Question

BOB’S SERVICE STATION AND DINER “Sylvia, we have been operating this service station and diner for many years. Lately, I have the feeling that my income has declined. I think that there are opportunities out there that I have not taken advantage of. I want to pass this business on to my sons and am not comfortable with our current position and strategy.” The words above, spoken to Sylvia, the primary accountant for Bob’s, reveal a number of concerns Bob has concerning his operation. Bob’s Service Station and Diner (Bob’s) is an independently owned service station and restaurant on a major interstate highway. Bob has been in operation for over a decade and customers have liked to frequent his business. Often they choose their routes to stop at places like his with low fuel prices and to enjoy food like the juicy burgers and good food Bob’s provides. He has a great reputation with his customers, especially truckers, and enjoys their business. Bob has noticed, however, that when busiest with truckers, fewer families stop by. Bob has made a pretty good living running the place. However, even though his income continues to seem satisfactory, it does not seem to buy as much as before. This perception, as well as the maturity of his sons, Jason and Bob Jr., has heightened Bob’s concern over the future of his operation. Bob wants to know what he can do to make this a more profitable business and pass on a more effective operation to his sons. Bob knows that his operation attracts many commercial truckers. However, he is also popular with families stopping to use the facilities and eat in the restaurant after filling up the family vehicle on vacations. Over the past decade Bob’s typical markup on diesel is about 1 cent and on gasoline is about 1.5 cents. This fuel pricing follows the typical process in this business of taking the delivery price and marking it up between 1 and 5 cents per gallon. Bob has also noticed an ebb and flow by season – summer and winter being highest and spring and fall being lower. (Winter is December, January, February. Summer is June, July and August.) Bob knows that he has some control over fuel prices and can alter the prices of his typical meal. The dilemma he faces is to know in what direction he should change them or whether or not he should modify his pricing practice at all. Also, he does not know what other activities or attractions he could add that might increase his profits. If he raises prices, he knows that he will reduce sales. At lower prices, he will sell more but incur greater costs. Bob is getting ready to step back from his business and turn the operation over to his sons. Before he does that, he wants to be comfortable in leaving his sons with a well-defined pricing strategy, based upon data. Following up on the expression of Bob’s future concerns, Sylvia, his accountant, has gathered a substantial amount of information regarding his firm’s performance over the past decade. This data is available in an Excel file on the course web site.

QUESTION: Use simple regression to estimate the marginal profit contribution from fuel sales. Use it again to estimate the marginal profit contribution from food sales. Compare and interpret your estimates.

Please find DATA here:

https://www.csun.edu/~ba44982/BUS302%20-%20Spring%202020/Case5/Bob's%20Service%20Station%20and%20Diner%20-%20Student%20Data%20Spreadsheet%20-%20rev%201.xlsx

Answer 1

To test whether the real profit of Bob changes significantly over time, a simple linear regression model is fitted over time. If the regression coefficient slope is significant then we can consider that the real profit change over time.

The given data is about the real profit made by Bob recorded monthly.

Let,

Y: Real profits

X: Regressor is time (We take 1,2,......108 values as X)

n = 108

We say that the change in real profit over time is significant if the regression line between Y and X is significant. i.e.

Linear regression model is given by

The least square estimate of Beta1 and Beta0 are'

S.E of is

Thus to check whether there is significant change in real profit, this can be done by testing the null hypothesis

H0:

vs.

H0 :

The test statistic is,

Therefore, Itcall < ttab, hence we accept the null hypothesis. Hence the change in real profit over time is not significant.

The slope is -21.05. This means that the average real profit decreases by $ 21.05 per month. But this decrease is not significant