Analytics/Jun_03/linregression.py

#!/usr/bin/env python3
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
plt.style.use('seaborn-darkgrid')

# create a dataframe
df = pd.read_csv("Salary_Data.csv")

# read x and y values
x = df.iloc[:,0]
y = df.iloc[:,1]

# number of rows
n = df.size//2

# summation of x and y 
sum_x = df.iloc[:,0].sum()
sum_y = df.iloc[:,1].sum()

# summation of x.y
sum_xy = (df.iloc[:,0] * df.iloc[:,1]).sum()

# compute theta_1 and theta_2 values
theta2 = (sum_xy - n*np.mean(x)*np.mean(y))/(sum(x**2) - n*np.mean(x)**2)
theta1 = (n*np.mean(x)*np.mean(y) - theta2*n*np.mean(x)**2)/(n*np.mean(x))

print("__________Linear Regression__________")

print("\ntheta1 = {}".format(theta1))
print("theta2 = {}".format(theta2))

E = [(y - theta1 - theta2*x)**2 for x,y in zip(x,y)]

print("\nSummation of epsilon-square: {}".format(sum(E)))

cal_y = [theta2*x + theta1 for x in x]

y = np.array(y)

print("\nObeserved y-values: {}".format(y))
print("Calculated y-values: {}".format(cal_y))

epsilon = [(y - cal_y) for y,cal_y in zip(y,cal_y)]
print("\nError term: {}".format(epsilon))

ax=plt.figure().add_subplot(111)
ax.plot(x, y, 'r--o', label='Observed Value')
ax.plot(x, cal_y, 'b--o', label='Calculated Value')
ax.set(xlabel='x', ylabel='y', title='Linear Regression')
plt.legend(); plt.savefig('linreg.png'); plt.show()