Linear regression analysis is a useful technique in business mathematics, among other spheres. In accounting-specifically cost and management accounting-it allows accountants to project costs given a range of values over specific cost periods. It is far superior to techniques such as expected values, scatter graphs and the high-low method in projecting costs and separating the fixed and variable components of semi-variable costs.
Also known as the least squares method, regression seeks to establish values for a linear equation-the line of best fit. It is only one of several methods of establishing the line of best fit. The linear equation, in the form y= a + b(x) represents a cost relationship, where y is the total cost, a is the fixed cost, b is the variable cost per unit and x is the level of activity or output. As such, one can also represent the linear equation in the following formula:
Total Costs = Fixed costs + (Variable cost per unit x output / activity level).
Total costs and the activity level are the related variables in this equation, while pairs of data for fixed and variable cost per unit are estimated based on the pairs of data for Total Cost and activity level.
Regression analysis allows the accountant to glean more information than correlation analysis. Correlation analysis provides a foundation in assessing the strength of the relationship between costs and activity levels. However, it does not provide a means of approximating values on the basis of an assumed linear relationship.
Linear regression analysis uses historical variables as inputs in order to establish the linear relationship between costs and the level of activity. Accountants use the result of regression analysis to predict total costs based on actual data. It is useful as a budgetary tool and can inform the planning and decision-making process.
Linear regression facilitates formation of estimates of complex relationships, particularly where the relationship is not immediately evident. Once the linear relationship is determined, managers can estimate total costs for any level of activity by plotting the information on a graph.
Although linear regression analysis is a useful method of separating semi-variable costs and forecasting, it has its limitations. Naturally, it is based on assumptions of a linear relationship and that Y is exclusively dependent on X. The reliability of predictions of the linear regression method is also predicated on the reliability and validity of the data provided.