I know this is pretty simple but the answer is not obvious in my old
texts and in business I have no expert colleague to whom to turn.
My purpose is to construct a model which will be used for best-possible
prediction from new input data.
I constructed a regression model, based on historical understanding of
the domain, using eight predictors and obtained the following data
about the model:
F(8,98) = 35.15
Adj R-squared = 0.7205
RMSE = 0.90373
I noted that three of the predictors had P>| t | around 0.2-0.24.
Eliminating those gave me model results:
F(5,101) = 54.49
Adj R2 = 0.7295
RMSE = 0.91067
So significance has gone up but so has error. I assume that the larger
model over-fits the data and, if I were arguing around causaility,
would prefer the more compact model. Yet, it seems that the larger
model just does a slightly better job of prediction. How do I think
about this? Generally, where do I stop in a predictive problem (there
are other inputs available)? Should I care that much about a minor RMSE
difference or just do a "judgement" check on error differences on new
data? I also did a decent (N=1000) bootstrap on the larger model and
confidence intervals around all the predictors appeared reasonable for
our purpose. Either of the above models serves better than our previous
approach although it seems (opinion) that the larger model does better
at the extremes.
Talking to myself, I wonder if I just need more data for analysis
(painful process) but is there a statistical approach to focussing on
that extreme-edge issue? Perhaps I should be looking for another
inflection point in the model - we have already found one at the other
end, which I omitted from the above for brevity. If so, how does one
find it other than by trial?
