Statistics Homework Solutions 206

Statistics Homework Solutions 206 - p (2.2). This is not...

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206 CHAPTER 8 Source DF SS MS F P Regression 3 20.346 6.782 1683.9 0.000 Residual Error 12 0.048329 0.0040275 Total 15 20.394 The F statistic for comparing this model to the full quadratic model is F 2 10 0 048329 0 045513 12 10 0 045513 10 0 309, P 0 10, so it is reasonable to drop x 2 1 and x 1 x 2 from the full quadratic model. All the remaining coefficients are signifi- cantly different from 0, so it would not be reasonable to reduce the model further. (c) The output from the MINITAB best subsets procedure is Response is y x x x 1 2 1 Mallows x x ˆ ˆ x Vars R-Sq R-Sq(adj) C-p S 1 2 2 2 2 1 98.4 98.2 61.6 0.15470 X 1 91.8 91.2 354.1 0.34497 X 2 99.3 99.2 20.4 0.10316 X X 2 99.2 99.1 25.7 0.11182 X X 3 99.8 99.7 2.2 0.062169 X X X 3 99.8 99.7 2.6 0.063462 X X X 4 99.8 99.7 4.0 0.064354 X X X X 4 99.8 99.7 4.1 0.064588 X X X X 5 99.8 99.7 6.0 0.067463 X X X X X The model with the best adjusted R 2 (0.99716) contains the variables x 2 , x 2 1 , and x 2 2 . This model is also the model with the smallest value of Mallows’ C
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Unformatted text preview: p (2.2). This is not the best model, since it contains x 2 1 but not x 1 . The model containing x 1 , x 2 , and x 2 2 , suggested in the answer to part (b), is better. Note that the adjusted R 2 for the model in part (b) is 0.99704, which differs negligibly from that of the model with the largest adjusted R 2 value. 19. (a) Predictor Coef StDev T P Constant 1 1623 17042 6 8201 006 t 059718 0088901 6 7174 007 t 2 00027482 000069662 3 9450 029 (b) Let x be the time at which the reaction rate will be equal to 0.05. Then 0 059718 2 00027482 x 05, so x 17 68 minutes. (c) 1 059718, s 1 0088901. There are 6 observations and 2 dependent variables, so there are 6 2 1 3 degrees of freedom for error....
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