A 31-run experiment was conducted with 6 independent predictor variables. The table below gives the SSres for all possible fitted models in the six variables. Select a “best” model using each of the approaches in a-f stated below. Variables in Model SSres Variables in Model SSres Variables in Model SSres Variables in Model SSres none 11.058 x3, x4 1.453 x2, x3, x4 1.041 x1, x3, x4, x5 0.561 x1 0.607 x3, x5 9.891 x2, x3, x5 9.362 x1, x3, x4, x6 0.555 x2 10.795 x3, x6 8.848 x2, x3, x6 8.838 x1, x3, x5, x6 0.561 x3 10.633 x4, x5 1.397 x2, x4, x5 1.030 x1, x4, x5, x6 0.553 x4 1.522 x4, x6 1.507 x2, x4, x6 1.192 x2, x3, x4, x5 0.958 x5 9.922 x5, x6 7.680 x2, x5, x6 7.679 x2, x3, x4, x6 0.995 x6 9.196 x1, x2, x3 0.498 x3, x4, x5 1.383 x2, x3, x5, x6 7.675 x1, x2 0.499 x1, x2, x4 0.450 x3, x4, x6 1.437 x2, x4, x5, x6 1.024 x1, x3 0.600 x1, x2, x5 0.477 x3, x5, x6 7.678 x3, x4, x5, x6 1.342 x1, x4 0.582 x1, x2, x6 0.367 x4, x5, x6 1.352 x1, x2, x3, x4, x5 0.412 x1, x5 0.597 x1, x3, x4 0.581 x1, x2, x3, x4 0.441 x1, x2, x3, x4, x6 0.311 x1, x6 0.576 x1, x3, x5 0.582 x1, x2, x3, x5 0.475 x1, x2, x3, x5, x6 0.364 x2, x3 10.168 x1, x3, x6 0.567 x1, x2, x3, x6 0.365 x1, x2, x4, x5, x6 0.313 x2, x4 1.218 x1, x4, x5 0.569 x1, x2, x4, x5 0.413 x1, x3, x4, x5, x6 0.545 x2, x5 9.479 x1, x4, x6 0.558 x1, x2, x4, x6 0.323 x2, x3, x4, x5, x6 0.939 x2, x6 9.192 x1, x5, x6 0.574 x1, x2, x5, x6 0.364 x1, x2, x3, x4, x5, x6 0.307 a. Backward elimination using F-test and removal alpha=0.05 b. Forward selection using F-test and entry alpha=0.05 c. Stepwise selection using F-test and entry and removal alpha=0.05 d. Backward elimination based on Mallows' Cp e. Forward selection based on Mallows' Cp f. Stepwise selection based on Mallows' Cp

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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Question

A 31-run experiment was conducted with 6 independent predictor variables. The table below gives the SS_res for all possible fitted models in the six variables. Select a “best” model using each of the approaches in a-f stated below.

Variables in Model	SSres	Variables in Model	SSres	Variables in Model	SSres	Variables in Model	SSres
none	11.058	x3, x4	1.453	x2, x3, x4	1.041	x1, x3, x4, x5	0.561
x1	0.607	x3, x5	9.891	x2, x3, x5	9.362	x1, x3, x4, x6	0.555
x2	10.795	x3, x6	8.848	x2, x3, x6	8.838	x1, x3, x5, x6	0.561
x3	10.633	x4, x5	1.397	x2, x4, x5	1.030	x1, x4, x5, x6	0.553
x4	1.522	x4, x6	1.507	x2, x4, x6	1.192	x2, x3, x4, x5	0.958
x5	9.922	x5, x6	7.680	x2, x5, x6	7.679	x2, x3, x4, x6	0.995
x6	9.196	x1, x2, x3	0.498	x3, x4, x5	1.383	x2, x3, x5, x6	7.675
x1, x2	0.499	x1, x2, x4	0.450	x3, x4, x6	1.437	x2, x4, x5, x6	1.024
x1, x3	0.600	x1, x2, x5	0.477	x3, x5, x6	7.678	x3, x4, x5, x6	1.342
x1, x4	0.582	x1, x2, x6	0.367	x4, x5, x6	1.352	x1, x2, x3, x4, x5	0.412
x1, x5	0.597	x1, x3, x4	0.581	x1, x2, x3, x4	0.441	x1, x2, x3, x4, x6	0.311
x1, x6	0.576	x1, x3, x5	0.582	x1, x2, x3, x5	0.475	x1, x2, x3, x5, x6	0.364
x2, x3	10.168	x1, x3, x6	0.567	x1, x2, x3, x6	0.365	x1, x2, x4, x5, x6	0.313
x2, x4	1.218	x1, x4, x5	0.569	x1, x2, x4, x5	0.413	x1, x3, x4, x5, x6	0.545
x2, x5	9.479	x1, x4, x6	0.558	x1, x2, x4, x6	0.323	x2, x3, x4, x5, x6	0.939
x2, x6	9.192	x1, x5, x6	0.574	x1, x2, x5, x6	0.364	x1, x2, x3, x4, x5, x6	0.307