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: pooja.s
RegisterNumber: 212223040146 
*/
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)
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)
#X = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
#y = np.array([2, 7, 11, 16])
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}")