How to remove effect of "in" predictors on "out" predictors in stepwiseregression?

Hi,

I am trying to understand how the effect of "in" predictors are removed from the "out" predictors in the native matlab code stepwisefit.m.

The code is doing the following but unfortunately I fail to understand why.

% Compute separate added-variable coeffs and their standard errors

xr = x - Q*(Q'*x); % remove effect of "in" predictors on "out" predictors

Any explanation as to what this is doing would be really helpful and highly appreciated.

Cheers,

Qazi

Answer 1

[Jeff Miller]

One way to think of it is that the "out" predictors will only improve the fit of the regression model if they bring in some new information not already provided by the "in" predictors. The "new" information provided by each "out" predictor is, by definition, information that is not already predictable from the "in" variables. So, to 'remove effect of "in" predictors on "out" predictors' is to extract the new information (xr) from the "out" predictors. The next step in the analysis will then be to see whether this new information actually improves predictions.

Hope that helps...

[Qazi Haque]

Thanks Jeff for the explanation. I understood that part but I was rather asking as to how the following line of code achives it, i.e. extract the new information:

xr = x - Q*(Q'*x); % remove effect of "in" predictors on "out" predictors

Any explanation on the above computation? Perhaps I am missing something...

[Jeff Miller]

No, sorry, I haven't gone through the computations in the code.

[Qazi Haque]

No worries Jeff, thanks.