Possum classification, Part II. A logistic regression model was proposed for classifying common brushtail possums into their two regions in Exercise 9.15. The outcome variable took value 1 if the possum was from Victoria and 0 otherwise.
| Estimate | SE | Z | Pr(Z) | |
| (Intercept) | 33.5095 | 9.9053 | 3.38 | 0.0007 |
| sex_ male | -1.4207 | 0.6457 | -2.20 | 0.0278 |
| skull_ width | -0.2787 | 0.1226 | -2.27 | 0.0231 |
| total_ length | 0.5687 | 0.1322 | 4.30 | 0.0000 |
| tail_ length | -1.8057 | 0.3599 | -5.02 | 0.0000 |
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Write out the form of the model. Also identify which of the variables are positively associated when controlling for other variables.
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Suppose we see a brushtail possum at a zoo in the US, and a sign says the possum had been captured in the wild in Australia, but it doesn’t say which part of Australia. However, the sign does indicate that the possum is male, its skull is about 63 mm wide, its tail is 37 cm long, and its total length is 83 cm. What is the reduced model’s computed probability that this possum is from Victoria? How confident are you in the model’s accuracy of this probability calculation?