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Unformatted text preview: Solutions to EndofSection and Chapter Review Problems 103 14.23 Comparing between model 1 and model 2, model 3 and model 4, and model 7 and model 8, cont. the pvalues of the t statistics for X 5 are all greater than 0.05. So X 5 should be dropped. Comparing between model 1 and model 5, the pvalue for X 2 is > 0.05. Hence, it should be dropped. Comparing between model 3 and model 5, the pvalue for X 3 is > 0.05. Hence, it should be dropped. Comparing between model 1 and model 9, the pvalue for X 1 is > 0.05. Hence, it should be dropped. The only variable left is X 4 . The pvalue of X 4 in model 13 is 0.0017 < 0.05. The 2 adj r in model 13 is also the largest and the standard error is the smallest among all the 14 models considered by the bestsubset approach. Hence, the final model we will use is 4 2969741.233+59660.0926 Y X =  . The residual plot reveals violation of the homoscedasticity assumption. HS Residual Plot200000015000001000000500000 500000 1000000 1500000 2000000 20 40 60 80 100 HS Residuals The normal probability plot suggests that the error distribution is quite normal. Normal Probability Plot200000015000001000000500000 500000 1000000 1500000 20000002.521.510.5 0.5 1 1.5 2 2.5 Z Value Residuals 104 Chapter 14: Multiple Regression Model Building 14.24 Let Y = passing rate, X 1 = % attendance, X 2 = Salary, X 3 = Spending. Based on a full regression model involving all of the variables: All VIF s are less than 5. So there is no reason to suspect collinearity between any pair of variables. The bestsubset approach yielded the following models to be considered: Adjusted Consider Model Variables Cp k R Square R Square Std. Error This Model? 1 X1 3.05 2 0.6024 0.5936 10.5787 No 2 X1X2 3.66 3 0.6145 0.5970 10.5350 No 3 X1X2X3 4.00 4 0.6288 0.6029 10.4570 Yes 4 X1X3 2.00 3 0.6288 0.6119 10.3375 Yes 5 X2 67.35 2 0.0474 0.0262 16.3755 No 6 X2X3 64.30 3 0.0910 0.0497 16.1768 No 7 X3 62.33 2 0.0907 0.0705 15.9984 No Comparing between model 3 and model 4, the pvalue of the t statistic for X 2 is 0.999. Hence, it should be dropped. Coefficients Standard Error t Stat Pvalue Intercept753.4085823 99.1450557 7.599053497 1.52907E09 % Attendance 8.501405843 1.06451847 7.986151559 4.223E10 Spending 0.005983693 0.003385191 1.767608559 0.084060786 From the above Excel output, the X 3 should also be dropped at 5% level of significance. The best model is the simple regression model 1 771.5869 8.8447 Y X =  + The residual plot suggests that a nonlinear model on % attendance may be a better model. % Attendance Residual Plot40302010 10 20 88 89 90 91 92 93 94 95 96 97 98 % Attendance Residuals Normal Probability Plot40302010 10 202.521.510.5 0.5 1 1.5 2 2.5 Z Value Residuals Solutions to EndofSection and Chapter Review Problems 105 14.24 The normal probability plot indicates that with the exception of thicker left tail, the error cont. distribution is quite normally distributed....
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Harris

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