21. An analyst used multiple linear regression to explore how a big box store's sales (y) are predicted by the store's advertising expenditure dollars (variable x1) and the advertising expenditure dollars of a specialty store (variable x2) in the same market. The estimated regression is y = 651.67 + 92.30x1 - 26.89x2. How are advertising expenditures and sales related in this scenario?
Answer: A
If the specialty store increases its advertising expenditures, it will decrease the big box store's sales.
The regression equation indicates that an increase in the advertising expenditures of the specialty store (x2) negatively impacts the sales of the big box store (y). Specifically, for every dollar increase in the specialty store's advertising, the big box store's sales decrease by approximately 26.89 dollars.
A) If the specialty store increases its advertising expenditures, it will decrease the big box store's sales.
This option is correct because the coefficient of x2 in the regression equation is -26.89, which signifies an inverse relationship. As the specialty store's advertising expenditures rise, the sales of the big box store decline, demonstrating a competitive effect.
B) If the big box store increases its advertising expenditures, its sales will decrease.
This option is incorrect. According to the regression model, an increase in the big box store's advertising expenditure (x1) results in an increase in sales (y) by 92.30 dollars for every additional dollar spent, indicating a positive relationship.
C) If the big box store decreases its advertising expenditures, its sales will increase.
This option is incorrect. The regression indicates that a decrease in the big box store's advertising expenditures would lead to a decrease in sales, as the relationship with x1 is positive. Therefore, reducing expenditures does not result in higher sales.
D) If the specialty store decreases its advertising expenditures, it will decrease the big box store's sales.
This option is incorrect. A decrease in the specialty store's advertising expenditures would likely increase the sales of the big box store, as indicated by the negative coefficient for x2. This suggests that less competition from the specialty store could benefit the big box store.
Conclusion
Option A is definitively correct as it accurately reflects the negative impact of the specialty store's advertising on the big box store's sales. The other options either misinterpret the relationships indicated by the regression coefficients or suggest incorrect outcomes based on the analysis provided. Understanding these relationships is crucial for analyzing competitive dynamics in advertising expenditures.