The method of least squares is a statistical technique to find the best-fitting line through a set of data points (Mowen, et al, 2018). It is most commonly referred to as a regression line, which I have used many times in my career. It can break apart the fixed and variable components of a mixed cost problem and address each component in a formula. To go a bit deeper, this best-fitting-curve is found by minimizing the sum of the squares of the residuals of each point and its distance to the line (Weisstein, n.d.).
Why is this method better than either the high-low method or the scattergraph method?
While the high-low method is quick and easy to compute, it suffers from only being practical in small sample sizes with little to no outliers on the top or bottom of the range (Mowen, 2018). If the values consistently rise with a flat slope, it makes sense. However, this is not how real-world data works.
The advantage of the method of least squares is that it will always produce consistent results. Basically, the best-fitting-line is the one in which the data points are closer to the line than to any other line. While the scattergraph method is a good visual representation of data and can be simple to create, it adds a level of subjectivity. The method of least squares, on the other hand, is objective.
Resources
Mowen, M. M., Hansen, D. R., & Heitger, D. L. (2018). Managerial accounting: The cornerstone of business decision making (7th ed.). Boston: Cengage Learning.
Weisstein, E. W. (n.d.). Least Squares Fitting. Retrieved from http://mathworld.wolfram.com/LeastSquaresFitting.html
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