How to do linear regression?

How to do a regression line ?

[Stephan]

Do you have access to Optimization Toolbox or to Curve Fitting Toolbox?

Answer 1

[Star Strider]

To do a simple linear least-square fit, see the mldivide,\ (link) function.

[Stephan]

Note that this solution only gives a correct answer, when the function passes through the origin of the coordinate system

y= m .* x + n ---> with n = 0

will give a correct answer. If n~=0 you get more bad results for m the more n is different from zero.

[Star Strider]

It gives a correct result if you include a column vector of ones with the independent variable to estimate the intercept:

B = [x(:) ones(size(x(:)))] \ y(:);                 % Estimate Parameters
yfit = [x(:) ones(size(x(:)))] * B;                 % Calculate Regression Line

figure
plot(x, y, 'pg')
hold on
plot(x, yfit, '-r')
hold off
grid

The polyfit (link) and polyval (link) options, with a polynomial order of 1, will also work.

[Stephan]

Nice,

and learned something again ;-)

[Star Strider]

Thank you!

Actually, I got the idea for the column of ones from the documentation for the regress (link) function when I first began using it, many years ago. (I simply forgot to include polyfit and friends initially.)

[Stephan]

I had to think about it for a few minutes. But after understanding what happens, i saw that this is a pretty nice approach.

Answer 2

[Image Analyst]

See my attached demo.