing sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.3, random_state=42)"
      ],
      "metadata": {
        "id": "dKRDGqzEtGhZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Linear Regression without regularization\n",
        "model_no_reg = LinearRegression()\n",
        "model_no_reg.fit(X_train, y_train)\n",
        "y_pred_no_reg = model_no_reg.predict(X_test)\n",
        "mse_no_reg = mean_squared_error(y_test, y_pred_no_reg)\n",
        "\n",
        "# Linear Regression with L2 regularization (Ridge)\n",
        "model_ridge = Ridge(alpha=1.0)\n",
        "model_ridge.fit(X_train, y_train)\n",
        "y_pred_ridge = model_ridge.predict(X_test)\n",
        "mse_ridge = mean_squared_error(y_test, y_pred_ridge)\n",
        "\n",
        "# Linear Regression with L1 regularization (Lasso)\n",
        "model_lasso = Lasso(alpha=1.0)\n",
        "model_lasso.fit(X_train, y_train)\n",
        "y_pred_lasso = model_lasso.predict(X_test)\n",
        "mse_lasso = mean_squared_error(y_test, y_pred_lasso)\n"
      ],
      "metadata": {
        "id": "0BXn6rIGthqw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'Mean Squared Error without regularization: {mse_no_reg:.2f}')\n",
        "print(f'Mean Squared Error with L2 regularization (Ridge): {mse_ridge:.2f}')\n",
        "print(f'Mean Squared Error with L1 regularization (Lasso): {mse_lasso:.2f}')\n"
      ],
      "metadata": {
        "id": "UHiL7SHntkHj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#<p style=\"font-family:JetBrains Mono; font-weight:normal; letter-spacing: 1px; color:#207d06; font-size:100%; text-align:left;padding: 0px; border-bottom: 3px solid #207d06;\">**Chapter 5:Neural Networks**</p>"
      ],
      "metadata": {
        "id": "tJyaQwDu9CvQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **References**\n",
        "[1-Machine Learning Exercises In Python, Part 1](https://www.johnwittenauer.net/machine-learning-exercises-in-python-part-1/)\n",
        "\n",
        "\n",
        "[2-Hands-on ML with Scikit-Learn, Keras & TF by Aurelien Geron](https://github.com/Akramz/Hands-on-Machine-Learning-with-Scikit-Learn-Keras-and-TensorFlow/tree/master)"
      ],
      "metadata": {
        "id": "YU6-STi20H_V"
      }
    }
  ]
}