HW9-Solutions

# HW9-Solutions - STAT 101 Agresti Homework 9 Solutions...

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STAT 101 - Agresti Homework 9 Solutions 11/20/10 Chapter 11 11.1. (a) (i) E ( y ) = 0.20 + 0.50(4.0) + 0.002(800) = 3.8; (ii) E ( y ) = 0.20 + 0.50(3.0) + 0.002(300) = 2.3. (b) E ( y ) = 0.20 + 0.50 x 1 + 0.002(500) = 1.20 + 0.50 x 1 . (c) E ( y ) = 0.20 + 0.50 x 1 + 0.002(600) = 1.40 + 0.50 x 1 . (d) For instance, consider x 1 = 3 for which E ( y ) = 1.70 + 0.002 x 2 . By contrast, when x 1 = 2, E ( y ) = 1.20 + 0.002 x 2 , which has a different y -intercept but the same slope of 0.002. 11.4. (a) D.C. appears to be an outlier in each of the partial regression plots. HS 6.0 3.0 0.0 -3.0 -6.0 MU 30 20 10 0 -10 Partial Regression Plot Dependent Variable: MU

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PO 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 MU 40 30 20 10 0 -10 Partial Regression Plot Dependent Variable: MU (b) ˆ y = –60.498 + 0.588 x 1 + 1.605 x 2 . For fixed poverty rate, the murder rate is predicted to increase by 0.588 for each additional percent increase of high school graduates. For fixed percentage of graduates, the murder rate is predicted to increase by 1.65 for each additional percent increase in the poverty rate. Model Summary(b) Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.636(a) 0.405 0.380 4.764 a Predictors: (Constant), PO, HS b Dependent Variable: MU Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta B Std. Error 1 (Constant) -60.498 24.615 -2.458 0.018 HS 0.588 0.260 0.351 2.256 0.029 PO 1.605 0.301 0.830 5.332 0.000 a Dependent Variable: MU (c) With D.C. removed, the predicted effect of poverty rate is reduced from 1.605 to 0.304, less than a fifth as large. In addition, note that the estimated effect of percent of high school graduates now has a negative partial coefficient rather than a positive one. So, outliers can be highly influential in a regression analysis. Model Summary(b) Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.582(a) 0.338 0.310 2.136 a Predictors: (Constant), PO_noDC, HS_noDC b Dependent Variable: MU_noDC Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta B Std. Error 1 (Constant) 18.912 12.437 1.521 0.135 HS_noDC -0.196 0.130 -0.278 -1.510 0.138 PO_noDC 0.304 0.164 0.340 1.846 0.071 a Dependent Variable: MU_noDC 11.5. (a) ˆ y = –3.601 + 1.2799 x 1 + 0.1021 x 2 . (b) ˆ y = –3.601 + 1.2799(10) + 0.1021(50) = 14.3. (c) (i) ˆ y = –3.601 + 1.2799 x 1 + 0.1021(0) = –3.601 + 1.2799 x 1 ; (ii) ˆ y = –3.601 + 1.2799 x 1 + 0.1021(100) = 6.609 + 1.2799 x 1 ; On average, for each increase of \$1000 in GDP, the percentage of people who use the Internet

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## This note was uploaded on 07/14/2011 for the course STA 101 taught by Professor Alan during the Fall '10 term at University of Florida.

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HW9-Solutions - STAT 101 Agresti Homework 9 Solutions...

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