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 7 production volumes and total cost data for a manufacturing operation.

Production Volume (units)	Total Cost ($)
400	4000
450	5000
550	5400
600	5900
700	6400
750	7800
800	7200

1. Use these data to estimate a regression equation that could be used to predict the total cost for a given production volume. Intercept ______ and Slope ______
2. What is the marginal cost per unit produced? (Remember what marginal cost is from Principle of Economics?)
3. The company’s production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation?

Answer 1

Data based on a sample of 7 production volumes and total cost for manufacturing operation is given. In this case volume is independent variable and cost is dependent variable. Let x denote the volume and y denote the total cost. Then the regression equation between the two variable is of the form

For obtaining the slope and the intercept, we minimize the residual sum of error given by

For minimizing the residual sum of error, we differentiate it with respect to the two paramter and we equate it to 0.This gives two normal equation which is given below

Therefore the paramter and slope of the equation is

To calculate A and B, let us consider the table given below

  

Now, we try to obtain to obtain the slope of the equation so consider the table below

Therefore the slope and intercept is

The regression equation is given by

Y=1300.15+(7.6704)*X

a) Intercept =1300.15 and Slope=7.6704.

b) In economy marginal cost is the total cost that arises when there is one unit increment in the quantity which is obtained by putting X=1. Therefore, the marginal cost is

c) If the production volume is 500 units then the total cost is given by

Y=1300.15+(7.6704)*500

Y=5135.35

Therefore, the total cost is 5135.35.