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?

Rationale

$65,000.

By substituting the advertising expenditure of $20,000 into the linear equation y = 2x + 25,000, we can predict the expected sales figure. This calculation reveals that the company should anticipate generating sales of $65,000 based on their advertising investment.

A ($40,000) YOUR ANSWER

This figure results from an incorrect calculation. If the company were to substitute an advertising expenditure of $7,500 into the equation (y = 2(7,500) + 25,000), it would yield $40,000. However, this does not reflect the $20,000 expenditure specified in the question.

B ($50,000) YOUR ANSWER

Choosing this option indicates a misunderstanding of the equation. If one mistakenly assumed a lower level of advertising expenditure, such as $12,500, it could yield a sales figure of $50,000. The correct approach, however, involves substituting the full $20,000 expenditure into the equation.

C ($65,000) CORRECT

This is the correct answer. By plugging in $20,000 for x in the equation (y = 2(20,000) + 25,000), the calculation becomes y = 40,000 + 25,000, resulting in expected sales of $65,000. This demonstrates how advertising expenditures translate directly into sales based on the given linear relationship.

D ($75,000) YOUR ANSWER

This option suggests a misunderstanding of the linear model. If the company spent $25,000 on advertising, the equation would yield $75,000 (y = 2(25,000) + 25,000). However, the question specifies an expenditure of $20,000, making this choice incorrect.

Conclusion

The regression analysis equation y = 2x + 25,000 effectively models the relationship between advertising expenditures and sales. By substituting the correct advertising expenditure of $20,000 into the equation, the company can accurately forecast expected sales of $65,000. Understanding how to apply the linear model is crucial for making informed financial decisions based on advertising investments.

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?

$65,000.

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