lathika-sunder / Implementation-of-Linear-Regression-Using-Gradient-Descent

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:

1. Hardware – PCs
2. 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: Lathika Sunder
RegisterNumber:  212221230054
*/

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):
# Add a column of ones to X for the intercept term 
  X = np.c_[np.ones(len(X1)), X1]
# Initialize theta with zeros
  theta = np.zeros(X.shape[1]).reshape(-1,1)
# Perform gradient descent 
  for _ in range(num_iters):

# Calculate predictions 
    predictions = (X).dot (theta).reshape(-1, 1)
# Calculate errors
    errors = (predictions - y).reshape(-1,1)
# Update theta using gradient descent 
    theta -= learning_rate * (1 / len(X1)) * X.T.dot(errors)
  return theta
data = pd.read_csv('50_Startups.csv', header=None)
# Assuming the last column is your target variable 'y' and the preceding columns are your features 'X' 
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)
# Example usage
#X = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
#y = np.array([2, 7, 11, 16])
# Learn model parameters
theta = linear_regression(X1_Scaled, Y1_Scaled)
# Predict target value for a new data point
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.