For the data in Example 14 on crime in Florida, the regression line between y = crime rate (number of crimes per 1000 people) and x = percentage living in an urban environment is ŷ = 24.5 + 0.56x.
a. Using the slope, find the difference in predicted crime rates between counties that are 100% urban and counties that are 0% urban. Interpret.
b. Interpret the correlation of 0.67 between these variables.
c. Show the connection between the correlation and the slope, using the standard deviations of 28.3 for crime rate and 34.0 for percentage urban.