Linear Algebra assignment

%in this exercise, you will investigate linear regression using gradient descent % and the normal equations %This is a training set of housing prices in Portland, Oregon, where %y are the prices and the inputs $x are the living area and the number of bedrooms. %we will use only living area in this assigment % initialize samples of x and y training dataset % x2 = load('ex3x.dat'); y = load('ex3y.dat'); %house cost x=x2(:,1); %only living area m = length(y); % store the number of training examples x = [ones(m, 1), x]; % Add a column of ones to x %the area values from your training data are actually in the second column of x #Gradient descent xorg=x(:,2); #normilze the data sigma = std(x); mu = mean(x); x(:,2) = (x(:,2) - mu(2))./ sigma(2); mse = zeros(100, 100); % initialize mse to 100x100 matrix of 0's w0 = linspace(100000,500000,100); w1 = linspace(1000,300000,100); for i = 1:length(w0) for j = 1:length(w1) t = [w0(i); w1(j)]; mse(i,j) =1/m* (y-x*t)'*(y-x*t); end end % Plot the surface plot % Because of the way meshgrids work in the surf command, we need to % transpose mse before calling surf, or else the axes will be flipped mse = mse'; figure; surf(w0, w1, mse); xlabel('\w0'); ylabel('\w1'); w = zeros(2, 1); iterations = 100 alpha = 0.07 cost=zeros(iterations,1); for iter = 1:iterations %insert your code here % cost(iter)=... % this is the code to calculate weights % w=w - your code * alpha; %end of your code wdraw0(iter)=w(1); wdraw1(iter)=w(2); end disp("w0g w1g"),disp(w); % now plot Cost % technically, the first cost at the zero-eth iteration % but Matlab/Octave doesn't have a zero index figure; plot(0:iterations-1, cost(1:iterations), '-') xlabel('Number of iterations') ylabel('Cost - mean square error ') #normilize 1650sf %caling 1650sf your code here: %newxs= your code newxs= disp("house prediction for 1650s, gradient descent:"),disp([1,newxs]*w); #plot data and regression line figure % open a new figure window # plot your training set (and label the axes): plot(xorg,y,'o'); ylabel('house cost') xlabel('house sf') hold yp=x*w; plot(xorg,yp,'-');