How do you apply the least-square regression?


Definition

The least-square regression is a statistical method that measures the average amount of change in the dependent variable (i.e. variable that changes in response to some other variable) which is associated with a unit change in one or more independent variables (i.e. variable that causes some positive variable to change). It defines the best fitting line as the one which minimizes the sum of squared errors. This method literally minimizes the prediction error, i.e. the distance between the model’s prediction and the actual observation for each volume over the relevant range (the red segments in the following diagram):


Illustration




Advantages

Least-square regressions use all available information to produce estimates. It is therefore less sensitive to any particular value. Moreover, the regression analysis also produces a coefficient of determination, also called R-square, which measures the percentage of variation in the dependent variable explained by the independent variable(s). The R-square is a measure of goodness-of-fit of the model (1 indicates a perfect fit, meaning that the cost equation explains all costs variations). Finally, another major advantage of least square regression is that you can introduce multiple cost drivers.


Limitations

The quantity of information necessary to obtain reliable estimates increases with the number of cost drivers added to the model (to prevent this problem, it is useful to model homogeneous costs). In addition, the regression makes several assumptions which must also be satisfied beyond linearity for estimates to be reliable: residuals should have a constant variance (no heteroscedasticity), be independent from each other and normally distributed. Moreover, in the case of multiple regression where you include several cost drivers, these cost drivers should not be too highly correlated to avoid the risk of multicollinearity. Specification analysis consists in testing these assumptions of regression analysis.


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