8 Linear Regression

1) Linear Regression with Gradient Descent with Random data

# -*- coding: utf-8 -*-

# Making the imports

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

#plt.rcParams['figure.figsize'] = (6, 4)

pd.options.display.max_rows=10

X=np.arange(1,9,2)

Y=np.arange(1,5)

# Building the model

m = 0

c = 0

L = 0.01  # The learning Rate

epochs = 1000  # The number of iterations to perform gradient descent

n = float(len(X)) # Number of elements in X

# Performing Gradient Descent

for i in range(epochs):

    Y_pred = m*X + c  # The current predicted value of Y

    D_m = (-2/n) * sum(X * (Y - Y_pred))  # Derivative wrt m

    D_c = (-2/n) * sum(Y - Y_pred)  # Derivative wrt c

    m = m - L * D_m  # Update m

    c = c - L * D_c  # Update c

print (m, c)

X_new=float(input('enter value of  X_new :'))

Y_pred_new =(m*X_new + c)

print( 'Y_pred_new :', Y_pred_new)

#Making predictions

Y_pred = m*X + c

plt.scatter(X, Y)

plt.plot([min(X), max(X)], [min(Y_pred), max(Y_pred)], color='red')  # regression line

plt.show()

2) Linear Regression with Gradient Descent 

# Linear Regression with Gradient Descent

# -*- coding: utf-8 -*-

# Making the imports

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

plt.rcParams['figure.figsize'] = (6, 4)

# Preprocessing Input data

data = pd.read_csv("https://raw.githubusercontent.com/hknarra/datasets/master/Salary_Data.csv", sep=',')

X = data.iloc[:, 0]

Y = data.iloc[:, 1]

plt.scatter(X, Y)

plt.show()

data.head()

# Building the model

m = 0

c = 0

L = 0.01  # The learning Rate

epochs = 1000  # The number of iterations to perform gradient descent

n = float(len(X)) # Number of elements in X

# Performing Gradient Descent

for i in range(epochs):

    Y_pred = m*X + c  # The current predicted value of Y

    D_m = (-2/n) * sum(X * (Y - Y_pred))  # Derivative wrt m

    D_c = (-2/n) * sum(Y - Y_pred)  # Derivative wrt c

    m = m - L * D_m  # Update m

    c = c - L * D_c  # Update c

print (m, c)

X_new=float(input('enter value of  X_new :'))

Y_pred_new =(m*X_new + c)

Y_pred_new

#Making predictions

Y_pred = m*X + c

plt.scatter(X, Y)

plt.plot([min(X), max(X)], [min(Y_pred), max(Y_pred)], color='red')  # regression line

plt.show()