If you operate a refinery and need to buy crude oil (and haven’t made a prior arrangement that locked in a lower price), the spot price for crude oil determines what you can expect to pay per barrel (42 gallons). The data for this exercise also include the price of gasoline sold at service stations to retail customers. Both series were compiled by the Department of Energy and represent national averages. The data are weekly from January 1997 through May 2012.
Motivation
(a) The rise of gasoline prices along with record profits at Exxon-Mobile produced stories of corporate greed. How could you use a statistical model to explain the rise of prices at the pump?
Method
(b) If price increases are immediately passed on to consumers on a 1-for-1 basis, what should you expect for the slope of a simple regression of the price of gas (in dollars per gallon) on the price of crude oil (in dollars per barrel)?
(c) Do you think it will be easier to work with prices directly or with percentage changes? Use plots of the time trends in the prices and in the percent-age changes to form your answer.
(d) Price changes are unlikely to immediately move through the system. It takes a while for refined oil to reach the pump. If the effects of price changes in crude take several weeks to reach the pump, what type of transformations of crude prices can you expect to be useful in explaining the rise in prices at the pump?
Mechanics
(e) Fit the simple regression of gasoline prices on contemporaneous prices of crude oil. Is the slope near what you expected?
(f) Examine the residuals from the simple regression that you ft in part (e). Do these meet the conditions for fitting the simple regression model? In particular, what flaw common to time series regressions is evident in the residuals from this model?
(g) Fit the simple regression of the percentage change in price of gasoline on the percentage change in the price of crude oil in the same period. What does the slope of this regression tell you?
(h) Do the residuals from the simple regression in percentage changes meet the conditions for fitting the SRM?
(i) Add six lags of the percentage change in the price of crude oil to the regression ft in part (g). (The model will then have seven predictors: the current percentage change as well as the percentage changes from the prior six weeks.) Does the ft improve by adding the collection of lags? What is the interpretation of the coefficients of the lagged variables?
(j) Does collinearity have a strong effect on the ft of the multiple regression in part (i)?
(k) Are the residuals from the regression ft in (i) nearly normal? Do any stand out?
(l) Does the model you created in part (i) satisfy the conditions of the multiple regression model?
Message
(m) What does this analysis mean for being able to predict future movements in the price of gasoline based on movements in the price of crude oil?