function run_mnk()
% Shows how to use minimal least squares method to fit data.
% It loads the file 'mnk.csv'.
%
% http://strijov.com

% Data generation
% x = linspace(0,10,200)'; % independent set is generated
% y = x + 1.5*sin(x) + randn(size(x,1),1); % dependent set is generated
% dlmwrite('mnk.csv', [x,y]);


% Load the file 
D = dlmread('data\mnk.csv');
% Store the data
x = D( :, 1:end-1 ); % All columns but the last are independent variables
y = D( :,end ); % The last column is independent variable.

% The first trial
% The regression is y = a x^2 + b x + c
A = [x.^2, x, ones(size(x))]; % quadratic function
w = inv(A'*A)*(A'*y); % the normal equation 
ym = w(1) .* x.^2 + w(2).* x + w(3); % the recovered regression

% The second trial
% The regression is y = a x + b sin(x) + c
A = [x, sin(x), ones(size(x))]; % quadratic function
w = inv(A'*A)*(A'*y); % the normal equation 
yr = w(1) .* x + w(2).* sin(x) + w(3); % the recovered regression

% Plot the results
plot(x,y,'b.'); hold on
plot(x,ym,'m-','LineWidth',2); 
plot(x,yr,'r-','LineWidth',2); hold off
title('Linear regression');
legend('sample data','y_{magenta}=w_1x^2+w_2+w_3','y_{red}=w_1x+w_2sin(x)+w_3',2);
xlabel('x');
ylabel('y');
return