\authorandnumber{Carlos C. Rodriguez}
\problemdate{Thu Feb 25 12:56:05 EDT 1999}
\textbook{Statistics by Freedman, Pisani and Purves}
\partname{3 The Regression Method for Individuals}
\chaptername{10 Regression}
\begin{problem}
\score{1}
 For all the men in the Health Examination Survey (ages 18
to 79),

 average height = 68 inches,  SD = 2.8 inches
 average weight = 168 pounds, SD = 28 pounds,  r = 0.4

The average weight of the men whose height was 66 inches is 160
pounds.  The average height of the men whose weight was 160
pounds is closest to
\begin{choice}
\gooditem{68}
\baditem{64}
\baditem{66}
\baditem{62}
\baditem{60}
\end{choice}

\begin{longanswer}
Solution.  Since $(160 -168)/28 = -8/28 = -2/7$ , a weight
of 160 pounds is 2/7 SD's below average.  Since
\[ r \times 2/7 = 0.4 \times 2/7 =  8/70 = .114 \]
the average height of the 160-pounders is
.114 SD's below the average height of everyone in the study, that
is,
\[ 68 - .114 \times 2.8 = 68 - .32 \approx 67.7 inches\]
The correct choice is 68 inches.
\end{longanswer}
\end{problem}
