Question

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 3,500 450 4,500 4,900 5,400 5,900 6,500 a. Compute bi and bo (to 1 decimal). Complete the estimated regression equation (to 1 decimal). b. What is the variable cost per unit produced (to 1 decimal)? c. Compute the coefficient of determination (to 3 decimals). Note: report pe between 0 and 1. po2 = What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)? % d. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: Cost Independent Variable: Unit Cost 746.666677.6 Unit Sample size: 6 R (correlation coefficient) = 0.9791271 R-sq 0.95868988 Estimate of error standard deviation: 241.52295 Parameter estimates: Parameter Estimate Std. Err. Alternative DF P-value T-Stat 746.66667 464.15993 0 41.6086409 Intercept 0.183 Slope 7.6 0.78881064 0 49.6347585 0.0006 Analysis of variance table for regression model: P-value Source DF SS MS F-stat Model 5415000 5415000 92.828571 0.0006 Error 4 233333.33 58333.333 Total 5 5648333.3 Predicted values: X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 500 114.98792 (4227.409, 4865.9243) (3803.9712, 5289.3621) 4546.6667

Hence,

a) b1 = 7.6

bo = 746.7

Regression equation:

y = 746.7 + 7.6 x

b) variable cost per unit = 7.6

c) r² = 0.959

Percent of variation explained = 95.9 %

d) Estimated cost = $ 4547