Statistics Homework Solutions 198

Statistics Homework Solutions 198 - 198 CHAPTER 8 (f)...

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Unformatted text preview: 198 CHAPTER 8 (f) 1683.5 (g) (1634.7, 1732.2) P 0 414 0 425 ¨ ¨ ¨ ¨ T 11 686 3 6197 P 0 000 0 007 ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¡ ¡ ¨ ¨ StDev 3 4545 0 0043503 ¨ ¨ ¨ ¡ Coef 40 370 0 015747 ¨ T 0 86215 0 83993 ¨ ¨ ¨ StDev 16 754 0 20637 P 0 044 0 180 0 006 ¨ Predictor Constant x2 ¨ ¨ ¡ (c) Coef 14 444 0 17334 T 2 4572 1 4885 3 9164 ¨ Predictor Constant x1 StDev 10 424 0 12353 0 0040542 ¨ (b) Coef 25 613 0 18387 0 015878 ¨ Predictor Constant x1 x2 ¨ 15. (a) (d) The model containing x2 as the only independent variable is best. There is no evidence that the coefficient of x1 differs from 0. The model y β0 β1 x2 ε is a good one. One way to see this is to compare the fit of this model to the full quadratic model. The ANOVA table for the full model is ¢ SS 4.1007 3.9241 8.0248 The ANOVA table for the model y Source Regression Residual Error Total DF 1 13 14 ¡ DF 5 9 14 MS 0.82013 0.43601 β0 ε is ¢ ¡ Source Regression Residual Error Total β1 x 2 SS 2.7636 5.2612 8.0248 ¢ ¢ MS 2.7636 0.40471 F 1.881 P 0.193 F 6.8285 P 0.021 From these two tables, the F statistic for testing the plausibility of the reduced model is 0 7667. ¤ ©¥ £ £ ¨ ¡ ¨ ¤ ¨ The null distribution is F4 9 , so P 0 10 (a computer package gives P that the reduced model is plausible. ¡ 1 0 573). The large P-value indicates ¨ ¡ 5 ¥ 3 9241 3 9241 9 ¡ 5 2612 ¨ ¨ ¡ ¡ 17. ...
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