Answer Happy

The common brushtail possum of the Australia region is a bit cuter than its distant cousin, the American opossum (see Figure 7.5 on page 318). We consider 104 brushtail possums from two regions in Australia, where the possums may be considered a random sample from the population. The rst region is Victoria, which is in the eastern half of Australia and traverses the southern coast. The second region consists of New South Wales and Queensland, which make up eastern and northeastern Australia. A logistic regression is used to differentiate between possums in these two regions. The outcome variable, called population, takes value 1 when a possum is from Victoria and 0 when it is from New South Wales or Queensland. We consider five predictors: sex male (an indicator for a possum being male), head length, skull width, total length, and tail length. Each variable is summarized in a histogram. The results of fitted logistic regression model is summarized in the table below. Estimate SE z Pr(>171) (Intercept) 39.2349 11.5368 3.40 0.0007 sex male -1.2376 0.6662 -1.86 0.0632 head length -0.1601 0.1386 -1.16 0.2480 skull width -0.2012 0.1327 -1.52 0.1294 total length 0.6488 0.1531 4.24 0.0000 tail length -1.8708 0.3741 -5.00 0.0000 a. Write out the logistic model using the point estimates of the model parameters.