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

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 regression equation y = 2x + 25,000, the company can calculate the expected sales figure. This calculation yields a sales estimate of $65,000.

A ($40,000) YOUR ANSWER

To arrive at a sales figure of $40,000, the equation would require x (advertising expenditure) to equal only $7,500, calculated as (40,000 - 25,000)/2. Therefore, this choice does not reflect the expected sales based on the planned advertising expenditure of $20,000.

B ($50,000) YOUR ANSWER

For the company to achieve $50,000 in sales, the advertising expenditure would need to be $12,500, derived from the equation (50,000 - 25,000)/2. This does not align with their actual planned expenditure of $20,000, making it an incorrect choice.

C ($65,000) CORRECT

This is the correct answer as substituting $20,000 into the equation yields y = 2(20,000) + 25,000 = 40,000 + 25,000 = 65,000. This calculation aligns perfectly with the company's advertising expenditure of $20,000.

D ($75,000) YOUR ANSWER

To generate sales of $75,000, the advertising expenditure would need to be $25,000, calculated as (75,000 - 25,000)/2. This choice exceeds the planned expenditure of $20,000 and thus does not accurately reflect the expected sales figure.

Conclusion

The regression equation y = 2x + 25,000 allows the company to predict sales based on advertising spending. By substituting the planned advertising expenditure of $20,000 into the equation, the expected sales figure of $65,000 is derived. Other options do not reflect the correct calculations based on the company's actual spending, reinforcing the importance of accurate application of regression analysis in forecasting sales.

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?

The company should expect to generate $65,000 in sales based on the given equation.

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