Dan Wigodsky
May 8, 2018
. . .
Open Intro Statistics, Problem 8:17
. . .
For reference, problem 17 follows a model for brushtail possums introduced in problem 15:
Here’s our problem:
a)
The formula that describes our model is:
\(ln(\frac{\pi}{1-\pi})=33.5095-1.4207(sex)-.2787(skull\ width)\)
\(+.5687(total\ length)-1.8057(tail\ length)\)
Total length is the variable that is positively associated.
Skull width, tail length and being male are negatively associated.
b)
\(ln(\frac{\pi}{1-\pi})=33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)\)
\(\large\pi=\frac{e^{33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)}}{1+e^{33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)}}=.006193144\)
. . .
This is a very clear probability. This particular prediction is quite strong. Overall, our model should be checked for deviance and residuals could be investigated to ensure our model is appropriate. We could compare our model to other possible models using AIC. We are pretty sure that the zoo did not choose the possum for qualities that our model covers. If their selection of possum were not random, then our model would not be appropriate.
May 8, 2018
For reference, problem 17 follows a model for brushtail possums introduced in problem 15:
Here’s our problem:
a)
The formula that describes our model is:
\(ln(\frac{\pi}{1-\pi})=33.5095-1.4207(sex)-.2787(skull\ width)\)
\(+.5687(total\ length)-1.8057(tail\ length)\)
Total length is the variable that is positively associated.
Skull width, tail length and being male are negatively associated.
b)
\(ln(\frac{\pi}{1-\pi})=33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)\)
\(\large\pi=\frac{e^{33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)}}{1+e^{33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)}}=.006193144\)
. . .
This is a very clear probability. This particular prediction is quite strong. Overall, our model should be checked for deviance and residuals could be investigated to ensure our model is appropriate. We could compare our model to other possible models using AIC. We are pretty sure that the zoo did not choose the possum for qualities that our model covers. If their selection of possum were not random, then our model would not be appropriate.
The formula that describes our model is:
\(+.5687(total\ length)-1.8057(tail\ length)\)
Total length is the variable that is positively associated.
Skull width, tail length and being male are negatively associated.
b)
\(ln(\frac{\pi}{1-\pi})=33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)\)
\(\large\pi=\frac{e^{33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)}}{1+e^{33.5095-1.4207(1)-.2787(63)+.5687(83)-1.8057(37)}}=.006193144\)
. . .
This is a very clear probability. This particular prediction is quite strong. Overall, our model should be checked for deviance and residuals could be investigated to ensure our model is appropriate. We could compare our model to other possible models using AIC. We are pretty sure that the zoo did not choose the possum for qualities that our model covers. If their selection of possum were not random, then our model would not be appropriate.