In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). Suppose a random sample of baseball players gave the following information. $$\begin{array} { c | c c c c c }
\hline x & 0.251 & 0.259 & 0.29 & 0.265 & 0.269 \
\hline y & 1.3 & 3.7 & 5.8 & 3.9 & 3.7 \
\hline
\end{array}$$ Compute r.
A)0.001
B)0.923
C)-0.923
D)-0.001
E)none of these choices

Question

In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). Suppose a random sample of baseball players gave the following information. $$\begin{array} { c | c c c c c } 
\hline x & 0.251 & 0.259 & 0.29 & 0.265 & 0.269 \
\hline y & 1.3 & 3.7 & 5.8 & 3.9 & 3.7 \
\hline
\end{array}$$ Compute r.
A)0.001
B)0.923
C)-0.923
D)-0.001
E)none of these choices

Quizplus · Accepted Answer

To compute the correlation coefficient $r$, we need to use the formula for $r$, which involves the means of $x$ and $y$, the standard deviations of $x$ and $y$, and the covariance of $x$ and $y$. Given the data, we calculate $r$ and find that it is approximately 0.923, indicating a strong positive linear relationship between batting average and home run percentage.