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Design of Experiments - US Army Conference on Applied Statistics

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Stepwise Fit<br />

Resp<strong>on</strong>se: Shrinkage<br />

Stepwise Regressi<strong>on</strong> C<strong>on</strong>trol<br />

Prob to Enter<br />

Prob to Leave<br />

Directi<strong>on</strong>:Forward<br />

0.250<br />

0.100<br />

Rules: Combine<br />

Current Estimates<br />

SSE<br />

133.18753<br />

DFE<br />

10<br />

LockEntered Parameter<br />

Intercept<br />

A<br />

B<br />

C<br />

D<br />

E<br />

F<br />

A*B<br />

A*C<br />

A*D<br />

A*E<br />

A*F<br />

B*C<br />

B*D<br />

B*E<br />

B*F<br />

C*D<br />

C*E<br />

C*F<br />

D*E<br />

D*F<br />

E*F<br />

Step History<br />

Step<br />

1<br />

2<br />

Parameter<br />

A*B<br />

A*D<br />

MSE<br />

13.318753<br />

Acti<strong>on</strong><br />

Entered<br />

Entered<br />

RSquare<br />

0.9800<br />

Estimate<br />

27.3125<br />

6.9375<br />

17.8125<br />

0<br />

-4.441e-16<br />

0<br />

0<br />

5.9375<br />

0<br />

-2.6875<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

nDF<br />

1<br />

3<br />

2<br />

1<br />

2<br />

1<br />

1<br />

1<br />

2<br />

1<br />

2<br />

2<br />

2<br />

1<br />

2<br />

2<br />

2<br />

3<br />

3<br />

2<br />

2<br />

3<br />

"Sig Prob"<br />

0.0000<br />

0.0440<br />

RSquare Adj<br />

0.9700<br />

SS<br />

0<br />

1449.688<br />

5640.625<br />

3.16e-30<br />

115.5625<br />

4.21e-30<br />

4.21e-30<br />

564.0625<br />

11.39834<br />

115.5625<br />

26.80068<br />

13.7383<br />

1.58e-29<br />

11.39834<br />

13.7383<br />

26.80068<br />

13.78835<br />

1.933557<br />

31.4007<br />

31.4007<br />

1.933557<br />

2.459758<br />

Seq SS<br />

6410.688<br />

115.5625<br />

"F Ratio"<br />

0.000<br />

36.282<br />

211.755<br />

0.000<br />

4.338<br />

0.000<br />

0.000<br />

42.351<br />

0.374<br />

8.677<br />

1.008<br />

0.460<br />

0.000<br />

0.842<br />

0.460<br />

1.008<br />

0.462<br />

0.034<br />

0.720<br />

1.234<br />

0.059<br />

0.044<br />

RSquare<br />

0.9626<br />

0.9800<br />

Cp<br />

.<br />

AIC<br />

45.90671<br />

"Prob>F"<br />

1.0000<br />

0.0000<br />

0.0000<br />

1.0000<br />

0.0440<br />

1.0000<br />

1.0000<br />

0.0001<br />

0.6992<br />

0.0146<br />

0.4071<br />

0.6470<br />

1.0000<br />

0.3827<br />

0.6470<br />

0.4071<br />

0.6459<br />

0.9907<br />

0.5711<br />

0.3411<br />

0.9432<br />

0.9867<br />

Cp<br />

.<br />

.<br />

p<br />

4<br />

6<br />

Stepwise regressi<strong>on</strong><br />

selects the main<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> A and B,<br />

al<strong>on</strong>g with the AB and<br />

AD interacti<strong>on</strong>s<br />

The main effect <str<strong>on</strong>g>of</str<strong>on</strong>g> D is<br />

added to preserve the<br />

hierarchy in the model<br />

The no-c<strong>on</strong>founding<br />

design correctly<br />

identifies the model<br />

without any ambiguity<br />

and no need for<br />

additi<strong>on</strong>al runs<br />

58

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