Medium1 markMultiple Choice
Area I: Business AnalysisBARArea IForecasting

CPA · Question 08 · Area I: Business Analysis

A company is using simple linear regression to forecast maintenance costs based on machine hours. The regression output provides the following equation: Y = $5,000 + $12X, where Y is the total maintenance cost and X is machine hours. The R-squared value is 0.85.<br/><br/>If the company expects to operate 2,500 machine hours next month, which of the following statements is correct regarding the forecasted cost?

Answer options:

A.

The forecasted cost is $30,000, and the R-squared indicates that 85% of the variance in machine hours is explained by maintenance costs.

B.

The forecasted cost is $35,000, and the R-squared indicates that 85% of the variance in maintenance costs is explained by machine hours.

C.

The forecasted cost is $35,000, and the R-squared indicates a weak correlation between machine hours and maintenance costs.

D.

The forecasted cost is $30,000, and the R-squared indicates that 85% of the data points fall exactly on the regression line.

How to approach this question

Plug the X value into the equation to get Y. Interpret R-squared as the % of variance in Y explained by X.

Full Answer

B.The forecasted cost is $35,000, and the R-squared indicates that 85% of the variance in maintenance costs is explained by machine hours.✓ Correct
1. Calculation: Total Cost (Y) = Fixed Cost ($5,000) + (Variable Rate ($12) x Machine Hours (2,500)). Y = $5,000 + $30,000 = $35,000.<br/>2. Interpretation: R-squared of 0.85 means 85% of the variation in the dependent variable (Maintenance Costs) is explained by the variation in the independent variable (Machine Hours).

Common mistakes

Misinterpreting R-squared direction; arithmetic errors.

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