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	4500
450	5500
550	5900
600	6400
700	6900
750	7500

Production Target	Est. Cost ($)
500

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).

Consider the given problem here we have given the data on “production” and the corresponding cost. So, here the cost function is given by.

=> TC = b0 + b1*q. Consider the following table.

So, here the estimated cost function is given by, => TC = 1746.67 + 7.6*Q, where the estimated value of “b0” and “b1” are “1746.67” and “7.6” respectively.

B).

Here the cost function is “TC = 1746.67 + 7.6*Q”, => MC = d(TC)/dQ = 7.6.

C).

The “R^2” is given by “0.9587”, => “95.87%” of the variation in TC is being explained by the production volume.

D).

Now, the estimated regression equation is given by.

=> TC = 1746.67 + 7.6*Q, => if “Q=500”, => TC = 1746.67 + 7.6*500 = 5,546.67, => the estimated value of “TC” is given by, “$5,546.67”.