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
550	4,900
600	5,400
700	5,900
750	6,500

1. Compute b₁ and b₀ (to 1 decimal).
   b₁  
   b₀  
   
   Complete the estimated regression equation (to 1 decimal).
   =   +  x
   
2. What is the variable cost per unit produced (to 1 decimal)?
   $
   
3. Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.
   r² =  
   
   What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
     %
   
4. 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:

Hence,

a) b1 = 7.6

b0 = 746.7

Regression equation:

y = 746.7 + 7.6 x

b) Change in annual sales = 7.6

c) r2 = 0.959

Percent of variation explained = 95.9 %

d) Predicted sales = $ 4547