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 Total Cost
(Units) ($)
400 4,000
450 5,000
550 5,400
600 5,900
700 6,400
750 7,000
1. Use the data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.
2. What is the variable cost per unit produced
3. Compute the coefficient of determination what percentage of the variation in total cost can be explained by production volume
4. The companys production schedule shows 500 units must be produced next month what is the estimated total cost of this operation.

Answer 1

Answer:

(1) $\text{Total Cost}=1246.67+7.60\ \text{Volume}$

(2) The variable cost per unit produced is $7.60.

(3) The coefficient of determination is 0.96 or 96%.

(4) The estimated total cost is $5,046.67.

Explanation:

A regression analysis for the provided data is performed on Microsoft Excel.

The output is attached below.

(1)

The estimated regression equation that could be used to predict the total cost for a given production volume is:

$\text{Total Cost}=1246.67+7.60\ \text{Volume}$

(2)

The variable cost per unit produced is given by the slope of the line.

The slope of a regression line represent the value of the dependent variable for one unit of the independent variable.

So, the variable cost per unit produced is $7.60.

(3)

Consider the regression output attached.

The coefficient of determination is 0.96 or 96%.

This implies that the percentage of the variation in total cost that can be explained by production volume is 96%.

(4)

For Volume = 500 units predict the total cost as follows:

$\text{Total Cost}=1246.67+7.60\ \text{Volume}$

                 $=1246.67+(7.60\times 500)\\\\=1246.67+3800\\\\=5046.67$

Thus, the estimated total cost is $5,046.67.