Linear Least-Squares Regression

Here is an M-file to implement linear regression. 

Linear Regression M-file

function [a,r2,syx] = linregr(x,y)

% linregr: linear regression curve fitting

%   [a, r2] = linregr(x,y): Least squares fit of straight line to data by solving the normal equations

% input:

%   x = independent variable

%   y = dependent variable

% output:

%   a = vector of slope, a(1), and intercept, a(2)

%   r2 = coefficient of determination

%   syx = standard error of estimate

n = length(x); % show number of data

if length(y)~=n, error('x and y must be same length'); end

% error checking to have complete number of data points

x = x(:); y = y(:); % convert to column vectors

sx = sum(x); sy = sum(y);

sx2 = sum(x.*x); sxy = sum(x.*y); sy2 = sum(y.*y);

a(1) = (n*sxy-sx*sy)/(n*sx2-sx^2); % a(1) = slope

a(2) = sy/n-a(1)*sx/n; % a(2) = intercept

r2 = ((n*sxy-sx*sy)/sqrt(n*sx2-sx^2)/sqrt(n*sy2-sy^2))^2;

Sr = sum((y-a(2)-a(1)*x).^2);

St = sum((y-mean(y)).^2);

syx = sqrt(Sr/(n-2)); 

% create plot of data and best fit line

xp = linspace(min(x),max(x),2);

yp = a(1)*xp+a(2);

% best fit line equation

plot(x,y,'o',xp,yp),xlabel('x'),ylabel('y')

% to generate plot of x vs y with circle marker and plot for best fit line

grid on