2. 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 based on the given equation.
By substituting the advertising expenditure of $20,000 into the equation y = 2x + 25,000, where x represents the advertising expenditure, we find that sales (y) will equal $65,000.
A) $40,000
This option is incorrect because substituting $20,000 into the equation yields a result far greater than $40,000. Specifically, using the equation y = 2(20,000) + 25,000 results in $65,000.
B) $50,000
This choice is also incorrect. The calculation would not yield $50,000 when placing $20,000 into the equation. The correct calculation shows that the sales figure is significantly higher than this amount.
C) $65,000
This is the correct answer. When the advertising expenditure of $20,000 is substituted into the equation, it results in y = 2(20,000) + 25,000, which equals $65,000, accurately reflecting the expected sales figure.
D) $75,000
This option is incorrect as well. Following the same substitution process, it is evident that the calculated sales figure will not reach $75,000, which is above the result derived from the equation.
Conclusion
The calculation clearly demonstrates that the expected sales figure is $65,000 when advertising expenditures are set at $20,000. All other options fail to align with the results of the regression equation, making option C the only correct choice.