% Linear regression example

% Brian D. Jeffs, Nov. 16, 2005

% Assumed input: XY: an N by 2 matrix
% first column is independent variable, X, sample, 
% second column is depedent variable, Y, sample

echo on
plot(XY(:,1),XY(:,2),'+');
xlabel('X')
ylabel('Y')
title('Scatter plot of X, Y data');
pause

mu_x = mean(XY(:,1));
mu_y = mean(XY(:,2));
var_x = var(XY(:,1));
C = cov(XY);
Cov_xy = C(1,2);

alpha = Cov_xy ./ var_x
beta = mu_y - Cov_xy / var_x * mu_x

X = sort(XY(:,1));
Y_p = alpha * X + beta;
plot(XY(:,1),XY(:,2),'+',X,Y_p, '-o');
xlabel('X')
ylabel('Y')
title('Scatter plot of X, Y data with regression fit');


echo off