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I need help with the following question.

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I am really lost, so any help/hint would be much appreciated! I am aware that for best fit model, we are looking for higher $R^2_{Adj}$, smaller $MS_{res}$, PRESS (Prediction error sum of squares), AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion).

mat95
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    It's a [shame](https://stats.stackexchange.com/a/20856/7290) students are still being given these questions in stats classes. – gung - Reinstate Monica Apr 19 '21 at 19:10
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    Please add the [tag:self-study] tag & read its [wiki](https://stats.stackexchange.com/tags/self-study/info). Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. – gung - Reinstate Monica Apr 19 '21 at 19:11
  • The biggest problem I am having is "efficiency". For example, for part (a) we have that Partial F-test = SSres(red) - SSres(full)/p / SSres(full)/(n-k), and so it takes ages to compute the p-value for all the 6 models.Then the same problem comes up again in the next points. Is there a quicker way? – mat95 Apr 23 '21 at 02:29

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