An accountant wishes to predict direct labor cost (y) on the basis of the batch

Question

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. Data for 12 production runs are given in Table 13.5, along with the Excel output from fitting a least squares regression line to the data.

A By using the formulas illustrated in Example 13.2 (see page 471) and the data provided, verify that (within rounding) b0 = 18.488 and b1 = 10.146, as shown on the Excel output.

B Interpret the meanings of b0 and b1. Does the interpretation of b0 make practical sense?

C Write the least squares prediction equation.

D Use the least squares line to obtain a point estimate of the mean direct labor cost for all batches of size 60 and a point prediction of the direct labor cost for an individual batch of size 60.

Explanation / Answer

A) Using Excel

From above excel th regression model is

y=18.4875+(10.14626)*x

B)

b1 - This is the SLOPE of the regression line. Thus this is the amount that the Y variable (dependent) will change for each 1 unit change in the X variable.
b0 - This is the intercept of the regression line with the y-axis. In otherwords it is the value of Y if the value of X = 0.
Y-hat = b0 + b1(x) - This is the sample regression line. You must calculate b0 & b1 to create this line. Y-hat stands for the predicted value of Y, and it can be obtained by plugging an individual value of x into the equation and calculating y-hat.

Here Slope b1 = 10.146

and intercept bo=18.4875

Yes, the interpretation of b0 make practical sense. Since b0 value is18.488 it is not zero. if it is zero it does not make any sense

C) prediction of the direct labor cost for an individual batch of size 60:

When x=60 then

the regression model is

y=18.488+(10.146)*x

y=18.488+10.146*60

y=627.25

SUMMARY OUTPUT Regression Statistics Multiple R 0.999636 R Square 0.999272 Adjusted R Square 0.999199 Standard Error 8.641541 Observations 12 ANOVA df SS MS F Significance F Regression 1 1024593 1024593 13720.47 5.04E-17 Residual 10 746.7624 74.67624 Total 11 1025340 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 18.48751 4.67658 3.953211 0.002716 8.067438 28.90758 8.067438 28.90758 X 10.14626 0.086621 117.1344 5.04E-17 9.953256 10.33926 9.953256 10.33926

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