420Hw10ans - STAT 420 Spring 2010 Homework #10 (due Friday,...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 . ( p-value 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 P-value = Area to the right of t. 0.10 < p-value < 0.25 . ( p-value 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 R-squared, Adjusted R-squared, and Akaikes Information Criterion (AIC). Multiple R-squared = 80 59 SYY SSRegr 80 21 1 SYY SSResid 1 = =- =- = 0.7375 ....
View Full Document

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.

Page1 / 14

420Hw10ans - STAT 420 Spring 2010 Homework #10 (due Friday,...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online