Calculate R squared from a linear regress

Hi, I have a set of scattered data and I can use the operator "\" to do a linear fit on the data. But is there a simple matlab function to get the R^2? I am trying to skip the calculation shown on page: https://www.mathworks.com/help/matlab/data_analysis/linear-regression.html

BTW, I don't have machine learning toolbox.

Thanks for any help. If there is no simple matlab function, then I will have to try to calculate by using the sample code shown on the above page.

Answer 1

[Star Strider]

It depends on the regression you’re doing. If you have a simple bivariable (as opposed to multivariable) linear regression, you can simply square one of the off-diagonal elements of the (2x2) matrix returned by corrcoef. It will give the same result.

[JFz]

Thanks. It is a simple bivariable linear regression.

[Star Strider]

My pleasure.

That will work.

If my Answer helped you solve your problem, please Accept it!

[JFz]

Thank you!

I am reading about it.

[Star Strider]

As always, my pleasure!

This will provide a sort of computational ‘proof’. It uses polyfit and polyval, not the backslant operator, otherwise being the same:

A = 1:100;                                      % Create Data
B = 1 + 2*A + 10*randn(size(A));                % Create Data

b = polyfit(A, B, 1);
f = polyval(b, A);

Bbar = mean(B);
SStot = sum((B - Bbar).^2);
SSreg = sum((f - Bbar).^2);
SSres = sum((B - f).^2);

R2 = 1 - SSres/SStot

R = corrcoef(A,B);
Rsq = R(1,2).^2

[JFz]

Thank you! This really helps a lot.

[Star Strider]

As always, my pleasure!