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 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 7000 What is the variable cost per unit produced?

Answer 1

The answer is $7.6

Step-by-step explanation:

We have to build up the regression equation to predict the total cost at a given production level to find out the estimated amount of variable cost per unit.

Denote the equation as: y = ax + b; where: a is the variable cost per unit; x is the units produced; b is fixed cost; y is total production cost at x units produced.

Apply the formula in Least Squares Regression, we have:

a = (n*Σ(x*y) - Σx * Σy) / [n*Σ(X^2) - (ΣX)^2], in which n = 6 observations: x0 denote production volume and y denote total cost at an x0 production volume. Thus, we have the below calcualtion:

Σ(x*y) = 400 * 4000 + 450 * 5000 +... + 750 *7000 = 20,090,000;

Σx = 400 + 450 + ...+ 750 = 3,450; (Σx)^2 = 11,902,500

Σy = 4,000 + 5,000 +...+7,000 = 33,700

Σx^2 = 400^2 + 450^2 + ... + 750^2 = 2,077,500

=> a = (6*20,090,000 - 3,450*33,700) / ( 6*2,077,500 - 11,902,500) = 7.6

So, variable cost per unit produced is $7.6.