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sol3 - Stat 201A HW3 Solution 1(a The estimated factorial...

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Stat 201A HW3 Solution 1. (a) The estimated factorial e ff ects are A B C D A:B A:C A:D B:C 3.0189 3.9759 -3.5962 1.9578 1.9341 -4.0078 0.0765 0.0960 B:D C:D A:B:C A:B:D A:C:D B:C:D A:B:C:D 0.0472 -0.0769 3.1375 0.0980 0.0191 0.0356 0.0141 E ff ects A, B, C, D, AB, AC, ABC appear to be important because they are relatively large. (b) The regression summary is Estimate Std. Error t value Pr(>|t|) (Intercept) 11.988062 0.050361 238.042 < 2e-16 *** A 1.509438 0.050361 29.972 1.74e-15 *** B 1.987938 0.050361 39.474 < 2e-16 *** C -1.798125 0.050361 -35.705 < 2e-16 *** D 0.978875 0.050361 19.437 1.49e-12 *** A:B 0.967062 0.050361 19.203 1.79e-12 *** A:C -2.003875 0.050361 -39.790 < 2e-16 *** A:D 0.038250 0.050361 0.760 0.459 B:C 0.048000 0.050361 0.953 0.355 B:D 0.023625 0.050361 0.469 0.645 C:D -0.038438 0.050361 -0.763 0.456 A:B:C 1.568750 0.050361 31.150 9.49e-16 *** A:B:D 0.049000 0.050361 0.973 0.345 A:C:D 0.009563 0.050361 0.190 0.852 B:C:D 0.017813 0.050361 0.354 0.728 A:B:C:D 0.007062 0.050361 0.140 0.890 Residual standard error: 0.2849 on 16 degrees of freedom Multiple R-Squared: 0.9977,Adjusted R-squared: 0.9956 The p-values confirms that A, B, C, D, AB, AC, ABC are significant. (c) The final regression model is ˆ y = 11 . 99 + 1 . 51 A + 1 . 99 B - 1 . 80 C + 0 . 98 D + 0 . 97 AB - 2 . 00 AC + 1 . 57 ABC (d) We shall examine the residuals from the final model. There is nothing unusual about the residuals. The plots are not shown here. (e) To minimize the crack length, we shall look at the ABC interaction plot first, which suggests to choose
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