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	4,200
450	5,200
550	5,600
600	6,100
700	6,600
750	7,200

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

SOLUTION

A. The regression line of Y on X is

Y = Ybar + (cov(x,y)/var(x)) (x-xbar)

=5616.6667 + (118750/941388.889) (X-575)

Y = 1246.667 + 7.6X

b) The variable cost per unit produced is 7.6

c) From excel,, r^2 = 0.9586, that mean, 95.86% of the variatio in total cost can be explained by prdouction volume

d) Given X = 500 units

Total cost of this operation is

Y = 1246.667 + 7.6X = 1246.667 + 7.6(500) = 5046.667