52. A company runs a regression analysis to determine sales based on advertising expenditures, which can be shown in a linear equation as y = 2x + 25,000. The company plans to spend $20,000 on advertising. Which sales figure should the company expect to generate based on the given equation?
Answer: C
The company should expect to generate $65,000 in sales.
By substituting the advertising expenditure of $20,000 into the equation y = 2x + 25,000, where x represents the advertising expenditure, the expected sales can be calculated as y = 2(20,000) + 25,000, resulting in $65,000.
A) $40,000
This option is incorrect because when $20,000 is plugged into the equation, it calculates $65,000, not $40,000. The value obtained from y = 2(20,000) + 25,000 does not support this figure.
B) $50,000
This option is also incorrect. Substituting $20,000 into the equation produces $65,000 in sales, not $50,000. The linear equation does not yield this amount based on the given input.
C) $65,000
This is the correct answer. By inserting the value of $20,000 into the equation y = 2(20,000) + 25,000, the computation results in $65,000, which represents the expected sales figure based on the company's planned advertising expenditure.
D) $75,000
This option is incorrect as well. The calculation using the equation with an advertising expenditure of $20,000 results in $65,000, not $75,000. Thus, this figure does not align with the output of the regression equation.
Conclusion
The correct expected sales figure is $65,000, derived directly from the equation by substituting the planned advertising expenditure. All other options fail to reflect the accurate calculation based on the linear model provided, confirming that C is definitively the right choice.