Observations (Xi, Yi), i = 1,...,n, are made from a bivariate normal population with parameters (μX, μY, Ï2X, Ï2Y, p), and the model Yi =

Observations (Xi, Yi), i = 1,...,n, are made from a bivariate normal population with parameters (μX, μY, σ2X, σ2Y, p), and the model Yi = α + βxi + εi is going to be fit.
(a) Argue that the hypothesis H0: β = 0 is true if and only if the hypothesis Ho: p = 0 is true.
(b) Show algebraically that

where r is the sample correlation coefficient, the MLE of p.
(c) Show how to test H0: p = 0, given only r2 and n, using Student's t with n - 2 degrees of freedom. (Fisher derived an approximate confidence interval for p, using a variance stabilizing transformation. See Exercise 11.4.)

TL- 2- V1- S/VS: