These data describe the sales over time at a franchise outlet of a major US oil company. Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a car wash. The response Sales gives the dollar sales of the convenience store. The explanatory variable Volume gives the number of gallons of gas sold, and Washes gives the number of car washes sold at the station.
(a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?
(b) Find the correlation between each pair of variables. Which correlation is largest? Explain why this correlation is so much larger than the others.
(c) Fit the multiple regression of sales on volume and the number of car washes. Show a summary of the fitted model. (Save the diagnostics for part (d).)
(d) Does the fitted model meet the conditions for using the MRM for inference?
(e) Assume that the model meets the conditions for the MRM. Interpret carefully the estimated slope for the number of car washes. In your interpretation, include a range for the effect of this variable.