function [y, err, w] = mark_lin(w, x)
% mark time series x, the linear function
%
% [idx, w, err] = mark_lin(w, x)
%
% w [1,W] parameters of the model here y = w(1) + w(2)*x;
% x [m,1] time series, the depended variable of the regression fit 
%
% y [m,1] the calculated depended variable
% err [scalar] the residual variance, MSE
% w [1,W] parameters of the function
%
% if the regression parameters are required, the Least Squares Method will
% be called, and the parameters will be returned together with new MSE.

% Example
% x = [1; 2; 3; 4; 5]
% w = [0.1 1.1]
% [y, err] = mark_lin(w, x)
% [y, err, w] = mark_lin(w, x)

m = length(x);
if nargout > 2
    w = lscov( [ones(size(x)), [1:m]'], x );
end    
y = w(1) + w(2) * (1:length(x))';
r = x-y;
err = ((r'*r) / m);   
return