more quickly. Part 5: Gradient Descent + Computing J for Linear regression with

Question

more quickly. Part 5: Gradient Descent + Computing J for Linear regression with multiple variables Previously, you implemented gradient descent on a univariate regression problem. The only difference now is that there is one more feature in the matrix X. The hypothesis function and the batch gradient descent update rule remain unchanged. You should complete the code in computeCostMulti.m and gradientDescentMulti.m to implement the cost function and gradient descent for linear regression with multiple variables. If your code in the previous part (single variable) already supports multiple variables, you can use it here too. Make sure your code supports any number of features and is well-vectorized. You can use size(X, 2)' to find out how many features are present in the dataset.

Explanation / Answer

computecostmulti.m

function J = computeCostMulti(X, y, theta)
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
% J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
% parameter for linear regression to fit the data points in X and y

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
% You should set J to the cost.

y_pred = X*theta;
sqr_Error = (y_pred-y).^2;
J = 1/(2*m)*sum(sqr_Error);

% =========================================================================

end

gradientdescentmulti.m

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
% theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
% taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);

for iter = 1:num_iters

% ====================== YOUR CODE HERE ======================
% Instructions: Perform a single gradient step on the parameter vector
% theta.
%
% Hint: While debugging, it can be useful to print out the values
% of the cost function (computeCostMulti) and gradient here.
%

delta = 1/m * X' * ((X * theta) - y);
theta = theta - alpha * delta;

% ============================================================

% Save the cost J in every iteration   
J_history(iter) = computeCostMulti(X, y, theta);

end

end

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