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 4,000 450 5,100 550 5,400 600 6,000 700 6,300 750 7,000 (a) Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. (Round your numerical values to two decimal places.) ŷ = (b) What is the variable cost (in dollars) per unit produced? $ (c) Compute the coefficient of determination. (Round your answer to three decimal places.) What percentage of the variation in total cost can be explained by production volume? (Round your answer to one decimal place.) % (d) The company's production schedule shows 500 units must be produced next month. Predict the total cost (in dollars) for this operation. (Round your answer to the nearest cent.) $

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.CR: Review Exercises

Problem 90CR

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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	4,000
450	5,100
550	5,400
600	6,000
700	6,300
750	7,000

(a)

Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. (Round your numerical values to two decimal places.)

ŷ =

(b)

What is the variable cost (in dollars) per unit produced?

(c)

Compute the coefficient of determination. (Round your answer to three decimal places.)

What percentage of the variation in total cost can be explained by production volume? (Round your answer to one decimal place.)

(d)

The company's production schedule shows 500 units must be produced next month. Predict the total cost (in dollars) for this operation. (Round your answer to the nearest cent.)

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