STAT 5102 Midterm: STAT 5102 UMN Spring 10 Test 3
Stat 5102 Final Exam May 12, 2010
Name Student ID
The exam is closed book and closed notes. You may use three 81
2×11
sheets of paper with formulas, etc. You may also use the handouts on “brand
name distributions” and Greek letters. Put all of your work on this test form
(use the back if necessary). Show your work or give an explanation of your
answer. No credit for numbers with no indication of where they came from.
The points for the questions total to 200. There are 10 pages and 8
problems.
1. [25 pts.] Find the Jeffreys prior for the Poi(µ) distribution. It is proper
or improper?
1
2. [25 pts.] The following Rweb output fits three linear models and does
tests of model comparison between them
Rweb:> out1 <- lm(y ~ x1 + x2 + x3)
Rweb:> out2 <- lm(y ~ poly(x1, x2, x3, degree = 2, raw = TRUE))
Rweb:> out3 <- lm(y ~ poly(x1, x2, x3, degree = 3, raw = TRUE))
Rweb:> anova(out1, out2, out3)
Analysis of Variance Table
Model 1: y ~ x1 + x2 + x3
Model 2: y ~ poly(x1, x2, x3, degree = 2, raw = TRUE)
Model 3: y ~ poly(x1, x2, x3, degree = 3, raw = TRUE)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 96 4206818
2 90 9312 6 4197506 7224.2845 <2e-16 ***
3 80 7747 10 1565 1.6164 0.1169
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
(a) Explain what these models are and why they are nested models.
2
(b) Explain why there are 6 degrees of freedom difference between model
1 and model 2 and why there are 10 degrees of freedom difference
between model 2 and model 3.
(c) If one has to choose among the models, which does one choose on
grounds of simplicity and statistical significance? Explain.
3
Document Summary
The exam is closed book and closed notes. 11 sheets of paper with formulas, etc. You may also use the handouts on brand name distributions and greek letters. Put all of your work on this test form (use the back if necessary). Show your work or give an explanation of your answer. No credit for numbers with no indication of where they came from. The points for the questions total to 200. Find the je reys prior for the poi( ) distribution. The following rweb output ts three linear models and does tests of model comparison between them. Rweb:> out1 out2 out3
