The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts.
$$
\begin{array}{lcc}
\text { District } & \begin{array}{c}
\text { Adjusted } \\
\text { Gross Income (\$) }
\end{array} & \begin{array}{c}
\text { Percent } \\
\text { Audited }
\end{array} \\
\text { Los Angeles } & 36,664 & 1.3 \\
\text { Sacramento } & 38,845 & 1.1 \\
\text { Atlanta } & 34,886 & 1.1 \\
\text { Boise } & 32,512 & 1.1 \\
\text { Dallas } & 34,531 & 1.0 \\
\text { Providence } & 35,995 & 1.0 \\
\text { San Jose } & 37,799 & 0.9 \\
\text { Cheyenne } & 33,876 & 0.9 \\
\text { Fargo } & 30,513 & 0.9 \\
\text { New Orleans } & 30,174 & 0.9 \\
\text { Oklahoma City } & 30,060 & 0.8 \\
\text { Houston } & 37,153 & 0.8 \\
\text { Portland } & 34,918 & 0.7 \\
\text { Phoenix } & 33,291 & 0.7 \\
\text { Augusta } & 31,504 & 0.7 \\
\text { Albuquerque } & 29,199 & 0.6 \\
\text { Greensboro } & 33,072 & 0.6 \\
\text { Columbia } & 30,859 & 0.5 \\
\text { Nashville } & 32,566 & 0.5 \\
\text { Buffalo } & 34,296 & 0.5
\end{array}
$$
a. Develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported.
b. At the .05 level of significance, determine whether the adjusted gross income and the percent audited are related.
c. Did the estimated regression equation provide a good fit? Explain.
d. Use the estimated regression equation developed in part (a) to calculate a $95 \%$ confidence interval for the expected percent audited for districts with an average adjusted gross income of $$\$ 35,000$$.