LINEAR REGRESSION

What is linear regression?

Linear regression is a common method to model the relationship between a dependent variable and one or more independent variables. Linear models are developed using the parameters which are estimated from the data.

SOURCE CODE:  

import numpy as np

import matplotlib.pyplot as plt

def estimate_coef(x, y):

# number of observations/points

n = np.size(x)

# mean of x and y vector

m_x = np.mean(x)

m_y = np.mean(y)

# calculating cross-deviation and deviation about x

SS_xy = np.sum(y*x) - n*m_y*m_x

SS_xx = np.sum(x*x) - n*m_x*m_x

# calculating regression coefficients

b_1 = SS_xy / SS_xx

b_0 = m_y - b_1*m_x

return (b_0, b_1)

def plot_regression_line(x, y, b):

# plotting the actual points as scatter plot

plt.scatter(x, y, color = "m",

marker = "o", s = 30)

# predicted response vector

y_pred = b[0] + b[1]*x

# plotting the regression line

plt.plot(x, y_pred, color = "g")

# putting labels

plt.xlabel('x')

plt.ylabel('y')

# function to show plot

plt.show()

def main():

# observations / data

x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

y = np.array([1, 3, 2, 5, 7, 8, 8, 9, 10, 12])

# estimating coefficients

b = estimate_coef(x, y)

print("Estimated coefficients:\nb_0 = {} \

\nb_1 = {}".format(b[0], b[1]))

# plotting regression line

plot_regression_line(x, y, b)

if __name__ == "__main__":

main()

OUTPUT:

Estimated coefficients:
b_0 = -0.0586206896552
b_1 = 1.45747126437

And graph obtained looks like this: