exercises for Tue Mar 7

1. On Tue Feb 28 I went through Sections 4.1-4.2, and also various aspects of Poisson regression, the sandwich matrix for regression, overdisperson, etc. We did the birds on islands exercise #20.

2. I've uploaded "com13a" for the Poisson models for birds on islands.

3. For next week, we're doing (body weight, brain weight) for n = 62 mammals. Write

library(MASS)
x0 <- mammals[ ,1] # body  in kg, range 0.005 to 6654.000
y0 <- mammals[ ,2] # brain in g,  range 0.14  to 5712.00

You'll find your own modest person as no. 32 in this list. Transform to (x,y) = (log x0, log y0), and then carry out model fitting and selection for y vs. x. Include a total of four models: (i) ordinary y = beta0 + beta1 x + N(0,\sigma^2); (ii) quadratic regression y = \beta_0 + \beta_1 x + \beta_2 x^2 + N(0,\sigma^2); (iii) linear regression but with varying \sigma, with \sigma_i = \sigma exp(\gamma (x_i - \bar x)); (iv) the widest model, with both \beta_2 and \gamma. Carry out AIC and BIC and AIC^* analysis, along with cross validation. Transform your models back to (x0,y0) scale.

Suppose you meet mammals in Gaustadskogen, of body weight 1.0, 20.0, 62.0 (a human!), 450.0 kg. Find estimates and 90% confidence intervals for their expected brain weights. Check if your own brain is adequate, or if it's too big.