implementation-of-linear-regression-using-gradient-descent's Introduction

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

1.Import the required library and read the dataframe.

2.Write a function computeCost to generate the cost function.

3.Perform iterations og gradient steps with learning rate.

4.Plot the Cost function using Gradient Descent and generate the required graph.

Program:

/*
Program to implement the linear regression using gradient descent.
Developed by: SUBASH E
RegisterNumber: 212223040209
import numpy as np
import pandas as pd
from sklearn.preprocessing import StandardScaler

def linear_regression(X1,y,learning_rate=0.01,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):
        predictions = (X).dot(theta).reshape(-1,1)
        errors = (predictions-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)
data.head()
X = (data.iloc[1:,:-2].values)
print(X)

X1=X.astype(float)
scaler = StandardScaler()
y=(data.iloc[1:,-1].values).reshape(-1,1)
print(y)

X1_Scaled=scaler.fit_transform(X1)
Y1_Scaled=scaler.fit_transform(y)
print(X1_Scaled)
print(Y1_Scaled)

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}")
*/