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1. Using minitab 16, for a regression model, how would I determine the ‘best’ regression equation by using an all-possible subset regression approach with suitable selection criteria (and how does one choose this "suitable selection criteria")?
2. (Original post by Bruce Harrisface)
Using minitab 16, for a regression model, how would I determine the ‘best’ regression equation by using an all-possible subset regression approach with suitable selection criteria (and how does one choose this "suitable selection criteria"?
Maybe this will help. The criterion that one uses for selecting between models depends upon the use that you're going to make of the final model. I don't use minitab, so I don't know which criteria it offers, but they will likely be to do with regression fit, explained variation or prediction accuracy.

BTW, all-subsets selection (and step-wise selection) are, in general, very poor methods of arriving at a final regression model. They were very popular a few years ago (hence they have been built into current software), but they have been shown to have very poor selection performance. Replaced these days with shrinkage techniques like the Lasso.
3. I've done the best subsets approach so now I have this table

How do I get the regression equation from this?
4. Sorry, wrong image
How would I get the equation from this table?
5. (Original post by Bruce Harrisface)
Sorry, wrong image
How would I get the equation from this table?
The selection criteria criteria you are given there are:

(i) R-squared: this measures the amount of explained variation in the regression. Higher is better.
(ii) Adjusted R-squared: same as (i) but with a penalty for the number of regression covariates. Tends to be favoured over (i) as it prefers "compact" regression equations.
(iii) Mallows Cp: this is equivalent to the Akaike Information Criterion (AIC), smaller is better subject to the expected value of Cp should be approximately equal to the number of covariates plus one (the constant).
(iv) S: the standard error of the regression. Again, smaller is better.

Here you have a whole bunch of choices with adjusted R-squared above 90%. Any of these would be good candidates. If you want to pick one then pick the fifth with adjusted R-squared of 91.3, though note that Mallows Cp might be a bit low, so you should check all of the regression diagnostics before you use it for inference or prediction.

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