exercises for Tue Mar 14

1. On Tue Mar 7 I spent time going through various models and details for the mammals dataset, including assessments of degree of outlyingness for human sapiens (our brains are too big). I also presented the basic Start Theorem of Ch 5, with more to come next week.

2. I've placed com14b and com14e on the website, concerning the n = 62 mammals and the four or five models. Run through them, make sure you understand what goes on, so that you can "copy and modify" when needed.

3. Exercises for Tue Mar 14: First, fit Model 5 to the mammals dataset, with linear mean beta0 + beta1 x and varying \sigma_i = \sigma \exp(\gamma_1 w_i + \gamma_2 w_i^2), where w_i = (x_i - xbar)/sx. Draw a 99% confidence band for E(Y | x), and translate back to (x0, y0) scale, i.e. body weight (in kg) and brain weight (in g). Estimate p = Pr(Y_0 at least 1320 g | x0 = 62 kg), which is a measure of our outlyingness. Do the same with the water opposum (with its small brain).

Then apply the Start Theorem of Ch 5 to compute tolerance radii in the following situations.

(a) Narrow model is N(\xi, 1), wide model is N(\xi, \sigma^2). How much must \sigma differ from 1, in order for wide estimation being better than narrow estimation?

(b) Narrow model is N(0,\sigma^2), wide model is N(\xi,\sigma^2). How much must \xi differ from 0 before wide model estimation is better?

(c) Find the stk 4160 exam set from 2009, and look at the "extended normal" of Exercise 1, but with only one extra parameter a1. Find the tolerance radius, i.e. how much must a1 differ from zero before estimators based on the 3-para model become better than those based on the classic 2-para model?