Several studies suggest that the number of violent crimes is related to temperature. Suppose the FBI investigated this relationship between temperature and the number of violent crimes in several...

Several studies suggest that the number of violent crimes is related to temperature. Suppose the FBI investigated this relationship between temperature and the number of violent crimes in several large cities in the United States. A random sample of days was obtained, and the average temperature (x, in °F) and the number of violent crimes per 100,000 people (y) were recorded for each day.

a. Construct a scatter plot for these data, and describe the relationship between the two variables.

b. Find the estimated regression line.

c. Find a 95% prediction interval for an observed number of violent crimes if the average temperature is 80°F. d. Find a 95% prediction interval for an observed number of violent crimes if the average temperature is 60°F.

A recent study suggests that the linguistic diversity in a community is related to the number of traffic accidents.25 A random sample of U.S. cities was obtained and the annual road fatalities per 1000 people (y) and the linguistic diversity (x, Greenberg diversity index) was recorded for each.