Question

Question 3: Jim's Lumber wanted to determine the relationship between its monthly operating costs and a potential cost driver, machine hours. The output of a regression analysis performed using Microsoft Excel showed the following information: 0.92 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 148,38 ANOVA df F 52.06221 Significance F 0.0000 1 Regression Residual Total SSMS 573116.9 573117 110083.1 11008 683200 10 11 t Coefficients Standard Error 1263.34 806.85 0.26 0.05 Stat 1.57 Intercept X Variable 1 P-value 0.15 0.00 Lower 95% (534.43) 0.15 Upper 95% 3061.11 0.37 5.10 A. Given this output, write the firm's monthly cost equation. 2 points

Answer 1

A)

The linear regression equation is given as

y = a + b x

where y = dependent variable = monthly operating costs

x = independent variable = machine hours

a = intercept

b = slope

Using the values from the regression output, the equation for the operating costs is

Monthly operating costs = 1263.34 + 0.26 $\times$ Machine hours

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B)

This equation can be used to predict the monthly operating costs because the value of R square from the regression output is 0.88 which suggests that 88% of the variation in the monthly operating costs can be explained from the variation in machine hours. The high value of R square suggest a measure of good fit between the variables, hence the equation should be used to predict the monthly operating costs.

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C)

When Jim's lumber uses 3200 machine hours during the month, the monthly operating cost is

Monthly operating costs = 1263.34 + 0.26 $\times$ 3200

Monthly operating costs = $ 2095.34