MidtermI

# MidtermI - Stat 511 Midterm I 24 February 2011 1 A...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stat 511 Midterm I 24 February 2011 1. A psychological study of memory randomly assigned six subjects to one of three combinations of study time (1 minute or 5 minutes) and refresher (present or absent). The three treatments had the following structure: Refresher Study time Absent Present 1 minute μ 1 A μ 1 P 5 minutes μ 5 A The 5 minutes study time, with refresher, treatment was not used in the study. There are two subjects for each of the three treatments that were used. The investigators propose to use a non-full rank additive factor effects model to analyze the data: Y ijk = μ + α i + β j + ijk . (a) Write out the X matrix for this model with 6 subjects. (b) Is the main effect of refresher, i.e. the average difference between refresher present and refresher absent, estimable? Briefly explain why or why not. (c) Is the response mean for the 5 minute study time, with refresher, treatment estimable? Briefly explain why or why not. 2. An observational study evaluated the association between 7 categorical factors and the number of hours spent playing video games in a week. We consider only data from the first 15 subjects. Each categorical factor has two levels and is coded as one column containing either 0 or 1. The X matrix for those subjects is: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Some additional, potentially useful, information: The Normal Gauss-Markov model Y = Xβ + , ∼ N (0 ,σ 2 ), was fit to the data. 1 Stat 511 Midterm I 24 February 2011 The eigen decomposition of P X , i.e. UDU = P X is U = - . 133- . 089 . 215 . 432- . 043 . 019 . 859- . 045 . 002 . 35 . 292- . 042- . 047- . 154 . 343- . 199 . 119 . 449- . 158 . 106- . 206 . 288- . 121- . 464 . 379 . 01 . 053 . 047 . 334 . 024- . 466 . 054- . 291 . 191- . 187 . 509 . 301 . 102- . 052 . 284- . 542 . 226- . 247- . 248 . 398- . 094 . 024 . 281 . 023 . 007 . 163- . 193- . 01 . 376- . 105 . 281 . 12 . 118- . 079 . 635- . 104- . 106- . 42 . 295- . 209- . 285- . 214- . 112 . 056 . 293 . 205- . 041 . 174- . 605 . 046 . 396- . 036- . 311- . 161 . 096 . 329 . 119 . 243 . 032 . 322- . 077 . 054 . 268- . 118- . 273 . 069- . 1 . 224 . 487- . 336- . 41 . 107 . 357 . 075- . 025- .....
View Full Document

## This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

### Page1 / 5

MidtermI - Stat 511 Midterm I 24 February 2011 1 A...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online