Applied Regression Analysis by Draper Norman R.; Smith Harry;

Author:Draper, Norman R.; Smith, Harry;
Language: eng
Format: epub
Publisher: Wiley
Published: 2014-08-07T04:00:00+00:00

15.6. SELECTION PROCEDURES APPLIED TO THE STEAM DATA

The steam data of Appendix 1A were subjected to selection procedure analysis by the MINITAB routines for stepwise regression, backward elimination, and best subsets regression using the following commands:

read C1-C10

[data from Appendix 1A]

end of data

stepwise CI C2-C10;

fenter = l

f remove = 1.

stepwise Cl C2-C10;

enter C2-C10;

fenter=10000;

fremove = 1.

breg Cl C2-C10;

best 3.

Remarks

We have deliberately set three F-values to 1. This is to produce a larger printout than would typically arise with larger F-values.

The stepwise procedure passes through five steps and the final equation contains X8, X2, X6, X5 and X10, entering in that order. If the default F-values of 4 were used, only X8 and X2 would enter because F6|8,2 = (1.85)2 = 3.42 < 4, at stage 3.

The backward elimination procedure successively eliminates X3, X1, and X5 and then stops at the point where the lowest F-value, for X4, is 2.03. Note that, if we had set fremove = 4 rather than 1, the same equation, containing X8, X2, X6, X10, X9, and X4 would have been obtained! (The order of the X’s is that of decreasing |t| values; this facilitates comparison with the stepwise order above.) We see that the two procedures produce different equations but that X8, X2, X6, and occur in both sets.

The best subsets printout with a choice of K = 3 equations in each set provides some clarification. It shows that the best pair is X8 and X2. The best triple is X8, X6, and X5, but the triple X8, X2, and X6 is close behind in terms of R2 value. Using four predictor variables contributes little to R2, and the jump from two to three X’s also adds little (about 2%). Both the equation with X8 and X2 and the equation with X2, and X6 seem like reasonable compromises here.

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