The Des Moines Register reported the ratings of high school sportsmanship as compiled by the Iowa High School Athletic Association. The participants and coaches from each school were rated by referees. (1 = superior, 5 = unsatisfactory.) A regression analysis of data on the average scores given to football players and coaches is shown below. Linear Fit FBParticipants $= 0.902 + 0.568$ FBCoaches Summary of Fit $\begin{array}{ll} \text { RSquare } & 0.452 \ \text { RSquare Adj } & 0.450 \ \mathrm{~s} & 0.355 \end{array}$ $\begin{array}{l} \text { Analysis of Variance }\ \begin{array}{lrrrr} \text { Source } & \text { DF } & \text { SS } &{\text { MS }} & \text { F Ratio } \ \text { Model } & 1 & 37.505 & 37.505 & 298.2723 \ \text { Error } & 362 & 45.518 & 0.126 & \text { Prob }\text { F } \ \text { C. Total } & 363 & 83.022 & &

Question

The Des Moines Register reported the ratings of high school sportsmanship as compiled
by the Iowa High School Athletic Association. The participants and coaches from each
school were rated by referees. (1 = superior, 5 = unsatisfactory.) A regression analysis
of data on the average scores given to football players and coaches is shown below.

Linear Fit
FBParticipants $= 0.902 + 0.568$ FBCoaches

Summary of Fit

$\begin{array}{ll}
\text { RSquare } & 0.452 \
\text { RSquare Adj } & 0.450 \
\mathrm{~s} & 0.355
\end{array}$

$\begin{array}{l}
\text { Analysis of Variance }\
\begin{array}{lrrrr}
\text { Source } & \text { DF } & \text { SS } &{\text { MS }} & \text { F Ratio } \
\text { Model } & 1 & 37.505 & 37.505 & 298.2723 \
\text { Error } & 362 & 45.518 & 0.126 & \text { Prob }>\text { F } \
\text { C. Total } & 363 & 83.022 & & <.0001
\end{array}
\end{array}$

a) Interpret the value of the correlation between the ratings of coaches and
participants.
b) Interpret the value of the coefficient of determination.
c) Interpret the value of the standard deviation about the least squares line.

Quizplus · Accepted Answer

The Answer is a) Correlation is

\sqrt { .452 } = .672

. This indicates a moderately strong linear relationship between rated sportsmanship for participants and coaches.
b)

r ^ { 2 } = .452

means that about

45 \%

of the observed differences in sportsmanship among participants can be explained by differences in coaches' sportsmanship.
c)

s = .355

is a measure of how far a typical point will be above or below the least squares line.

The Des Moines Register Reported the Ratings of High School =0.902+0.568= 0.902 + 0.568=0.902+0.568

The Des Moines Register Reported the Ratings of High School $= 0.902 + 0.568$