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add ML ex1 and ex2
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‎ML/ex1/computeCost.m

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function J = computeCost(X, y, theta)
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%COMPUTECOST Compute cost for linear regression
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% J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
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% parameter for linear regression to fit the data points in X and y
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% Initialize some useful values
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m = length(y); % number of training examples
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% You need to return the following variables correctly
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J = 0;
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the cost of a particular choice of theta
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% You should set J to the cost.
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for i = 1:m
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costi = X(i, :) * theta - y(i, :);
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J = J + costi * costi;
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endfor
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J = J / (2 * m);
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% =========================================================================
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end

‎ML/ex1/computeCostMulti.m

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function J = computeCostMulti(X, y, theta)
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%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
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% J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
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% parameter for linear regression to fit the data points in X and y
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% Initialize some useful values
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m = length(y); % number of training examples
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% You need to return the following variables correctly
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J = 0;
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the cost of a particular choice of theta
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% You should set J to the cost.
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% =========================================================================
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end

‎ML/ex1/ex1.m

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%% Machine Learning Online Class - Exercise 1: Linear Regression
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the
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% linear exercise. You will need to complete the following functions
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% in this exericse:
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%
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% warmUpExercise.m
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% plotData.m
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% gradientDescent.m
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% computeCost.m
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% gradientDescentMulti.m
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% computeCostMulti.m
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% featureNormalize.m
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% normalEqn.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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% x refers to the population size in 10,000s
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% y refers to the profit in $10,000s
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%
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%% Initialization
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clear ; close all; clc
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%% ==================== Part 1: Basic Function ====================
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% Complete warmUpExercise.m
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fprintf('Running warmUpExercise ... \n');
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fprintf('5x5 Identity Matrix: \n');
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warmUpExercise()
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% ======================= Part 2: Plotting =======================
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fprintf('Plotting Data ...\n')
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data = load('ex1data1.txt');
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X = data(:, 1); y = data(:, 2);
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m = length(y); % number of training examples
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% Plot Data
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% Note: You have to complete the code in plotData.m
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plotData(X, y);
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =================== Part 3: Gradient descent ===================
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fprintf('Running Gradient Descent ...\n')
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X = [ones(m, 1), data(:,1)]; % Add a column of ones to x
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theta = zeros(2, 1); % initialize fitting parameters
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% Some gradient descent settings
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iterations = 1500;
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alpha = 0.01;
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% compute and display initial cost
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computeCost(X, y, theta)
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% run gradient descent
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theta = gradientDescent(X, y, theta, alpha, iterations);
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% print theta to screen
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fprintf('Theta found by gradient descent: ');
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fprintf('%f %f \n', theta(1), theta(2));
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% Plot the linear fit
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hold on; % keep previous plot visible
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plot(X(:,2), X*theta, '-')
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legend('Training data', 'Linear regression')
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hold off % don't overlay any more plots on this figure
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% Predict values for population sizes of 35,000 and 70,000
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predict1 = [1, 3.5] *theta;
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fprintf('For population = 35,000, we predict a profit of %f\n',...
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predict1*10000);
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predict2 = [1, 7] * theta;
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fprintf('For population = 70,000, we predict a profit of %f\n',...
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predict2*10000);
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% ============= Part 4: Visualizing J(theta_0, theta_1) =============
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fprintf('Visualizing J(theta_0, theta_1) ...\n')
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% Grid over which we will calculate J
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theta0_vals = linspace(-10, 10, 100);
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theta1_vals = linspace(-1, 4, 100);
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% initialize J_vals to a matrix of 0's
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J_vals = zeros(length(theta0_vals), length(theta1_vals));
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% Fill out J_vals
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for i = 1:length(theta0_vals)
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for j = 1:length(theta1_vals)
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t = [theta0_vals(i); theta1_vals(j)];
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J_vals(i,j) = computeCost(X, y, t);
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end
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end
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% Because of the way meshgrids work in the surf command, we need to
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% transpose J_vals before calling surf, or else the axes will be flipped
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J_vals = J_vals';
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% Surface plot
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figure;
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surf(theta0_vals, theta1_vals, J_vals)
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xlabel('\theta_0'); ylabel('\theta_1');
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% Contour plot
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figure;
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% Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
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contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
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xlabel('\theta_0'); ylabel('\theta_1');
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hold on;
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plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);

