What percentage of the variation in total cost can be explained by the production volume?

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

  1. Use these 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 company’s production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation?

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What percentage of the variation in total cost can be explained by the production volume?

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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 3,700
450 4,700
550 5,100
600 5,600
700 6,100
750 6,700
  1. Compute b1 and b0 (to 1 decimal).
    b1 
    b0 

    Complete the estimated regression equation (to 1 decimal).
     =  +  x

  2. What is the variable cost per unit produced (to 1 decimal)?
    $
  3. Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1.
    r2 = 

    What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
     %

  4. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?

Expert Solution

What percentage of the variation in total cost can be explained by the production volume?

What percentage of the variation in total cost can be explained by the production volume?

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What percentage of the variation in total cost can be explained by the production volume?

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A: Solution

What measure in linear regression analysis provides the percent of variation?

The Coefficient of Determination measures the percent variation in the response variable (y) that is explained by the model.

What is the estimated regression line?

Using these estimates, an estimated regression equation is constructed: ŷ = b0 + b1x . The graph of the estimated regression equation for simple linear regression is a straight line approximation to the relationship between y and x.

What is the purpose of regression analysis?

Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.

Why is regression analysis important in business?

Regression analysis is all about data. It helps businesses understand the data points they have and use them – specifically the relationships between data points – to make better decisions, including anything from predicting sales to understanding inventory levels and supply and demand.