Implementation-of-Linear-Regression-Using-Gradient-Descent

AIM:

To write a program to predict the profit of a city using the linear regression model with gradient descent.

Equipments Required:

Hardware – PCs
Anaconda – Python 3.7 Installation / Jupyter notebook

Algorithm

Import the necessary libraries and Dataset
set learning rate and number of iterations and define Linear Regression function with gradient descent
Normalize the Dataset values using Standard Scaler
use the defined linear regression function to predict the Profit value for given R&D Spend, Administration and Marketing Spend.

Program:

/*
Program to implement the linear regression using gradient descent.
Developed by: Bhargava S
RegisterNumber:  212221040029
*/
import numpy as np
import pandas as pd
from sklearn.preprocessing import StandardScaler
def linear_regression(X1,y,learning_rate=0.1,num_iters=1000):
    X = np.c_[np.ones(len(X1)),X1]
    theta = np.zeros(X.shape[1]).reshape(-1,1)
    for _ in range(num_iters):
        prediction = (X).dot(theta).reshape(-1,1)
        
        errors = (prediction - y).reshape(-1,1)
        
        theta -= learning_rate * (1/len(X1)) * X.T.dot(errors)
        
    return theta
data = pd.read_csv('50_Startups.csv',header=None)
X = (data.iloc[1:,:-2].values)
X1 = X.astype(float)
scaler = StandardScaler()
y =  (data.iloc[1:,-1].values).reshape(-1,1)
X1_Scaled = scaler.fit_transform(X1)
Y1_Scaled = scaler.fit_transform(y)


theta = linear_regression(X1_Scaled,Y1_Scaled)

new_data = np.array([165349.2,136897.8,471784.1]).reshape(-1,1)
new_Scaled = scaler.fit_transform(new_data)
prediction = np.dot(np.append(1,new_Scaled),theta)
prediction = prediction.reshape(-1,1)
pre = scaler.inverse_transform(prediction)
print(f"Predicted value: {pre}")

Output:

Result:

Thus the program to implement the linear regression using gradient descent is written and verified using python programming.

Bhargava-Shankar / Implementation-of-Linear-Regression-Using-Gradient-Descent