Simple Linear Regression

Simple Linear Regression

Implement simple linear regression using gradient descent in python. Read training dataset from

file, build linear regression model and predict the output for few unseen data samples.

Use minimum three datasets for experimentation. Salary_Data.csv is provided as an example.

In [7]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

In [8]:

plt.rcParams['figure.figsize'] = (6.0, 4.0)

In [9]:

data = pd.read_csv('Salary_Data.csv')

In [10]:

X = data.iloc[:, 0]
Y = data.iloc[:, 1]
plt.scatter(X, Y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Training Data')
plt.show()

In [25]:

theta1 = 9449.967223163576
theta0 = 25792.16716735611
alpha = 0.01 # The learning Rate
m = float(len(X)) # Number of elements in X
epsilon = 0.000001
CostOld=9999
diff = 1
iterations = 1

In [26]:

while abs(diff) > epsilon:
    Y_pred = theta1*X + theta0 # The current predicted value of Y
    Cost = (1/m) * sum((Y_pred-Y)**2)
    # C.append(Cost)
    D_theta1 = (1/m) * sum(X * (Y_pred - Y)) # Derivative wrt theta1
    D_theta0 = (1/m) * sum(Y_pred - Y) # Derivative wrt theta0
    theta1 = theta1 - alpha * D_theta1 # Update theta1
    theta0 = theta0 - alpha * D_theta0 # Update theta0
    #print (Cost)
    diff = CostOld - Cost
    CostOld = Cost
    iterations = iterations + 1
print ("Iterations = ", str(iterations))
print ("theta0 = ", theta0, "theta1 = ", theta1)
#plt.plot(C)
plt.scatter(X, Y)
plt.plot(X, Y_pred, color = 'red')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Fitting the Linear Hypothesis')
plt.show()

Iterations =  4
theta0 =  25792.167376520094 theta1 =  9449.967192124517

In [28]:

test_X = 1.2
Y_pred = theta1*test_X + theta0
print("Salary Prediction for Experience of ", str(test_X), " years =", round(Y_pred,2))

Salary Prediction for Experience of  1.2  years = 37132.13

In [ ]: