Linear Regression

linear regressing fit to line in the method of gradient descent for minimizing square error

based on
http://www.mathworks.com/matlabcentral/fileexchange/6716-orthogonal-linear-regression

http://en.wikipedia.org/wiki/Linear_least_squares

http://www.youtube.com/watch?v=5u4G23_OohI

use
%prepare some data
xdata=0:0.1:10;
ydata=2+7*xdata+6*randn(size(xdata));

%compare with normal linear regression
p0=polyfit(xdata,ydata,1);
yy0=polyval(p0,xdata);
%plot to compare data with linear fits

%% my func
xi = xdata';yi=ydata';theta_st=[ 0 0];nsteps=150;mindiff=1e-3;learnrate=1e-5;
[theta_out,err_vec,theta_vec] = gradient_descent_opt(xi,yi,theta_st,nsteps,mindiff,learnrate);
ygrad=theta_out(1)+theta_out(2)*xdata;

figure(1)
plot(xdata,ydata,'.',xdata,ygrad,xdata,yy0,':');
xlabel('x');ylabel('y')
title('. org ,: polyval, r my')