STATS 403 Midterm: STAT 403 Exam 2 Fall 2009
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Express you answers clearly and show work where appro- priate. 1: suppose we are interested in the correlation between a person"s annual income i (in thousands of dollars), and the number of years y between the person"s purchases of a new car. We have good data on y , and can assume that it is measured exactly. However income is measured as i = i + e, where e is a random measurement error term with mean zero and variance 2. Assume that the population correlation coe cient between i and y is = 0. 3, the standard deviation of i is 12, and the standard deviation of y is 3. E is uncorrelated with i and y . (a) let denote the sample correlation coe cient between i and y . 3: suppose we are working with a measurement x that may be used to diagnose whether someone has a particular disease.
