Linear Regression

%     plotData.m
%     gradientDescent.m
%     computeCost.m
%% Note: Creating the function here itself but You have to complete the code in the respective files for the assignment.


% x refers to the population size in 10,000s
% y refers to the profit in $10,000s

clear ; close all; clc

%% =======================  Plotting =======================
fprintf('Plotting Data ...\n')
data = load('ex1data1.txt');                   % A text file with Comma seperated values of X and Actual y.
X = data(:, 1); y = data(:, 2);
m = length(y);                                 % number of training examples

% Plot Data

function plotData(x, y)
figure; % open a new figure window
plot(x,y,'rx', 'MarkerSize', 10);            % rx -> red crosses 
xlabel='population';
ylabel='revenue';
end

plotData(X, y);


fprintf('Program paused. Press enter to continue.\n');
pause;

%% =================== Cost and Gradient descent ===================

X = [ones(m, 1), data(:,1)];                % Add a column of ones to x
theta = zeros(2, 1);                        % initialize theta0(intercept) & theta1 (slope) to 0

% Some gradient descent settings
iterations = 1500;
alpha = 0.01;

% Compute Cost
function J = computeCost(X, y, theta)
m = length(y);
J=(1/(2*m))*sum((X*theta - y).^ 2);
end

fprintf('\nTesting the cost function ...\n')
J = computeCost(X, y, theta);
fprintf('With theta = [0 ; 0]\nCost computed = %f\n', J);
fprintf('Expected cost value (approx) 32.07\n');

% further testing of the cost function
J = computeCost(X, y, [-1 ; 2]);
fprintf('\nWith theta = [-1 ; 2]\nCost computed = %f\n', J);
fprintf('Expected cost value (approx) 54.24\n');

fprintf('Program paused. Press enter to continue.\n');
pause;
 
 
fprintf('\nRunning Gradient Descent ...\n')
% Gradient Descent
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
m = length(y);
J_history = zeros(num_iters, 1);
for iter = 1:num_iters
    theta=theta-alpha*(1/m)*(X'*(X*theta-y));
    J_history(iter) = computeCost(X, y, theta);
end

theta = gradientDescent(X, y, theta, alpha, iterations);

fprintf('Theta found by gradient descent:\n');
fprintf('%f\n', theta);
fprintf('Expected theta values (approx)\n');
fprintf(' -3.6303\n  1.1664\n\n');

                           % Plot the linear fit on the same Plot as above
                           
hold on;                                      % keep previous plot visible
plot(X(:,2), X*theta, '-')
legend('Training data', 'Linear regression')
hold off 

%% =================== % Predict values for population sizes of 35,000 and 70,000  ===================

predict1 = [1, 3.5] *theta;
fprintf('For population = 35,000, we predict a profit of %f\n',...
    predict1*10000);
predict2 = [1, 7] * theta;
fprintf('For population = 70,000, we predict a profit of %f\n',...
    predict2*10000);

fprintf('Program paused. Press enter to continue.\n');
pause;

%% ============= Part 4: Visualizing J(theta_0, theta_1) =============================

fprintf('Visualizing J(theta_0, theta_1) ...\n')

% Grid over which we will calculate J
theta0_vals = linspace(-10, 10, 100);
theta1_vals = linspace(-1, 4, 100);

% initialize J_vals to a matrix of 0's
J_vals = zeros(length(theta0_vals), length(theta1_vals));

% Fill out J_vals
for i = 1:length(theta0_vals)
    for j = 1:length(theta1_vals)
	  t = [theta0_vals(i); theta1_vals(j)];
	  J_vals(i,j) = computeCost(X, y, t);
    end
end


% Because of the way meshgrids work in the surf command, we need to
% transpose J_vals before calling surf, or else the axes will be flipped
J_vals = J_vals';
% Surface plot
figure;
surf(theta0_vals, theta1_vals, J_vals)
xlabel('\theta_0'); ylabel('\theta_1');

% Contour plot
figure;
% Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
xlabel('\theta_0'); ylabel('\theta_1');
hold on;
plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);