Answer Happy

5. [Total 14 points) Suppose that you have data {X, Y},i = 1,..., n and run a linear regression Y, Bo + Bi X + U. The OLS estimators of (Bo, bı) are (Bo, Bi). Now your friend uses the same data except that there is a change in the units of measurement on both Y, and Xi. Her data are {X*,Y*), i = 1, ..., n, where Y,+=ayi + c and X* = bX+ d. Here a, b, c, d are four constants. She runs a regression of Y/* on X/* and obtains her OLS estimator (Bo*, B1*). (a) (3 points) Let p be the sample correlation coefficient based on your data {X, Y), and let p* be the sample correlation coefficient based on your friend's data {X/* , Y,*). What is the relationship (b) (12 points) Suppose that you know a, b, c, d and X and Y, then obtain your friend's estimator (Bo*, B1*) based on your estimator (Bo, Bi). I.e., write (Bo*, B1*) in terms of a, b, c, d, X, Y, and (Bo, B1). (C) (5 points) Let R? be your R-squared based on your regression and R* be her R-squared based on her regression. What is relationship between your R2 and her R2*. [Please justify your answer and show steps. If you cannot work it out fully, you can also use your intuition to guess the answers for partial credits.]