/*
Program to implement the linear regression using gradient descent.
Developed by: Gunaseelan G
RegisterNumber: 212221230031
*/
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 Gradienrt 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 of city (10,000s)")
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)))