Question

An important application of regression analysis in accounting is in the estimation of cost. Bycollecting data on volume and cost and using the least squares meathod 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

A. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.

Answer 1

To develop an estimated regression equation, we can use the least squares method to calculate the line of best fit between the production volume and total cost. The estimated regression equation would be Total Cost = 2833.33 + 4.67 * Production Volume.

Step-by-step explanation:

To develop an estimated regression equation, we can use the least squares method to calculate the line of best fit between the production volume (independent variable) and total cost (dependent variable).

Step 1: Calculate the mean of the production volume and total cost.

Step 2: Calculate the differences between each production volume and the mean production volume, and each total cost and the mean total cost.

Step 3: Multiply the differences calculated in Step 2 to get the products.

Step 4: Calculate the sum of the products calculated in Step 3.

Step 5: Calculate the squared differences for the production volume.

Step 6: Calculate the sum of the squared differences for the production volume.

Step 7: Calculate the slope of the regression line using the formulas: b = sum(products) / sum(squared differences of production volume).

Step 8: Calculate the y-intercept of the regression line using the formula: a = mean total cost - (b * mean production volume).

Step 9: Write the equation of the regression line in the form ŷ = a + bx.

In this case, the estimated regression equation would be: Total Cost ($) = 2833.33 + 4.67 * Production Volume (units).