‎ML/ex1/ex1_multi.m

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%% Machine Learning Online Class
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% Exercise 1: Linear regression with multiple variables
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the
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% linear regression exercise.
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%
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% You will need to complete the following functions in this
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% exericse:
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%
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% warmUpExercise.m
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% plotData.m
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% gradientDescent.m
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% computeCost.m
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% gradientDescentMulti.m
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% computeCostMulti.m
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% featureNormalize.m
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% normalEqn.m
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%
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% For this part of the exercise, you will need to change some
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% parts of the code below for various experiments (e.g., changing
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% learning rates).
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%
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%% Initialization
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%% ================ Part 1: Feature Normalization ================
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%% Clear and Close Figures
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clear ; close all; clc
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fprintf('Loading data ...\n');
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%% Load Data
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data = load('ex1data2.txt');
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X = data(:, 1:2);
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y = data(:, 3);
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m = length(y);
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% Print out some data points
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fprintf('First 10 examples from the dataset: \n');
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fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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% Scale features and set them to zero mean
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fprintf('Normalizing Features ...\n');
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[X mu sigma] = featureNormalize(X);
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% Add intercept term to X
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X = [ones(m, 1) X];
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%% ================ Part 2: Gradient Descent ================
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% ====================== YOUR CODE HERE ======================
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% Instructions: We have provided you with the following starter
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% code that runs gradient descent with a particular
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% learning rate (alpha).
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%
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% Your task is to first make sure that your functions -
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% computeCost and gradientDescent already work with
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% this starter code and support multiple variables.
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%
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% After that, try running gradient descent with
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% different values of alpha and see which one gives
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% you the best result.
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%
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% Finally, you should complete the code at the end
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% to predict the price of a 1650 sq-ft, 3 br house.
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%
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% Hint: By using the 'hold on' command, you can plot multiple
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% graphs on the same figure.
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%
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% Hint: At prediction, make sure you do the same feature normalization.
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%
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fprintf('Running gradient descent ...\n');
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% Choose some alpha value
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alpha = 0.01;
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num_iters = 400;
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% Init Theta and Run Gradient Descent
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theta = zeros(3, 1);
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[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);
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% Plot the convergence graph
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figure;
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plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
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xlabel('Number of iterations');
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ylabel('Cost J');
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% Display gradient descent's result
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fprintf('Theta computed from gradient descent: \n');
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fprintf(' %f \n', theta);
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fprintf('\n');
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% Estimate the price of a 1650 sq-ft, 3 br house
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% ====================== YOUR CODE HERE ======================
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% Recall that the first column of X is all-ones. Thus, it does
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% not need to be normalized.
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price = 0; % You should change this
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% ============================================================
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fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
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'(using gradient descent):\n $%f\n'], price);
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% ================ Part 3: Normal Equations ================
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fprintf('Solving with normal equations...\n');
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% ====================== YOUR CODE HERE ======================
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% Instructions: The following code computes the closed form
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% solution for linear regression using the normal
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% equations. You should complete the code in
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% normalEqn.m
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%
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% After doing so, you should complete this code
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% to predict the price of a 1650 sq-ft, 3 br house.
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%
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%% Load Data
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data = csvread('ex1data2.txt');
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X = data(:, 1:2);
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y = data(:, 3);
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m = length(y);
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% Add intercept term to X
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X = [ones(m, 1) X];
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% Calculate the parameters from the normal equation
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theta = normalEqn(X, y);
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% Display normal equation's result
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fprintf('Theta computed from the normal equations: \n');
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fprintf(' %f \n', theta);
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fprintf('\n');
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% Estimate the price of a 1650 sq-ft, 3 br house
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% ====================== YOUR CODE HERE ======================
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price = 0; % You should change this
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% ============================================================
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fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
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'(using normal equations):\n $%f\n'], price);
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