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Unformatted text preview: Stat 500 — 2009 Midterm II — Solution Notes about my answers are marked by • General things about my grading: • If I wrote math error, you had the right idea/equation, but made a mistake in the calculation. I deducted one point for these. • The exam had many places where results from early parts were used in subsequent parts. I deducted points for the mistake when (and only when) they occurred. I did not deduct subsequent points because your answer(s) in later parts didn’t match mine. If you did the right things in subsequent parts, I gave you full credit. • These solutions indicate some common mistakes. If you don’t understand a comment on your exam or something in these solutions, please come and see me (or call/e-mail if you’re offcampus). • If I misadded points, or you don’t understand why I deducted points, please see / call / e-mail me. 1. Health of factory workers (a) correlation coefficient, r=0.838. You are interested in association between two observed quantities, not prediction. • If you wanted to use a regression slope, which slope is the correct one, i.e. should X be the H or the L variable? (b) se = s e / q Σ( x i- ¯ x ) 2 = 4 . 95 / √ 1428 = 0 . 131 (c) T = b 1 /se = 1 . 91 / . 131 = 15 . 1. df=101, p < 0.0001. (d) Source d.f. SS MS F Model 1 5576 5576 227.6 Error 101 2474.2 24.50 c.total 102 8050.2 • Common mistakes were: 2 df for model: remember model SS are the comparison of intercept model to intercept + slope. That’s a difference of 1 d.f. Misplaced SS: c.total SS is the error SS for the intercept only model error is the error SS for the regression. Model SS is the difference (e) the prediction for L i = 32. • No need to calculate prediction sd’s. For a simple linear regression, the most precise prediction is at the mean X. L i = 32 is closest to the mean. (f) Assumption diagnosis explanation lack of fit no evid. resid vs. pred plot is flat equal var. no evid. resid vs. pred plot has equal spread non-normality no evid. QQ plot is nearly linear independence no evid. design suggests o.u. = e.u. “no evid.” above means “no evidence of a problem” • You can’t tell independence from the plots. Need to look at the design....
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- Fall '08
- Regression Analysis, Error SS, Yi Yi, Partial regression coefficient