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# Regression of Labor Cost and Batch Size

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An accountant wishes to predict direct labor cost (y) on the basis of the batch size (x) of a product produced in a job shop. Using labor cost and batch size data for 12 production runs, the following Excel Output of a Simple Linear Regression Analysis of the Direct Labor Cost Data was obtained. The scatter plot of this data is also shown. (See attachment for full problem description)

Regression Statistics

Multiple R 0.99963578
R Square 0.999271693
Adjusted R Square 0.999198862
Standard Error 8.641541
Observations 12

ANOVA
df SS MS F Significance F
Regression 1 1024593 1024593 13720.47 5.04436E-17
Residual 10 746.7624 74.67624
Total 11 1025340

Coefficients Standard Error t Stat P-value
Intercept 18 4.67658 3.953211 0.00271
BatchSize(X) 10 0.08662 117.13 5.04436E-17

Answer the following questions based on the information provided above:

a. Write the regression equation for the LaborCost (y) and BatchSize (x). Note that your equation has to identify the point estimates for &#61538;0 and &#61538;1 in the equation:
y = &#61538;0 + &#61538;1x

b What do you conclude about the relationship between LaborCost (y) and BatchSize (x)? Use the different test statistics provided in the data to support your case.

c. Interpret the meanings of b0 and b1. Does the interpretation of b0 make practical sense for this case? Think carefully about what the value of x will be when y = b0 .

d Estimate the value of LaborCost for a batch size of 10. Use your regression equation and show all your steps.
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#### Solution Summary

This solution determines the regression equation of labor cost and batch size and answers the questions to interpret b0 and b1, and estimating the value of labor cost. All steps are shown with full workings.

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