
The data for this question relate to air pollution in 41 American  cities.
The variables measured were:

\vspace{2mm}

\begin{center}
\begin{tabular}{ll}
\sf{SO2}: & annual mean $\mbox{SO}_2$ content ($\mu$g per $\mbox{m}^3$). \\
\sf{temp}: & average annual temperature ($^\circ$F). \\
\sf{manu}: & number of manufacturing plants employing $\ge 20$ workers. \\
\sf{pop}: & population size (in thousands). \\
\sf{wind}: & average annual wind speed  (mph). \\
\sf{prep}: & average annual precipitation (inches). \\
\sf{days}: & average number of days with percipitation per year. \\
\end{tabular}
\end{center}

\vspace{5mm}

\begin{enumerate}
\item{}
A ordinary regession model that predicts the expected value of \sf{SO2}
using the remaining variables as regressors was obtained using the 
following commands in R:
\begin{verbatim}
> usair.fit<-lm(SO2~.,data=usair.df)
> summary(usair.fit)
Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept) 108.29560   46.18128   2.345  0.02519 * 
temp         -1.22725    0.60602  -2.025  0.05101 . 
manu          0.06497    0.01823   3.565  0.00114 **
pop          -0.03910    0.01557  -2.512  0.01709 * 
wind         -3.18212    1.85407  -1.716  0.09548 . 
prep          0.48142    0.35518   1.355  0.18448   
days         -0.03163    0.15711  -0.201  0.84170   
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 14.84 on 33 degrees of freedom
Multiple R-Squared: 0.5304,	Adjusted R-squared: 0.4451 
F-statistic: 6.213 on 6 and 33 DF,  p-value: 0.0001929 
\end{verbatim}

\item
A set of diagnostic plots for the model from part (A)

\centerline{\epsfig{figure=usair.p1.ps,width=4in,height=6.in,angle=-90}}


\item 
\begin{verbatim}
all.poss.regs(usair.df[,-1],log(usair.df$SO2))
> apr
    rssp sigma2 adjRsq     Cp temp manu pop wind prep days
1 12.198  0.321  0.275 24.673    1    0   0    0    0    0
1 13.066  0.344  0.224 28.989    0    0   0    0    0    1
1 14.987  0.394  0.110 38.546    0    1   0    0    0    0
2 10.640  0.288  0.351 18.925    1    0   0    0    0    1
2 10.661  0.288  0.349 19.030    1    0   0    0    1    0
2 10.887  0.294  0.336 20.150    1    1   0    0    0    0
3  9.049  0.251  0.432 13.011    1    1   0    1    0    0
3  9.073  0.252  0.431 13.129    1    0   0    1    1    0
3  9.430  0.262  0.409 14.906    1    0   0    1    0    1
4  7.183  0.205  0.537  5.729    1    1   0    1    1    0
4  7.746  0.221  0.500  8.531    1    1   0    1    0    1
4  8.078  0.231  0.479 10.182    1    1   1    1    0    0
5  6.644  0.195  0.559  5.047    1    1   1    1    1    0
5  7.093  0.209  0.529  7.279    1    1   1    1    0    1
5  7.170  0.211  0.524  7.666    1    1   0    1    1    1
6  6.634  0.201  0.546  7.000    1    1   1    1    1    1
\end{verbatim}


\centerline{\epsfig{figure=usair.p2.ps,width=4in,height=6.in,angle=-90}}


\item{}

\centerline{\epsfig{figure=usair.p3.ps,width=4in,height=6.in,angle=-90}}




\end{enumerate}
