Question

For my homework, I'm supposed to answer the following,

Petro Corporation is a large petroleum company that owns and operates gasoline stations throughout Canada. The company wants to expand revenue by building new stations. Therefore, the senior management wants someone to help them understand what a good strategy is to operate the new stations in order to have more sales from those stations with reasonable investment in building and operating them. You are a business analyst working for the company. And your boss assigns the project to you. The data tab named FUEL contains information from 192 self-service gas stations in one-year period. GALLONS is the average monthly fuel sales (both gasoline and diesel) in number of gallons. A station that operates 24 hours a day is indicated when HOURS=1; HOURS=0 for those open 18 hours per day. CARWASH is 1 if the station has a car wash on site and 0 if not. When LOCATION=1, that station is located along a highway either in a metropolitan or rural area. LOCATION=2 indicates a station located at an inner-city or metropolitan location but not along a highway. Finally, rural stations not alongside highways are noted by LOCATION=3.

My question is what kind of statistical test should I be using for this?

Answer 1

It is suggested to use the technique of regression analysis

Dependent variable:

• GALLONS is the average monthly fuel sales (measured by the ratio scale of measurement)

Independent variables:

• HOURS with the value 1 if open 18 hours a day, and value 0 otherwise (measured by the nominal scale of measurement)
• CARWASH with value 1 if the station has a car wash, and value 0 otherwise (measured by the nominal scale of measurement)
• LOCATION (measured by the nominal scale of measurement).

The expected regression equation is in the form of:

GALLONS = bo + b1* hours + b2*carwash + b3*location

If the gasoline station is open 18 hours a day, the average monthly fuel sales is b1 units more as compared to the station who is not open 18 hours a day. If the gasoline station has a car wash, the average monthly fuel sales is b2 units more as compared to the station who does not has a car wash. With one unit increase in location, the average monthly fuel sale is increased by b3 units. Y

Hypothesis test of Model:

Null Hypothesis: Hoi: Model is not significant. V/s Alternative Hypothesis: H1i: Model is significant. I use F test statistic to test this. If p-value < alpha, I reject Ho at 5% level of significance otherwise I fail to reject it.

Hypothesis test of slope

Null Hypothesis: Hoi: βi=0, βi is not significant, i.e. Xi should be included in the model. V/s Alternative Hypothesis: H1i: βi≠0, βi is significant, i.e. Xi should not be included in the model. If p-value < alpha, I reject Hoi at 5% level of significance otherwise I fail to reject it.