STAT 5102 Midterm: STAT 5102 UMN Spring 12 Test 3
Stat 5102 Final Exam May 12, 2012
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.] This problem is about the Beta(θ, 2) distribution. (Hint: Use
the gamma function recursion formula to eliminate gamma functions from
the PDF.)
(a) Find the Jeffreys prior.
(b) Say whether it is proper or improper.
1
2. [25 pts.] The following Rweb output fits a linear model and does several
tests of model comparison about it.
Rweb:> out <- aov(y ~ trt * blk)
Rweb:> summary(out)
Df Sum Sq Mean Sq F value Pr(>F)
trt 3 120.78 40.26 39.052 6.29e-13 ***
blk 5 41.48 8.30 8.046 1.42e-05 ***
trt:blk 15 43.99 2.93 2.844 0.00306 **
Residuals 48 49.49 1.03
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(a) Explain what models are being compared (what is the null, what is
the alternative) in each of the three tests that goes with each of the
three P-values in the rightmost column of the table.
(b) Explain where the degrees of freedom come from for each of the de-
grees of freedom listed in the leftmost column of the table. How many
levels must the factor trt have had, and how many levels must the
factor blk have had? How many data values were there in all, that
is, what was the length of the response vector y?
2
(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. 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: [25 pts. ] This problem is about the beta( , 2) distribution. (hint: use the gamma function recursion formula to eliminate gamma functions from the pdf. ) (a) find the je reys prior. (b) say whether it is proper or improper. The following rweb output ts a linear model and does several tests of model comparison about it. Rweb:> out
