Thanks for the guidance on how to evaluate the contribution of u^2 in the second model.
I can easily clone some existing code to compute t and its associated p for u^2 for each cell of the model (but note that I will only do so when the cells are non-empty for all four combinations of subset x MoSS | each (fold, set, length.)
But before doing so, I have one minor question about your formula:
estimated coefficient of the extra predictor in the second model t = ----------------------------------------------------------------. estimated standard error of that estimated coefficient
By analogy to the formula for t that you gave me for doing the 2-way t?s:
the denominator term ?estimated standard error of that estimated coefficient? should simply mean the variance of the coefficient in question. Is that the case? If not, what do you mean by ?estimated standard error? and why isn?t it simply the variance in this case?
Also, can you answer the following questions.
?A totally equivalent way is to get F = (RSS1/RSS2 - 1)*(n-k), where RSS1 and RSS2 are the Residual Sums of Squares from fitting the two models. Refer F to the F-distribution with df = (1,n-k). F = t^2.
A. If I understand what you wrote here, then I really don?t have to fit the model to get RSS1,RSS2 and then compute F from them. Rather, I can just square t. Is that the case?
B. Even if I can just square t to get F, is getting RSS1 and RSS2 by ?fitting the two models? something I can do programatically myself with instructions from you? Or do I have to look for an appropriate GSL module akin to Ivo?s regression module, one that I can tuck inside a PERL program? (Remember ? I am R-less and Mathematica-less.)
?No matter how small the p is, it doesn't mean SEP1/SEP2 is big enough to get excited about, that using the first model instead of the second would increase the SEP by enough to worry about.?
Since there is no equivalent of u^2 in the regression c on (u,e,u*e), I don?t understand where the other SEP is coming from.
By SEP1 and SEP2, do you mean the SEP?s of the two regressions themselves ( c on (u,e,u*e) and c on (u,e,u*e,u^2) ), rather than the SEP?s of any particular coefficients of these two regressions?
If so, can you tell me how to compute the SEP for a regression itself? So far, I don't think I've done this yet, and Ivo's module only reports out the SE's of coefficients, not an SE for a regresssion itself.