Correlation and Regression

Abstract

Two dimensional random variables are frequently investigated in engineering and scientific applications. Normal distribution is commonly assumed as a theoretical model for the population of two dimensional random variables. The mutual linear dependence of the two variables is described by the coefficient of correlation. Regression lines are used to analyse the dependence of one random variable, on one hand as the dependent variable, on the other as the independent variable. While the correlation is a symmetrical property with respect to the two random variables, regression is influenced by the choice of a dependent or independent variable. The estimate of the coefficients of correlation and regression from sample data is an extremely important task, as only limited samples for two dimensional random variables are commonly available. For the same reason testing concerning the coefficient of correlation and regression is an essential step in many engineering and scientific applications.