Basics of Linear Regression
The linear regression techniques, which are used in Demand Planning for univariate forecasting and causal analysis, arebased on the least squares method. The following topic briefly explains the concepts behind this method. It is not intended as a substitute for experience with statistics. For suggestions for further reading seeBackground Reading.
In the case of linear regression this relationship between the independent variable X and the dependent variable Y is assumed to be linear as shown in the graph below. For the sake of the simplicity only one independent variable is examined here. The principles are the same for multiple linear regression with several independent variables.
There are several ways of measuring the error between a sample of measured data points and an estimate or forecast of this behavior (seeForecast Accuracy Measurements and Measures of Fit). In our case the sum of the squares is the measure used to represent the total error. This consists of a term that is due to the variation in X, the explained variation, and a residual term due to random errors
The linear regression algorithm attempts to maximize the explained variation and thus minimize the residual variation.