/*
Program to implement the linear regression using gradient descent.
Developed by: MANO M
RegisterNumber: 212221040100
*/
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 (10,1000s)")
plt.ylabel("Profit ($10,000)")
plt.title("Profit Prediction")
def computeCost(X,y,theta):
  m=len(y) #length of the training data
  h=X.dot(theta) #hypothesis
  square_err=(h-y)**2
  return 1/(2*m) * np.sum(square_err) #returning ] 
  data_n=data.values
m=data_n[:,0].size
X=np.append(np.ones((m,1)),data_n[:,0].reshape(m,1),axis=1)
y=data_n[:,1].reshape(m,1)
theta=np.zeros((2,1))
computeCost(X,y,theta) #Call the function
def gradientDescent(X,y,theta,alpha,num_iters):
  m=len(y)
  J_history=[]
  for i in range(num_iters):
    predictions=X.dot(theta)
    error=np.dot(X.transpose(),(predictions -y))
    descent=alpha * 1/m * error
    theta-=descent
    J_history.append(computeCost(X,y,theta))
  return theta,J_history  
theta,J_history = gradientDescent(X,y,theta,0.01,1500)
print("h(x) ="+str(round(theta[0,0],2))+" + "+str(round(theta[1,0],2))+"x1")
plt.plot(J_history)
plt.xlabel("Iteration")
plt.ylabel("$J(\Theta)$")
plt.title("Cost function using Gradient Descent")
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)))