# Chap14_part2 - Solutions to End-of-Section and Chapter...

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Unformatted text preview: Solutions to End-of-Section 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 p-values 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 p-value for X 2 is > 0.05. Hence, it should be dropped. Comparing between model 3 and model 5, the p-value for X 3 is > 0.05. Hence, it should be dropped. Comparing between model 1 and model 9, the p-value for X 1 is > 0.05. Hence, it should be dropped. The only variable left is X 4 . The p-value 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 best-subset 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 Plot-2000000-1500000-1000000-500000 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 Plot-2000000-1500000-1000000-500000 500000 1000000 1500000 2000000-2.5-2-1.5-1-0.5 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 best-subset 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 p-value of the t statistic for X 2 is 0.999. Hence, it should be dropped. Coefficients Standard Error t Stat P-value Intercept-753.4085823 99.1450557 -7.599053497 1.52907E-09 % Attendance 8.501405843 1.06451847 7.986151559 4.223E-10 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 Plot-40-30-20-10 10 20 88 89 90 91 92 93 94 95 96 97 98 % Attendance Residuals Normal Probability Plot-40-30-20-10 10 20-2.5-2-1.5-1-0.5 0.5 1 1.5 2 2.5 Z Value Residuals Solutions to End-of-Section 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 University-West Lafayette.

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Chap14_part2 - Solutions to End-of-Section and Chapter...

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