Exercise 8.17

Igor Balagula
November 19, 2015

Problem Description

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Part A

Write out the form of the model. Identify which of the variables are positively associated when controlling for other variables.

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\( log\frac{\hat{p_i}}{1+\hat{p_i}} = 33.5095-1.4207sex\_male-0.2787skull\_width \)

\( +0.5687total\_length-1.8057tale\_length \)

\( total\_length \) is the only variable that has a positive association with a possum being from Victoria.

Part B

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 Audtralia, but it doesn't say which part of Australia. However, the sign does indicate that the possum is male, its skull is about 63mm wide, its tail is 37cm long, and its total length is 83cm. What is the probability that this possum is from Victoria?

\( log\frac{\hat{p_i}}{1+\hat{p_i}} = 33.5095-1.4207*1-0.2787*63+0.5687*83-1.8057*37 \)

\( log\frac{\hat{p_i}}{1+\hat{p_i}} = -5.0781 \)

\( \hat{p_i}=\frac{e^{-5.0781}}{1+e^{-5.0781}}=0.0062 \)

The probability is very low (0.0062) that the possum is from Victoria.