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 regression equation $y = 2x + 25,000$, we find that the expected sales figure is $65,000.

A ($40,000) YOUR ANSWER

To arrive at this figure, one would have to incorrectly calculate the equation, perhaps by misapplying the values or misinterpreting the coefficients. Specifically, substituting $20,000 into the equation yields different results, indicating that this choice is not derived from the correct application of the regression formula.

B ($50,000) YOUR ANSWER

This choice may result from an incorrect understanding of the linear relationship between advertising expenditure and sales. By using the equation $y = 2(20,000) + 25,000$, one should find a higher sales figure than $50,000, making this option an underestimation of expected sales.

C ($65,000) CORRECT

This is the correct calculation. Substituting $20,000 for $x$, we compute $y = 2(20,000) + 25,000$ which results in $y = 40,000 + 25,000 = 65,000$. This is the expected sales figure based on the regression analysis.

D ($75,000) YOUR ANSWER

This figure suggests an overestimation of sales given the linear equation provided. A calculation error or a misunderstanding of the linear relationship could lead to this option being chosen, as the correct computation results in $65,000 instead of $75,000.

Conclusion

The regression analysis indicates a direct relationship between advertising expenditures and expected sales. By correctly substituting the planned advertising expense of $20,000 into the equation $y = 2x + 25,000$, the company can accurately anticipate sales of $65,000. Misinterpretations of the equation can lead to significant underestimations or overestimations, emphasizing the importance of precise calculations in data analysis.

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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