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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 1 A 1 P 5 minutes 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 nonfull rank additive factor effects model to analyze the data: Y ijk = + i + 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 GaussMarkov model Y = X + , N (0 , 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 .....
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 Spring '08
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