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Unformatted text preview: Stat 511 Homework 11 solution Spring 2011 Due: 5pm, Tuesday Apr 19 1. The data in school.txt come from an educational study. The full study has 3 treatments, but we will only look at data from one treatment. Treatments were randomly assigned to 8th grade classrooms in 3 schools in each of 4 school districts. Performance on a standardized test was measured for each student in each classroom. There are a total of 24 classrooms and 573 students. We will ignore the multiple levels of vairability and consider a model with a random effect for classroom and a random effect for student. Note that one of these random effects is commonly called “error”. (a) Estimate the variance components (variability between classrooms and variability among students within a classroom) using REML. The appropriate model is Y ij = μ + α i + ǫ ij where 1 ≤ i ≤ 24, 1 ≤ j ≤ n i , α i ∼ (0 , σ 2 α ) the variability among classroom and ǫ ij ∼ (0 , σ 2 ǫ ) the variability among studentswithin a classroom. > temp < lmer(score~(1class),data=d) > summary(temp) Linear mixed model fit by REML Formula: score ~ (1  class) Data: d AIC BIC logLik deviance REMLdev 3592 36051793 3589 3586 Random effects: Groups Name Variance Std.Dev. class (Intercept) 63.00 7.9373 Residual 26.03 5.1020 Number of obs: 573, groups: class, 24 (b) Estimate the mean score for this treatment and its standard error. Fixed effects: Estimate Std. Error t value (Intercept) 61.837 1.636 37.79 (c) You have been asked by the teacher of classroom 17 to report that class’s average per formance on this exam. Report the appropriate value....
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 Spring '08
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 Normal Distribution, Quantile, QQ plot, Shapiro–Wilk test, BLUP

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