sleep_grades_regression.py

#
#
# Regression and Classification programming exercises
#
#


#
#    In this exercise we will be taking a small data set and computing a linear function
#    that fits it, by hand.
#    

#    the data set

import numpy as np

sleep = [5,6,7,8,10]
scores = [65,51,75,75,86]


def compute_regression(sleep,scores):

    #    First, compute the average amount of each list

    avg_sleep = np.mean(sleep)
    avg_scores = np.mean(scores)
    print "avg_sleep ", avg_sleep
    print "avg_scores ", avg_scores

    #    Then normalize the lists by subtracting the mean value from each entry

    normalized_sleep = np.subtract(sleep, avg_sleep)
    normalized_scores = np.subtract(scores, avg_scores)
    print "normalized_sleep ", normalized_sleep
    print "normalized_scores ", normalized_scores

    #    Compute the slope of the line by taking the sum over each student
    #    of the product of their normalized sleep times their normalized test score.
    #    Then divide this by the sum of squares of the normalized sleep times.

    sleep_times_score = np.multiply(normalized_sleep, normalized_scores)
    print "sleep_times_score ", sleep_times_score
    sleep_squares = np.square(normalized_sleep)
    print"sleep_squares ", sleep_squares
    
    sum_sleep_times_score = np.sum(sleep_times_score)
    sum_sleep_squares = np.sum(sleep_squares)
    slope = sum_sleep_times_score/sum_sleep_squares
    print "slope ", slope

    #    Finally, We have a linear function of the form
    #    y - avg_y = slope * ( x - avg_x )
    #    Rewrite this function in the form
    #    y = m * x + b
    #    Then return the values m, b

    m = slope
    b = avg_scores - (slope * avg_sleep)
    print "b ", b

    return m,b


if __name__=="__main__":
    m,b = compute_regression(sleep,scores)
    print "Your linear model is y={}*x+{}".format(m,b)

    for i in np.arange(2, 6):
        coeffs = np.polyfit(scores, sleep, i)
        print "coeffs for degree {} : {}".format(i, coeffs)