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Unformatted text preview: STAT 420 Spring 2010 Homework #10 (due Friday, April 23, by 4:00 p.m.) 1. Do NOT use a computer for this problem. Consider the following salary data for the full professors in the Department of Philosophical Engineering at Anytown State University in thousands of dollars per month ( Y ) and x 1 ( years in rank ). Females Males x 1 2 3 3 4 x 1 4 5 5 6 Y 2 3 5 6 Y 8 6 12 10 Consider the model Y = + 1 x 1 + 2 x 2 + e , where the dummy variable x 2 is the indicator for males ( i.e., x 2 = 0 for females, x 2 = 1 for males ). Then X T X = 4 20 4 20 140 32 4 32 8 , ( X T X ) 1 =  5 . 1 5 . 25 . 1 5 . 25 . 75 . 25 . 1 75 . 5 . 2 , X T Y = 36 234 52 , and =  2 5 . 1 5 . . a) Complete the ANOVA table for the significance of the regression test. State the null hypothesis. Is the regression significant at = 0.05? n = 8, p = 2. Source SS df MS F Regression 59 p = 2 29.5 7.0238 Residual (Error) 21 n p 1 = 5 4.2 Total 80 n 1 = 7 H : 1 = 2 = vs H 1 : at least one of 1 , 2 is not zero. Critical Value: F 0.05 ( 2 , 5 ) = 5.79 . Decision: Reject H . ( pvalue 0.0353 ) b) Does there seem to be discrimination against females? Test H : 2 = 0 vs. H 1 : 2 > 0 at a 5% level of significance. Var( 2 ) = C 22 s 2 = 1.5 4.2 = 6.3. Test Statistic: t = 3 . 6 2 0.79682 . Critical Value: t 0.05 ( 5 ) = 2.015. Decision: Do NOT Reject H . 1.476 = t 0.10 ( 5 ) > t > t 0.25 ( 5 ) = 0.727 Pvalue = Area to the right of t. 0.10 < pvalue < 0.25 . ( pvalue 0.23085 ) c) Find the partial correlation coefficient of Y and x 1 , with the effects of gender removed. Var( 1 ) = C 11 s 2 = 0.25 4.2 = 1.05. Test Statistic for H : 1 = 0: t = 05 . 1 5 . 1 1.46385. r Y X 1 X 2 = ( 29 5 46385 . 1 46385 . 1 1 2 2 t t + = + p n 0.5477 . d) Construct a 90% prediction interval for the monthly salary of a female full professor with 5 years in rank. female professor with 5 years in rank X T = [ 1 5 0 ] Y = 1 ( 0.5 ) + 5 1.5 + 0 2 = 7. X T C X = [ ]  5 1 5 . 1 5 . 25 . 1 5 . 25 . 75 . 25 . 1 75 . 5 . 2 5 1 = [ ]  25 . 1 50 . 25 . 1 5 1 = 1.25. r a V ( Y ) = [ 1 + X T C X ] s 2 = ( 1 + 1.25 ) 4.2 = 9.45. t 0.05 ( 5 ) = 2.015. 7 2.015 9.45 7 6.194 e) Find the values of the Multiple Rsquared, Adjusted Rsquared, and Akaikes Information Criterion (AIC). Multiple Rsquared = 80 59 SYY SSRegr 80 21 1 SYY SSResid 1 = = = = 0.7375 ....
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This note was uploaded on 04/08/2012 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Stepanov

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