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Unformatted text preview: Statistics 512: Review Problems for Exam 2 and Final Exam (Fall 2010) 1. Using the matrices from least squares estimation, what are the entries of the vector X e ? 2. For a model with 5 predictors and 40 observations, if R 2 is 0.3 what is the test statistic for the ANOVA F test? 3. Suppose you run a regression with response vector Y and design matrix X . Suppose further that Y is the vector of predicted values based on the least squares estimates. If you then regress Y on X , what would be the new predicted values Y ? (Hint: Y = HY .) 4. In multiple testing, the concept of coherence means that if any single parameter hypothesis (e.g., H : 1 = 0) is rejected, then all joint null hypotheses containing that null hypothesis (e.g., H : 1 = 2 = 0) are rejected. On the other hand, the concept of consonance means that if a joint null hypothesis is rejected, then at least one component hypothesis is rejected. (That is, if H : 1 = 2 = 0 is rejected, then either H : 1 = 0 is rejected or H : 2 = 0 is rejected or both are rejected.) Which of these two concepts is violated in the presence of serious multicollinearity? 5. Two different laboratory procedures were used to find the amount of calcium in a collection of orange juice samples. The correlation between the two measures was 0.99. Does this imply that the value given by the first procedure was approximately the same as the value given by the second procedure for each of the samples analyzed? Explain why or why not....
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