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Question

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. Use α=0.05


Screen Shot 2019-08-01 at 7.35.21 PM.png


a.    Backward elimination F-test.

b.    Forward selection F-test.

c.    Stepwise regression F-test.

d.    Backward elimination based on Mallows' Cp

e.    Forward selection based on Mallows' Cp

f.     Stepwise regression based on Mallows' Cp

Screen Shot 2019-08-01 at 7.35.21 PM.png

Variables in Model
Variables in Model
Variables in Model
SSree
Variables in Model
none
11.058
*3, x4
1 453
x2, x3, x4
1.041
x1, x3, x4, x5
D.561
x1
0.607
*3, x5
9.891
x2, x3, X5
9.362
x1, x3, x4, x6
D.555
x2
10.795
*3, X6
6 848
X2, X3, X6
8.838
x1, x3, x5, x6
D.561
X3
10.633
X4, x5
1 397
x2, x4, x5
1.030
x1, x4, x5, x6
D.553
1.522
X4, X6
1 507
x2, X4, X6
1.192
x2, x3, x4, x5
D.958
X5
9.922
x5, x6
7.680
*2, *5, X6
7.679
x2, x3, x4, x6
D.995
X6
9.196
*1, x2, x3
0.498
X3, X4, X5
1.383
x2, x3, x5, x6
7.675
x1, x2
0.499
*1, x2, x4
0.450
X3, X4, X6
1.437
x2, x4, *5, X6
1.024
x1, x3
D.600
*1, x2, x5
0.477
x3, x5, X6
7.678
x3, x4, x5, X6
1.342
x1, x4
0.582
*1 x2, X6
0.367
x4, x5, X6
1.352
x1, x2, x3, x4, x5
x1, x5
D.412
0.597
*1, x3, x4
0.581
x1, x2, x3, x4
0.441
x1, x2, x3, x4, x6
D.311
x1, x6
0.576
*1, X3, X5
0.582
x1, x2, x3, x5
0.475
x1, x2, x3, x5, x6
D.364
X2, x3
10.168
*1, X3, X6
0.567
x1, NZ, X3, X6
0.365
x1, x2, x4, x5, x6
D.313
x2, x4
1.218
*1, x4, x5
0.569
x1, x2, x4, x5
0.413
x1, x3, x4, x5, x6
D.545
x2, x5
9.479
*1, x4, X6
0.558
x1, x2 x4 x6
0.323
x2, X6
x2, x3, x4, X5, x6
0.939
9.192
x1, x5, X6
0.574
x1, x2, x5, x6
0.364
x1, x2, x3, x4, x5, x6
0.307

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