Question: Screening Techniques

1. Consider the best subset output given below. What is the best subset of variables? State your reasons.
   Best Subsets Regression: y1 versus x1, x2, x3, x4
   Response is y
   Mallows x x x x
   Vars R-Sq R-Sq(adj) Cp S 1 2 3 4
   1 38.0 34.5 51.2 41.106 X
   1 34.7 31.1 54.8 42.174 X
   2 64.8 60.7 24.1 31.852 X X
   2 62.1 57.7 27.1 33.050 X X
   3 86.1 83.5 3.1 20.650 X X X
   3 83.1 79.9 6.3 22.758 X X X
   4 86.2 82.5 5.0 21.268 X X X X
2. Consider the Stepwise Regression, Backward Elimination output given below. What is the resulting subset of variables? What is the resulting MSE ?

Stepwise Regression: y versus x1, x2, x3, x4

Backward elimination. Alpha-to-Remove: 0.1

Response is y on 4 predictors, with N = 10

Step 1 2 3

Constant 85.75 137.53 197.91

x1 -15.9 -15.2 -13.1

T-Value -3.10 -3.25 -2.74

P-Value 0.027 0.018 0.029

x2 2.4 2.1

T-Value 1.47 1.45

P-Value 0.202 0.198

x3 1.8

T-Value 0.56

P-Value 0.603

x4 3.07 3.03 2.96

T-Value 8.22 8.80 8.08

P-Value 0.000 0.000 0.000

S 102 95.6 103

R-Sq 96.26 96.03 94.64

R-Sq(adj) 93.27 94.04 93.11

Mallows Cp 5.0 3.3 3.2

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