Chapter 11.4, Problem 15Q

A common saying in golf is “You drive for show, but you putt for dough.” To see if there is any truth in this assertion, data for ninety-six top money-winning golfers were examined. For each, their money earnings in 2014 ( $y$, in $ millions), their average yards per drive $\left(v\right)$, and their average number of putts $\left(x\right)$ were tallied.

• (a) Show that the correlation coefficient between the putting average and earnings reveal a slightly stronger relationship than that for driving and earnings. Use the following sums:

  $\begin{array}{l}{\displaystyle \underset{i=1}{\overset{96}{\sum }}{v}_i=27,989,}{\displaystyle \underset{i=1}{\overset{96}{\sum }}{v}_i^2}=8,167,723,\\ {\displaystyle \underset{i=1}{\overset{96}{\sum }}{y}_i}=230.87,{\displaystyle \underset{i=1}{\overset{96}{\sum }}{y}_i^2=734.32,}\\ {\displaystyle \underset{i=1}{\overset{96}{\sum }}{v}_i{y}_i=67658.00,}\end{array}$ and also ${\displaystyle \underset{i=1}{\overset{96}{\sum }}{x}_i}=169.31,{\displaystyle \underset{i=1}{\overset{96}{\sum }}{x}_i^2}=298.64,{\displaystyle \underset{i=1}{\overset{96}{\sum }}{x}_i{y}_i}=406.37$

• (b) For each correlation $r$, compute $r^2$ to show that neither the $v$ nor the $x$ variable alone is a good predictor of earnings.