Question

An important application of regression analysis in accounting is cost estimation. By developing an estimated
regression equation relating volume and cost, an analyst can estimate the cost associated with a particular
manufacturing volume. Consider the following sample production volumes and total cost data.
Production Volume (units) Total Cost ($)
400 6590
450 8235
550 8895
600 9720
700 10,540
750 11,530
a. Use these data to develop an estimated regression equation that could be used to predict the total cost for a
given production volume.
b. Compute the coefficient of determination. Interpret the coefficient of determination in terms of the percentage of the variability in total cost that can be explained by the regression of cost on production volume.
c. The company’s production schedule shows that 580 units must be produced next month. Determine the
estimated cost for this operation.
d. Use a one percent level of significance to test whether the production volume is significantly related to the
total cost and state your conclusion.
e. Support your results in part (d) with an interval estimate of the slope of the regression (i.e. the variable cost of production)
f.prepare ANOVA table

Answer 1

Here we use excel function. Data >> Data Analysis>>> Regression >>>

then for y range select data column total cost and for x range select data column as production volume.

Excel output as follow :

a)  estimated regression equation that could be used to predict the total cost for a given production volume.

Total cost = 2387.7966 + 12.1127 * Production volume

b)   Compute the coefficient of determination. Interpret the coefficient of determination in terms of the percentage of the variability in total cost that can be explained by the regression of cost on production volume.

Coefficient of determination denoted by R-square = 0.9420 = 94.20 %

So we interpreat it as , 94.20% of the variability in total cost that can be explained by the regression of cost on production volume.

c ) The company’s production schedule shows that 580 units must be produced next month. Determine the
estimated cost for this operation.

we sure regression line as , Total cost = 2387.7966 + 12.1127 * 580 = 9413.17

d)  Use a one percent level of significance to test whether the production volume is significantly related to the
total cost and state your conclusion.

H0 : the production volume is not significantly related to the total cost

H1 :the production volume is significantly related to the total cost

So from ANOVA table p- value = 0.0013 < 1% ; since reject H0

Conclusion : At 1% level of significance we conclude that , the production volume is significantly related to the
total cost and state your conclusion

e. Support your results in part (d) with an interval estimate of the slope of the regression (i.e. the variable cost of production)

confidence interval is as 7.9410 to 16.2844 . so we say that value of coefficient of variable cost production is lies in this interval so the production volume is significantly related to the
total cost and state your conclusion

f ) In excel output you already get confidence interval .