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 ($)
400	5000
450	6000
550	6400
600	6900
700	7400
750	8000
Production Target	Est. Cost ($)
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

In order to compute the regression coefficients, we need the squares and sum of squares of production and cost. We shall make use of the table below:

	Vol	cost	x^2	y^2	x*y
	400	5000	160000	25000000	2000000
	450	6000	202500	36000000	2700000
	550	6400	302500	40960000	3520000
	600	6900	360000	47610000	4140000
	700	7400	490000	54760000	5180000
	750	8000	562500	64000000	6000000
Total	3450	39700	2077500	268330000	23540000

Let us denote the production volume by x and the cost by y. We have n=6.

(a).  

Now

  

The intercept is

  

(a). Compute b₁ and b₀ (to 1 decimal).

Complete the estimated regression equation (to 1 decimal).

(b). According to this model, what is the change in cost (in dollars) for every unit produced (to 1 decimal)?

The change in cost is $7.6 for every unit produced.

(c). The correlation coefficient is given by

  

  

The coefficient of determination is

Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.

r² =0.9587

What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?

95.9%

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)?

The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation is $6047.