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# Multiple Regression and Model Building

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Multiple Regression and Model Building 11 2 a 0 506 346 1 941 900 2 429 060 b y 506 346 941 900x1 429 060x2 c SSE 151 016 MSE 8883 s 94 251 Chapter 11 We expect about 95 of the y values to fall within 2s or 2 94 251 or 188 502 units of the fitted regression equation d H0 1 0 Ha 1 0 The test statistic is t 1 0 s 941 900 3 42 275 08 1 The rejection region requires 2 05 2 025 in each tail of the t distribution with df n k 1 20 2 1 17 From Table VI Appendix B t 025 2 110 The rejection region is t 2 110 or t 2 110 Since the observed value of the test statistic falls in the rejection region t 3 42 2 110 H0 is rejected There is sufficient evidence to indicate 1 0 at 05 e For confidence coefficient 95 05 and 2 025 From Table VI Appendix B with df n k 1 20 2 1 17 t 025 2 110 The 95 confidence interval is 2 t 025 s 429 060 2 110 379 83 429 060 801 441 2 1230 501 372 381 f R2 R Sq 45 9 45 9 of the total sample variation of the y values is explained by the model containing x1 and x2 R2a R Sq adj 39 6 39 6 of the total sample variation of the y values is explained by the model containing x1 and x2 adjusted for the sample size and the number of parameters in the model Multiple Regression and Model Building 379 g To determine if at least one of the independent variables is significant in prediction y we test H0 1 2 0 Ha At least one i 0 From the printout the test statistic is F 7 22 Since no level was given we will choose 05 The rejection region requires 05 in the upper tail of the F distribution with 1 k 2 and 2 n k 1 20 2 1 17 From Table IX Appendix B F 05 3 59 The rejection region is F 3 59 Since the observed value of the test statistic falls in the rejection region F 7 22 3 59 H0 is rejected There is sufficient evidence to indicate at least one of the variables x1 or x2 is significant in predicting y at 05 11 4 h The observed significance level of the test is p value 0 005 Since the p value is so small we will reject H0 for most reasonable values of There is sufficient

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