Rishabendran/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. Use the standard libraries in python for Gradient Descent.
2. Upload the dataset and check any null value using .isnull() function.
3. Declare the default values for linear regression
4. Calculate the loss usinng Mean Square Error
5. Predict the value of y.
6. Plot the graph respect to hours and scores using scatter plot function.

Program:

/*
Program to implement the linear regression using gradient descent.
Developed by: Rishabendran R
RegisterNumber: 212219040121
*/
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

data = pd.read_csv("/content/ex1.txt",header=None)

plt.scatter(data[0],data[1])
plt.xticks(np.arange(5,30,step=5))
plt.yticks(np.arange(-5,30,step=5))
plt.xlabel("Population of City(10,000s")
plt.ylabel("Profit ($10,000)")
plt.title("Profit Prediction")

def computeCost(X,y,theta):
  m = len(y)
  h = X.dot(theta)
  square_err = (h-y)**2
  return 1/(2*m) * np.sum(square_err)

data_n = data.values
m = data_n[:,0].size
X = np.append(np.ones((m,1)),data_n[:,0].reshape(m,1),axis=1)
y = data_n[:,1].reshape(m,1)
theta = np.zeros((2,1))
computeCost(X,y,theta)

def gradientDescent(X,y,theta,alpha,num_iters):
  m = len(y)
  J_history = []

  for i in range(num_iters):
    predictions = X.dot(theta)
    error = np.dot(X.transpose(),(predictions-y))
    descent = alpha * 1/m * error
    theta -= descent
    J_history.append(computeCost(X,y,theta))

  return theta,J_history

theta,J_history = gradientDescent(X,y,theta,0.01,1500)
print("h(x) ="+str(round(theta[0,0],2))+" + "+str(round(theta[1,0],2))+"x1")

plt.plot(J_history)
plt.xlabel("Iteration")
plt.ylabel("$J(\Theta)$")
plt.title("Cost function using Gradient Descent")

plt.scatter(data[0],data[1])
x_value = [x for x in range(25)]
y_value = [y*theta[1]+theta[0] for y in x_value] 
plt.plot(x_value,y_value,color="r")
plt.xticks(np.arange(5,30,step=5))
plt.yticks(np.arange(-5,30,step=5))
plt.xlabel("Population nof City (10,000)")
plt.ylabel("Profit($10,000)")
plt.title("Profit Prediction")

def predict(X,theta):
  predictions = np.dot(theta.transpose(),X)
  return predictions[0]

predict1 = predict(np.array([1,3.5]),theta)*10000
print("For population = 35,000, we predict a profit of $"+str(round(predict1,0)))

predict2 = predict(np.array([1,7]),theta)*10000
print("For population = 70,000, we predict a profit of $"+str(round(predict2,0)))

Output:

Result:

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