A Sports Analyst Was Interested in Finding Out How Well

question 696

Essay

A sports analyst was interested in finding out how well a football team's winning
percentage (stated as a proportion) can be predicted based upon points scored and points
allowed. She selects a random sample of 15 football teams. Each team played 10 games.
She decided to use the point differential, points scored minus points allowed as the
predictor variable. The data are shown in the table and regression output given below. $\begin{array}{|c|c|}\hline \text { Point Diff } & \text { Win Pct } \\\hline-75 & .100 \\\hline-60 & .300 \\\hline-40 & .200 \\\hline-33 & .300 \\\hline-21 & .400 \\\hline-15 & .500 \\\hline 5 & .500 \\\hline 14 & .700 \\\hline 20 & .600 \\\hline 28 & .700 \\\hline 31 & .800 \\\hline 45 & .900 \\\hline 56 & .700 \\\hline 72 & .600 \\\hline 80 & 1.000 \\\hline\end{array}$

Regression Analysis: Win Pct versus Point Diff
$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 0.51802 & 0.03071 & 16.87 & 0.000 \\ \text { Point Diff } & 0.0049500 & 0.0006682 & 7.41 & 0.000 \end{array}$
$$S = 0.117511 \quad R - S q = 80.88 \quad R - S q ( a d j ) = 79.48$$
Is there evidence of an association between Point Differential and Winning Percentage? Test an appropriate hypothesis and state your conclusion in the proper context.