function A = warmUpExercise() %WARMUPEXERCISE Example function in octave % A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix
% ============= YOUR CODE HERE ============== % Instructions: Return the 5x5 identity matrix % In octave, we return values by defining which variables % represent the return values (at the top of the file) % and then set them accordingly. A = eye(5); % =========================================== end
function plotData(x, y) %PLOTDATA Plots the data points x and y into a new figure % PLOTDATA(x,y) plots the data points and gives the figure axes labels of % population and profit.
% ====================== YOUR CODE HERE ====================== % Instructions: Plot the training data into a figure using the % "figure" and "plot" commands. Set the axes labels using % the "xlabel" and "ylabel" commands. Assume the % population and revenue data have been passed in % as the x and y arguments of this function. % % Hint: You can use the ‘rx’ option with plot to have the markers % appear as red crosses. Furthermore, you can make the % markers larger by using plot(…, ‘rx’, ‘MarkerSize’, 10);
figure; % open a new figure window plot(x,y,’rx’,’MarkerSize’,10); ylabel(‘Profit in $10,000s’); xlabel(‘Population of City in 10,000s’);
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters) %GRADIENTDESCENT Performs gradient descent to learn theta % theta = GRADIENTDESCENT(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 (computeCost) and gradient here. % theta-=alpha/m*((X*theta-y)'*X)'; % ============================================================
% Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta);
function J = computeCost(X, y, theta) %COMPUTECOST Compute cost for linear regression % J = COMPUTECOST(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
% ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta % You should set J to the cost.
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
% ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta % You should set J to the cost.
function [X_norm, mu, sigma] = featureNormalize(X) %FEATURENORMALIZE Normalizes the features in X % FEATURENORMALIZE(X) returns a normalized version of X where % the mean value of each feature is 0 and the standard deviation % is 1. This is often a good preprocessing step to do when % working with learning algorithms.
% You need to set these values correctly X_norm = X; mu = zeros(1, size(X, 2)); sigma = zeros(1, size(X, 2));
% ====================== YOUR CODE HERE ====================== % Instructions: First, for each feature dimension, compute the mean % of the feature and subtract it from the dataset, % storing the mean value in mu. Next, compute the % standard deviation of each feature and divide % each feature by it’s standard deviation, storing % the standard deviation in sigma. % % Note that X is a matrix where each column is a % feature and each row is an example. You need % to perform the normalization separately for % each feature. % % Hint: You might find the ‘mean’ and ‘std’ functions useful. %
function [theta] = normalEqn(X, y) %NORMALEQN Computes the closed-form solution to linear regression % NORMALEQN(X,y) computes the closed-form solution to linear % regression using the normal equations.
theta = zeros(size(X, 2), 1);
% ====================== YOUR CODE HERE ====================== % Instructions: Complete the code to compute the closed form solution % to linear regression and put the result in theta. %