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\Large
36-617: Applied Linear Models\\
Fall 2021\\
HW05 -- Due Mon Oct 4, 11:59pm
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\begin{itemize}

\item Please turn the homework in online as a pdf to Gradescope, using the link provided on the assignment page in canvas.cmu.edu, 
under Assignments.  
\item This week we are discussing Ch 6 of Sheather.  Next week we will move on to Ch 7.

\item Data files (where needed) for these exercises are in the ``0 - textbooks'' folder in the files area on canvas, unless otherwise noted below.  

\item There are two major exercises below; each one has ``parts''.

\item Work on Project 01 will begin with hw06.

\end{itemize}


\section*{Exercises}

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\item Sheather, Ch 6, p 224, \#5 (look familiar?).

\item Return to the ``beauty'' data from Gelman \& Hill (2009), p. 51, \#5 (data and documentation in the hw05 folder on canvas).  
\begin{enumerate}
\item Should any of the variables in the data set be transformed before being used in a regression model?  List each variable that is not a dummy variable, and for each of these, 
\begin{itemize}
\item Say whether the variable should be transformed (yes or no)
\item If yes, indicate what transformation you would make
\item Justify these two answers, using both evidence from the data and other considerations
\end{itemize}
Note: being able to communicate with a client or collaborator matters, so there may be instances where either (a) a transformation might help, but you decide against it since it would be difficult to explain to a client/collaborator, or (b) an automatic method like Box-Cox might suggest one power, but you pick a simpler power ``nearby'' because it is easier to explain to a collaborator/client.

\item Fit the model that regresses {\tt courseevaluation} onto all other variables, except for {\tt profnumber}, {\tt multipleclass}, and the 30 {\tt class} variables ({\tt class1} through {\tt class30}).  Use the transformations you recommended in part (a).  Make a table indicating 
\begin{itemize}
\item The t-statistics for each variable
\item The VIFs for each variable
\end{itemize}
in your model.  

\item 
On the basis of this table, and what you know about the definitions of the variables, would you eliminate any variables in your model?  Why or why not?

\item Why might the methods used in parts (b) and (c) not be adequate for deciding which variables to keep, and which ones to eliminate, in a regression model?


% \item What would have changed, and what would have stayed the same, in the table for part (b), if you had used the variable {\tt profevaluation} instead of {\tt courseevaluation} for the dependent variable?

\end{enumerate}

\end{enumerate}

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% \item Ch 5, p. 147, \#2. 

% \item Ch 5. pp. 147ff, \#3.  Kind of a dumb problem the way it is set up.... 

% \item From Gelman \& Hill, Ch 3, consider
% 
% -- \#5 p 54, the beauty data
% 
% -- \#1, p 49, the pyth data -- kind of abstract the way it's set up...  also, no data seems to be available!  PROLLY GOOD WITH EFFORT



\end{enumerate}


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