STAT 410 96-2 Assignment 8 Solutions

6.1 You must decide whether or not it appears that inequality 6.18 is satisfied. So you compute the sample correlations, means and standard deviations and check.
6.4 The answer is (b). The question is which estimate has smaller mean squared error. If n is reasonably large bias is negligible and so the estimate ybar/xbar is better if the population satisfies 6.18. Thus y and x need to be positively correlated with a fairly high correlation.
6.5 You are trying to estimate Y=68 so you have to work out the separate and combined ratio estimates for each of 36 possible samples subtract 68 from each value, square and average to get E[(est- Y)^2]. Since MSE = Variance + Bias^2 you should work out bias = average of the 36 estimate values -68 and square it and see how big a fraction this is of the MSE.
7.1 The estimate is 11600 + 200 [ 2 + (-5) + (-2) + (-2) + ... ] / 10 = 11080. You get a variance estimate by noticing that you just averaged 10 numbers. The estimated variance is [(2- (-2.6))^2 + (-5 -(-2.6))^2 + ...]/9 x (1-10/200) / 10.
7.2 You would need to work out the estimated standard error using linear regression. You will find the slope estimate is not much different than 1 and that the resulting variance estimate is only a bit smaller. This improvement is probably compensated for by the bias in the linear regression method.
7.7 Postponed to the next assignment