You are a local restauranteur in your small to mid-sized town.You hypothesize th
ID: 1129092 • Letter: Y
Question
You are a local restauranteur in your small to mid-sized town.You hypothesize that your sales are a function of your own advertising and that of other three restaurants in town.You decide to obtain 9 months (or 36 weeks) of data on your sales, your advertising expenditures, and the total advertising expenditure of the other three restaurants in order to generate a regression equation.Your multiple regression equation will take the form:
Sales = a + b(Advertising) + c(Competitor Advertising)
where “a” is the intercept, “b” is the coefficient associated with your advertising expenditures (in dollars per week), and “c” is the coefficient associated with the advertising expenditures of the other three restaurants (in dollars per week). You decide that using parameter estimates that are statistically significant at the 10 percent level or better are adequate.
1. What sign do you expect the coefficients a, b, and c to have?
2. Interpret the coefficients a, b, and c. Use the regression output below:
Dependent Variable
Sales
R2
F-Ratio
p-Value on F
Observations
30
0.2247
4.781
0.0150
Variable
Parameter Estimate
Standard Error
T-Ratio
p-Value
Intercept
17508.0
63821.0
2.74
0.0098
Advertising
0.8550
0.3250
2.63
0.0128
Competitor Advertising
-0.284
0.164
-1.73
0.0927
3. Does your advertising expenditure have a statistically significant effect on your sales? Reference the appropriate p-value in your answer.
4. Does advertising by the other three restaurants affect your sales in a statistically significant way? Reference the appropriate p-value in your answer.
5. What fraction of the total variation in sales of your restaurant remains unexplained? What can you do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation?
6. What is the expected level of sales each week when you spend $40,000 per week and the combined advertising expenditures for the other three restaurants are $100,000 per week?
Dependent Variable
Sales
R2
F-Ratio
p-Value on F
Observations
30
0.2247
4.781
0.0150
Explanation / Answer
1.
I expect a>0, i.e. some levels of sales would exist even without advertising expenditure.
Further, I expect b > 0 i.e. as level of own advertising will increase our own Sales will increase.
Also, it is expected that as competitor advertising will increase, our own sales will decrease. That is, c < 0.
2. In the regression output we notice that the results hold true as per our expectations-
a. Intercept is positive.
b. Own advertising coefficient is positive. That is, as own advertising will increase by 1 unit, then Sales will increase by 0.8550 units.
c. Competitor advertising’s coefficient is negative. That is, as competitor’s advertising will increase by 1 unit, own sales will decrease by 0.284 units.
3. The own advertising affects Sales positively in a statistically significant way at 10% level of significance. This is because p-value is less than 0.10.
4. At 10% level of significance, the competitor advertising affects Sales negatively in a statistically significant way at 10% level of significance. This is because p-value is less than 0.10.
PS: According to chegg guidelines in event of multiple parts, only first four are attempted. However, you may repost the qsn asking for solution of specific questions/parts.
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