# Coursera: Machine Learning-- Andrew NG (Week 2) [Assignment Solution]

These solutions are for reference only.try to solve on your ownbut if you get stuck in between than you can refer these solutions

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## warmUpExercise.m

function A = warmUpExercise() % function [y1,...,yN] = myfun(x1,...,xN) % above function 'myfun' takes argument (x1,...,xN) and returns y1,...,yN % Return the 5x5 identity matrix in octave A = eye(5); end

## plotdata.m

function plotData(x, y) %PLOTDATA Plots the data points x and y into a new figure plot(x, y, 'rx', 'MarkerSize', 10); % Plot the data % 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); ylabel('Profit in $10,000s'); % Set the y ? axis label xlabel('Population of City in 10,000s'); % Set the x ? axis label figure; % open a new figure window end

## computeCost.m

function J = computeCost(X, y, theta) % J = COMPUTECOST(X, y, theta) computes the cost for linear regression % using theta as the parameter for linear regression to fit the data % points in X and y m = length(y); i = 1:m; J = (1/(2*m)) * sum( ((theta(1) + theta(2) .* X(i,2)) - y(i)) .^ 2); % Un-Vectorized end

## gradientDescent.m

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters) % theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by % taking num_iters gradient steps with learning rate alpha m = length(y); J_history = zeros(num_iters, 1); for iter = 1:num_iters k = 1:m; t1 = sum((theta(1) + theta(2) .* X(k,2)) - y(k)); % Un-Vectorized t2 = sum(((theta(1) + theta(2) .* X(k,2)) - y(k)) .* X(k,2)); % Un-Vectorized theta(1) = theta(1) - (alpha/m) * (t1); theta(2) = theta(2) - (alpha/m) * (t2); % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta); end end

## computeCostMulti.m

function J = computeCostMulti(X, y, theta) % 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 m = length(y); % number of training examples J = (1/(2*m)) * (X * theta - y)' * (X * theta - y); % Vectorized end

## gradientDescentMulti.m

**function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
% theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
% taking num_iters gradient steps with learning rate alpha
m = length(y);
J_history = zeros(num_iters, 1);
for iter = 1:num_iters
theta = theta - alpha * (1/m) * (((X*theta) - y)' * X)'; % Vectorized
J_history(iter) = computeCostMulti(X, y, theta);
end
end**

## featureNormalize.m

function [X_norm, mu, sigma] = featureNormalize(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. mu = mean(X); sigma = std(X); t = ones(length(X), 1); X_norm = (X - (t * mu)) ./ (t * sigma); % Vectorized end

## normalEqn.m

**function [theta] = normalEqn(X, y)
% NORMALEQN(X,y) computes the closed-form solution to linear
% regression using the normal equations.
theta = pinv(X' * X) * (X' * y); % Vectorized
end**