It’s rare that you’ll find a gas station these days that only sells gas. It’s become more common to find a convenience store that also sells gas. These data describe the sales over time at a franchise outlet of a major U.S. 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 column labeled Sales gives the dollar sales of the convenience store, and the column Volume gives the number of gallons of gas sold.
(a) Scatterplot Sales on Volume. Does there appear to be a linear pattern that relates these two sequences?
(b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate rep-resents a large extrapolation and is consequently not reliable.
(c) Interpret the summary values r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) Estimate the difference in sales at the convenience store (on average) between a day with 3,500 gallons sold and a day with 4,000 gallons sold.
(e) This company also operates franchises in Canada. At those operations, gas sales are tracked in liters and sales in Canadian dollars. What would your equation look like if measured in these other units? (Note: 1 gallon = 3.7854 liters, and use the exchange rate $1 = $1.1 Canadian.) Include r2 and se as well as the slope and intercept.
(f) The form of the equation suggests that selling more gas produces increases in sales at the associated store. Does this mean that customers come to the station to buy gas and then happen to buy something at the convenience store, or might the causation work in the other direction?
(g) On one day, the station sold 4,165 gallons of gas and had sales of $1,744 at the attached convenience store. Find the residual for this case. Are these sales higher or lower than you would expect?
(h) Plot the residuals from this regression. If appropriate, summarize these by giving the mean and SD of the collection of residuals. What does the SD of the residuals tell you about the ft of this equation?