A company uses regression analysis to forecast maintenance costs. The regression output is: Y = $50,000 + $2.50X, where Y is total maintenance cost and X is machine hours. The R-squared value is 0.85. If the company expects to operate 40,000 machine hours next month, which of the following statements is correct?

Answer options:

The forecasted cost is $100,000, and the model explains 15% of the variability.

The forecasted cost is $150,000, and the model is not reliable because R-squared is less than 0.90.

The forecasted cost is $150,000, and the independent variable (machine hours) explains 85% of the variation in maintenance costs.

The forecasted cost is $100,000, and the coefficient of correlation is 0.85.

How to approach this question

Plug the X value into the regression equation. Interpret R-squared as the percentage of variance explained.

Full Answer

C.The forecasted cost is $150,000, and the independent variable (machine hours) explains 85% of the variation in maintenance costs.✓ Correct

Calculation: Y = $50,000 + ($2.50 * 40,000) = $50,000 + $100,000 = $150,000. Interpretation: R-squared (Coefficient of Determination) measures the goodness of fit; 0.85 means 85% of the change in maintenance costs is explained by the change in machine hours.

Common mistakes

Confusing R-squared with Correlation Coefficient (r); calculation errors.

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