\authorandnumber{Carlos C. Rodriguez}
\problemdate{Thu Feb 25 13:07:51 EDT 1999}
\textbook{Statistics by Freedman, Pisani and Purves}
\partname{3 The Regression Method for Individuals}
\chaptername{10 Regression}
\begin{problem}
\score{1}
A doctor selects at random 400 patients admitted to a large
metropolitan hospital. For each patient, he records the
temperature taken when the patient is first admitted and the
temperature 24 hours later. He finds that the temperatures taken
when the patients are first admitted have an average of 101
degrees and an SD of 1.5 degrees. The temperatures taken 24 hours
after admission average 99 degrees, with SD equal to 0.5 degrees.
The correlation between the two sets of temperatures is 0.6. The
scatter diagram of the temperatures is football-shaped, and the
histograms of both sets of temperatures follow the normal curve.
 Consider those patients who had temperatures of 103 degrees
when first admitted.  Their temperatures 24 hours later have an
average value closest to

\begin{choice}
\gooditem{99.7}
\baditem{100.4}
\baditem{102}
\baditem{97.4}
\baditem{98.7}
\end{choice}

\begin{longanswer}
The average temperature after 24 hours for someone with
innitial temperature of 103 degrees is given by the hight
of the regression line of temps. 24 hours later on innitial temps.

Hence,
\[ Final temp = 0.6\left(\frac{103-101}{1.5}\right) = 1.3 SUs. \]

Transforming to degrees this is,
\[ Final temp = 99 + 1.3\times 0.5 = 99.7 degrees \]

\end{longanswer}
\end{problem}
