Chapter 11.4, Problem 14Q

Burglary and larceny both involve the illegal taking of something of value. The difference, simply put, is that burglary involves unlawful entry to a structure, while larceny does not. While the two crimes might seem similar, the correlation between the two is quite low. A data set to be used for such an analysis is the annual rates of burglary, $x$, and larceny, $y$, from 1975 to 2010. Both variables give the number of crimes per 100,000 U.S. citizens. Calculate the $xy$ correlation. Use the following sums:

$\begin{array}{l}{\displaystyle \underset{i=1}{\overset{36}{\sum }}{x}_i=994.7700,}{\displaystyle \underset{i=1}{\overset{36}{\sum }}{x}_i^2}=28462.1047,\\ {\displaystyle \underset{i=1}{\overset{36}{\sum }}{y}_i}=254.6900,{\displaystyle \underset{i=1}{\overset{36}{\sum }}{y}_i^2=1816.1417,}\\ {\displaystyle \underset{i=1}{\overset{36}{\sum }}{x}_i{y}_i=7051.2633}\end{array}$