syms k;
x1 = linspace(100,200,101); %area of the house
w = 7000; %cost/meter square
y1 = 3 * x1.^2 + 3000; %price of the house

%Scaling and normalizing of the data set
x = sd(x1);
y = sd(y1);

t0 = 0; %initialize theta as zero
t1 = 0; %initialize theta as zero
a = 0.001; %setting learning rate(alpha)
m = 5;
i = 0; %number of iteration(to measure performance of the algorithm)
%While loop to get the required theta to minimize cost function
while true
   i = i + 1;
   j(i) = cost_function(t0, t1, x, y);
   term_0 = (a/m) * (t0 + t1*summation(x) - summation(y));
   term_1 = (a/m) * (t0 * summation(x) + t1 * summation(x .^2) - summation(x .* y));
   temp0 = t0 - term_0;
   temp1 = t1 - term_1;
   if temp0 == t0 && temp1 == t1
       break;
   end
   t0 = temp0;
   t1 = temp1;
end
%calculating the prediction function and plotting the results
h = t0 + t1*x;
num_iterations = linspace(1, i, i);


subplot(1,2,1)
plot(x, y,'.');
hold on;
plot(x, h, 'r');
hold off;
subplot(1,2,2),plot(num_iterations, j);
xlabel('Number of Iterations');
ylabel('Cost Function (J)');