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Name \rule{3in}{0.01in}\\[0.5in]
Email \rule{3in}{0.01in}

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\Large Reading Quiz for Sheather Chapter 8
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% ~\\[1em]

% \begin{enumerate}

\noindent
{\bf [Based on Sheather, Ch 8, \#1]}\\
Chapter 6 of Bradbury (2007), a book on baseball, uses regression analysis to
compare the success of the 30 Major League Baseball teams. For example, the
author considers the relationship between $x_i$ , market size (i.e., the population in
millions of the city associated with each team) and $Y_i$, the number of times team
$i$ made the post-season playoffs in the $m_i=10$ seasons between 1995 and 2004.   The author found that ``it is hard to find much correlation between market size (population of the host city) and\ldots{} success in making the playoffs. The relationship\ldots{} is quite weak.''
%
Bradbury's analysis was similar to this:

%\begin{tabular}{p{3in}p{3in}}
%\parbox{3in}{
%\small\tt\obeylines
\begin{verbatim}
> with(baseballdata, plot(PlayoffAppearances ~ Population))
> summary(lm.1 <- lm(PlayoffAppearances ~ Population, 
+ data=baseballdata))
...
Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   1.7547     0.7566   2.319   0.0279 *
Population    0.1684     0.1083   1.555   0.1311
...
Multiple R-squared:  0.07952,   Adjusted R-squared:  0.04664
> abline(lm.1)
\end{verbatim}
%}
\includegraphics[width=3in]{raw-data-plot.jpeg}
%\multicolumn{2}{l}{Figure 1}
%\end{tabular}

~\\[2em]
Another researcher did an analysis like that on the back of this page.

\clearpage


\begin{verbatim}
> ProbOfPlayoffAppearance <- baseballdata$PlayoffAppearances/10
> with(baseballdata,plot(ProbOfPlayoffAppearance~Population))
> summary(glm.1 <- glm(cbind(PlayoffAppearances,10-PlayoffAppearances) 
+ ~ Population,data=baseballdata,family=binomial))
...
Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.45843    0.21102  -6.911  4.8e-12 ***
Population   0.07807    0.02751   2.838  0.00455 **
...
> curve(invlogit(cbind(1,x)%*%coef(glm.1)), add=T)
\end{verbatim}

\includegraphics[width=3in]{phat-data-plot.jpeg}

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\begin{enumerate}
\item Which analysis (the one on the front of the quiz, or on the back) is likely to produce a model whose assumptions are better satisfied (and therefore has more believable results)?

\item Why?

\vfill

\item Can we use AIC and BIC to compare the models from the two analyses?  

\item Why or why not?

\vfill

\end{enumerate}


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