Applied Statistics

8Regression Analysis

8.1 Introduction

The term regression stems from Galton (1885) who described biological phenomena. Later Yule (1897) generalised this term. It describes the relationship between two (or more) characters, which at this early stage were considered as realisations of random variables. Nowadays regression analysis is a theory within mathematical statistics with broad applications in empirical research.

Partially, we take notations from those of functions in mathematics. A mathematical function describes a deterministic relation between variables. So is the circumference c of a circle dependent on the radius r of this circle, c = 2rπ.

Written in this way the circumference is called the dependent variable and the radius is called the independent variable or more generally in a function

where x is called the independent variable and y the dependent variable. The role of these variables can be interchanged under some mathematical assumptions by using the (existence assumed) inverse function

In contrast to mathematics, in empirical sciences such functional relationships seldom exist. For instance, let us consider height at withers and age, or height at withers and chest girth of cattle. Although there is obviously no formula by which one can calculate the chest girth ...