# 420Hw05 - y = 252 a Test H ρ = 0 vs H a> 0 at the α =...

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STAT 420 Spring 2008 Homework #5 (due Friday, February 29, by 4:00 p.m.) 1. For the prostate data, fit a model with lpsa as the response and the other variables as predictors. a) Plot the residuals vs. the fitted values. Check the constant variance assumption for the errors. ( 4.3 (a) ) b) Make a histogram and a Normal Q-Q plot for the residuals. Check the normality assumption for the errors. ( 4.3 (b) ) 2. A society of bird watchers has collected data from several towns on stork sighting ( x ) and human births ( y ) to test the widely expressed belief that storks bring babies. Assume that ( X , Y ) have a bivariate normal distribution. The data are given in the table below: Storks, x 18 16 10 20 14 26 22 Babies, y 27 15 13 21 19 39 27 Σ x = 126, Σ y = 161, Σ x 2 = 2,436, Σ y 2 = 4,175, Σ x y = 3,150, Σ ( x x ) 2 = 168, Σ ( y y ) 2 = 472, Σ ( x x ) ( y y ) = Σ ( x x

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Unformatted text preview: ) y = 252. a) Test H : ρ = 0 vs. H a : > 0 at the α = 0.01 level of significance. What can you say about the p-value of this test? b) Does it follow from part (a) that storks do bring babies? Explain . c) Test H : = 0.50 vs. H a : > 0.50 at the α = 0.05 level of significance. What can you say about the p-value of this test? d) Construct a 95% confidence interval for . 100 ( 1 – α ) % confidence interval for ρ : & & ± ² ³ ³ ´ µ +-+-1 1 , 1 1 b b a a e e e e , where 3 2 1 1 2 ln---+ = n r r a z α , 3 2 1 1 2 ln-+-+ = n r r b z . 2.5 Using the prostate data, plot lpsa against lcavol . Fit the regressions of lpsa on lcavol and lcavol on lpsa . Display both regression lines on the plot. At what point do the two lines intersect? Hint 1: If x = m y + b , then y = m 1 x – m b . Hint 2: abline( y-intercept , slope ) 3.5 Find a formula relating R 2 and the F-test for the regression....
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## This note was uploaded on 02/10/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

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420Hw05 - y = 252 a Test H ρ = 0 vs H a> 0 at the α =...

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