Homework 2 Solutions 6.50. We know that if U = (n 1)S 2 / 2 2 , then E(U ) = n 1 and V (U ) = 2(n 1). Using n1 Equation (6.12) with X = U , k = 1/2, and = n 1 we get E( U ) = 2(n/2)/[(n 1)/2]. a. E(S 2 ) = E[ 2 U/(n 1)] = 2 E(U )/(n 1) =
Homework 3 Solutions 7.4. a. X Y is an unbiased estimator for 1 2 since E(X Y ) = 1 2 . To see this, E(X Y ) = E(X) E(Y ) = 1 m
m
E(Xi )
i=1
1 n
n
E(Yi ) = 1 2
i=1
For the observed data, the estimate of 1 2 is x y = 121.44 113.80 = 7.
In an experiment, with n=13 observations, the estimated regression line is y=0.365+ 0.967x. I am giving you the following MSE=0.0373 and MSR=1.0427. a) Calculate SSE. b) Calculate the estimated variance of the regression c) Calculate the Coefficient