The federal highway commission wanted to study if speed limit and auto fatalities were related. Below are the speed limits of 8 randomly selected highways (that are similar in length) and the corresponding number of yearly fatalities on that highway.

Speed limit (mph): 70 70 60 65 70 55 65 80

Fatalities: 9 12 8 10 14 8 9 15

a. Draw a scatter plot

b. What is r? Use r to describe the correlation

c. Perform a hypothesis test for correlation

d. Draw a linear regression equation

e. What is the slope of this regression equation? Explain what this slope means in the context of this problem.

f. Use the regression equation to predict the number of fatalities on a highway that has a speed limit of 75

g. Draw a 95% confidence interval for your prediction above

h. Predict the speed limit of a highway that had 45 fatalities last year. Does this work well? Explain.

i. Determine r^2 and explain what it means in the context of this problem