% Linear Algebra: Theory and Applications
% Ward Cheney & David Kincaid
% JBPub.com (c) 2008 
% File: exp726.m
% Example 7.2.6

% Fitting a linear least square polynomial to 
% the given data.  This Matlab program evaluates
% a and b for the Linear Least Squares.
% 'polyfit' fits a polynomial of degree n, here
% n = 1. 

% evaluating a and b for Linear Least Squares:
xdata = [1.0 2.0 2.5 3.0]
ydata = [3.7 4.1 4.3 5.0]
ls = polyfit(xdata, ydata, 1)
pause

% evaluating the value of the function phi:
d =ls(1)*xdata + ls(2) - ydata
phi = sum(d.^2)	
pause

% plotting the linear least square on a finer data range:
x = 0  :0.1:4
y = polyval(ls, x)
plot(xdata, ydata, 'ok', x, y, '-r')
title('Linear least squares fit')
xlabel('x axis'), ylabel('y axis')