Definition Regression

Regression indicates a relationship between two or more variables. In a regression analysis, it is assumed that there is a directed linear interdependence, i.e. there exists a dependent variable and at least one independent variable. Which variable is dependent or independent must be possible to deduce on a logical basis.

With the help of regression analysis we can calculate a regression function, which describes the dependence of the two variables with a straight line. The calculated regression line allows us to make predictions for the dependent variable by inserting a value for the independent variable. Reverse inferences are not allowed, though.

Regression analyzes are often performed for variables that have a correlation, i.e. a statistical dependence has previously been determined.

An example:

We have determined that there is a positive correlation for the two cardinal features age and wealth. If there is a rise in one variable, the other variable will rise as well. On a logical basis we can determine that 'age' is the independent variable – older age means more assets. The conclusion that more wealth leads to higher age would be illogical.

Now, with the help of a regression analysis, we can determine the slope of the regression line. In this case: If the age of an American rises by one year, his assets will rise by an average of $2,500 (=the regression coefficient).

Important: This statement does not describe a causal relationship, i.e. it does not imply that a higher age equals higher assets. It simply states that a linear interdependence between the two variables can be observed.