%% Machine Learining----Linear Regression

 close all

 clear

 %%data load

 Year = linspace(,,);

 Price = [,2.5,2.9,3.147,4.515,4.903,5.365,5.704,6.853,7.791,8.561,,11.28,12.9];

 %%train data

 alpha = 0.01;

 theta = [,];

 obj_old = 1e10;

 tor = 1e-;

 tic;

 for time = :

     delta = zeros(,);

     objective = ;

     hypothesis = theta() + theta() * Year;

     drawnow;

     subplot(,,);

     plot(Year,Price,'rx',Year,hypothesis);

     for i = :

         delta = (theta() + theta() * Year(i) - Price(i)) * [,Year(i)] + delta;

         objective = (theta() + theta() * Year(i) - Price(i)) * (theta() + theta() * Year(i) - Price(i))+ objective;

     end

     theta = theta - alpha * delta / ;

     fprintf('objective is %.4f\n', objective);

     if abs(obj_old - objective) < tor

         fprintf('torlerance is samller than %.4f\n', tor);

         break;

     end

     obj_old = objective;

     subplot(,,);

     plot(toc,obj_old);

     axis([   ]) %xmin是x最小，xmax是x最大，ymin，ymax类似

     hold on;

 end