Question 1. To obtain an initial overview of the data, calculate the minimum, average, and maximum value of the variables Sales, Fuel Volume, TV, and Radio.
Minimum Value:
The minimum value of variable sales is 23,688.
The minimum value of Fuel Volume is 60,227.
The minimum value of TV is 0.
The minimum value of Radio is 0.
Average Value:
The average value of variable sales is 24,968
The average value of Fuel Volume is 63,107.
The average value of TV is 91.
The average value of Radio is 101.
Maximum Value:
The maximum value of variable sales is 26,765.
The maximum value of Fuel Volume is 65,196.
The maximum value of TV is 180.
The maximum value of Radio is 237.
Table 1:  Sales  Fuel Volume  TV  Radio 
Minimum Vale 
23,688 
60,227 
0 
0 
Average Value 
24,968 
63,107 
91 
101 
Maximum Value 
26,765 
65,196 
180 
237 
Question 2. Customers visit EuroPet’s gas stations to buy gasoline and convenience items at the colocated cstores. For an investigation of the relationship between cstore sales and gasoline sales run a regression of sales against fuel volume.
The Regression model has been used to determine the relationship between sales and the Fuel volume and the results are shown in the Table 2 below and the following below questions have been answered using the Regression model shown in the Exhibit 1.
2.a Is there a statistically significant relationship between cstore sales and fuel volume?
There is a statistical significant relationship between cstore and fuel volume and it shows that at 95% significance level, the fuel volume would be 0.71025. It means that the sales volume of c store is not totally dependent on the fuel volume, but it is independent and any changes in the fuel volume will not affect the sales value of the cstore and the relationship between these two sales and fuel volume is highly independent.
2.b Provide estimates for average cstore sales in the data set for weeks when fuel volume levels were at the smallest, average, and largest observed value, respectively.
The estimates for average cstore sales when fuel volume is minimum is around (–0.516642547), the average value is around (0.10355302) and the largest observed value is around (0.723748586). These values come across at the points where fuel volume values are minimum, average and maximum respectively.
2.c Provide respective 95 percent intervals for your three estimates in part b. Comment on the widths of the three intervals.
With the data used to create the regression model, the plot has been created using the 95% confidence interval level with the conditional mean, when fuel volume is 0.1035 the sales interval values are in between 20714.27 to 57581.29 and the margin of error is around 1169.32.
2.d Comment on the relationship (cause and effect) between cstore sales and fuel volume.
The relationship between cstore and fuel volume is weak as the fuel volume is not affecting the sales of the cstore, but the fuel volume is helping with the sales of the cstore. So if there would be lower customers to fill up their car’s fuel they would also purchase from the cstore but that would not impacted in higher relationship.
Question 3. Run a regression of cstore sales against TV and radio GRPs.
Refer the Excel sheet and Exhibit 1 for the regression model.
3.a Do the two advertising variables have a statistically significant effect on cstore sales?
The two advertising variable TV and Radio has significant impact on the sales of cstore is highly positive, representing the strong effects they have on cstore. The significance defines that cstore sales is dependent on the advertising made on TV and radio and it generates more awareness among the customers purchase from the cstores while fueling their cars. The significant of TV and Radio is around 0.9747.
3.b Provide an estimate for cstore sales for a particular week with 40 TV GRPs and 80 radioGRPs.
The sales of cstore in a particular week in which the TV GRP would be around 40 and Radio GRPs would be around 40 is given below:
Table 2:
ANOVA 


df 
SS 
MS 
F 
Significance F 
Regression 
2 
81002.5667 
40501.28335 
0.02563308 
0.974783708 
Residual 
7 
11060277.83 
1580039.69 

Total 
9 
11141280.4 
3.c Provide a 95 percent interval for your answer in part b.
The significant interval level shown above in the table is around 0.9747.
3.d Emily Tyler demands proof of the profitability of cstore advertising. Based on your regression, does advertising appear too sufficiently boost cstore sales to justify the advertising spend? Provide an estimate for the net impact of cstore advertising.
The net impact of the advertising that would boost the sale is given in the below table.
Table 3:
RESIDUAL OUTPUT 

Observation 
Predicted Sales 
Residuals 
Standard Residuals 
1 
25026.00213 
162.0021327 
0.14613659 
2 
25026.00213 
1217.002133 
1.09781605 
3 
25053.95554 
577.9555409 
0.52135395 
4 
25053.95554 
225.0444591 
0.203004919 
..............
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EuroPet SA was a multinational company operating gas stations in many European countries. There was a growing tendency to supermarkets to make filling stations in their retail operations, which develops into a serious threat to EuroPet. As a result, in the mid1990s, the company began to develop its own brand and convenience stores with gas stations combined. However, the company is spending more money on advertising stores than its competitors did. Management now had to decide if the increase in sales due to promotional efforts justified the cost of advertising by analyzing market data from one large metropolitan area. Marseille, France "Hide
Karl Schmedders, I. Lyle Campbell Source: Kellogg School Management 12 pages. Publication Date: December 31, 2007. Prod. #: KEL368PDFENG