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.

In the Microsoft Excel Online file below you will find a sample of production volumes and total cost data for a manufacturing operation. Conduct a regression analysis to explore the relationship between total cost and production volume and then answer the questions that follow.

Production Volume (units)	Total Cost ($)
400	4100
450	5100
550	5500
600	6000
700	6500
750	7100

1. Compute b₁ and b₀ (to 1 decimal).

   b₁

   b₀

   Complete the estimated regression equation (to 1 decimal).

   =  + x

2. According to this model, what is the change in cost (in dollars) for every 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

a)

x = Production Volume, y = total cost

X	Y	X⋅Y	X⋅X
400	4100	1640000	160000
450	5100	2295000	202500
550	5500	3025000	302500
600	6000	3600000	360000
700	6500	4550000	490000
750	7100	5325000	562500

b1 = 7.6

b0 = 1346.7

y = 1346.7 + 7.6 x

b) 7.6

c)

r = 0.9791

r² = 0.959

95.9 percentage of the variation in total cost can be explained by the production volume

d)

x = 500

y = 1346.7 + 7.6 ( 500)

y = 5146.7

= 5147