My solutions to the exercises:

**Part 1 : Warm up exercise**function A = warmUpExercise() %WARMUPEXERCISE Example function in octave % A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix A = []; % ============= 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

**Part 2 : Compute cost for one variable**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 J = 0; % ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta % You should set J to the cost. predictions = X*theta; squaredError = (predictions-y) .^ 2; J = (1/(2*m))*(sum(squaredError)); % ========================================================================= end

**Part 3: Gradient descent for one variable**function [theta, J_history] = gradientDescent(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 (computeCost) and gradient here. % predictions = X*theta; errors = predictions-y; mulAndSum = errors' * (X); right = (alpha*mulAndSum)/m; theta = theta-(right'); % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta); end end

**Part 4 : Feature normalization**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. % for i = 1:size(X)(2) mu(1, i) = mean(X(:,[i:i]));end for i = 1:size(X)(2) sigma(1, i) = std(X(:, [i:i]));end for i = 1:size(X)(1) for j = 1:size(X)(2) X_norm(i, j) = ((X(i, j)-mu(1, j))/sigma(1, j)); end end % ============================================================ end

**Part 5: Compute Cost for Multiple Variables**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. predictions = X*theta; squaredError = (predictions-y) .^ 2; J = (1/(2*m))*(sum(squaredError)); % ========================================================================= end

**Part 6: Gradient Descent for Multiple Variables**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 (computeCost) and gradient here. % predictions = X*theta; errors = predictions-y; mulAndSum = errors' * (X); right = (alpha*mulAndSum)/m; theta = theta-(right'); % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCostMulti(X, y, theta); end end

**Part 7: Normal Equations**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. % % ---------------------- Sample Solution ---------------------- theta = (pinv(X'*X)*X'*y); % ------------------------------------------------------------- % ============================================================ end

it says not enough input arguements.. what do i do?

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