- 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

The questions.