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 Total Cost (units) ($) 400 450 550 600 700 750 4,100 X 5,100 5,300 6,000 6,300 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? $ X (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.) $
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 Total Cost (units) ($) 400 450 550 600 700 750 4,100 X 5,100 5,300 6,000 6,300 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? $ X (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.) $
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.FOM: Focus On Modeling: Fitting Lines To Data
Problem 6P
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Transcribed Image Text: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 Total Cost
(units)
($)
400
450
550
600
700
750
4,100
X
5,100
5,300
6,000
6,300
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?
X
(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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