You are a local restauranteur in your small to mid-sized town.You hypothesize th
ID: 1129091 • 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) The sign of the parameter is determined by looking at the parameter estimates of intercept, advertisement and competitor advertisement. So for intercept coeffecient is postive, advertisement is positive and competitor advertisement is negative.
2) The coeffecients a,b,&c determines the relationship between the independent variables and the dependendt variable.
a is the intercept , which tells that sales (y variable) will be at 30 units if no other factor effect it.
b is the coeffecient which tells that if advertisement increase by one unit then the sales will increase by .8550 units.
C is the coeffecient which tell uc that id competitors advertising increase by one unit then the sales of our company will decrease by .284units.
3)For adversiting expenditure to be statistically significant the p-value should be less tha.05. If we see the p-value of advertisinf expenditure then it is .0098 which is less than .05. Hence it is statistically significant.
4)The p value of other competitor advertisemne tis .0927 which is more than .05. Hence it is not significant.
5) R2 value tell us about how much percentage of sales(y) is explained by the independent variable. The r2 vakue is .2247. which means 22.47% is explained whereas 100-22.47=77.53% is unexplained . The power of the explanatory variable is low. other explanatory variable like marketing expense, geographical presence etc can be used.
6) Just substitute the values given in the equation to get the expected sales.
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