how to return the R-squared using lscov command

How can I get the R-squared using the LSCOV command?

[Matt J]

What is R?

Answer 1

[Wayne King]

I'm not sure whether your A matrix can be interpreted as a design matrix for a linear model and B is your response vector (here I'm using the input designations in lscov), but if that is the case, then the classic R-squared would be.

X = lscov(A,B);
xhat = A*X;
resid = xhat-B;
SSE = norm(resid,2)^2;
TSE = norm((B-mean(B),2)^2;
R2 = 1-SSE/TSS;

Alternatively, you could use something like:

X = lscov(A,B);
xhat = A*X;
r2 = norm(xhat,2)^2/norm(B,2)^2;

The l2-norm of xhat is less than or equal to the l2 norm of the B vector. If A*X is a good fit for B, then the norm of xhat will be close to the l2 norm of B and the ratio will be close to 1.

If A*X is bad fit for B, then the ratio will be small.

[Matt J]

This would only work if LSCOV is called with no more than 2 input args, i.e., if it is unweighted least squares. With the syntax

 x=lscov(A,B,V)

you would perhaps need

 resid = xhat-B;
 resid = dot(resid,V\resid);

[Tom Lane]

I would recommend computing both SSE and TSS using weights.