Chapter 13, Problem 35PS

What is the relationship between the price of crude oil and the price you pay at the pump for gasoline? The file Oil & Gasoline contains the price $\text{(\$)}$ for a barrel of crude oil (Cushing, Oklahoma, Spot price) and a gallon of gasoline (U.S. average conventional spot price) for 338 weeks. ending June 2, 2017.

a. Construct a scatter plot with the price of oil on the horizontal axis and price of gasoline on the vertical axis.

b. Use the latest-squares method to develop a simple linear regression equation to predict the price of a gallon of gasoline using the price of a barrel of crude oil as the independent variable.

c. Interpret the meaning of the slop, $b_1,$ in this problem.

d. Plot the residuals versus the time period.

e. Compute the Durbin-Watson statistic.

f. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals?

g. Based on the results of (d) through (f), is there reason to question the validity of the model?

h. What conclusions can you reach concerning the relationship between the price of a barrel of crude oil and the price of a gallon of gasoline?