Regression Analysis

Abstract

Linear regression analysis is one of the most important statistical methods. Itexamines the linear relationship between a metric-scaled dependent variable (alsocalled endogenous, explained, response, or predicted variable) and one or moremetric-scaled independent variables (also called exogenous, explanatory, control, orpredictor variable). We illustrate how regression analysis work and how it supportsmarketing decisions, e.g., the derivation of an optimal marketingmix.We also outlinehow to use linear regression analysis to estimate nonlinear functions such as amultiplicative sales response function. Furthermore, we show how to use the resultsof a regression to calculate elasticities and to identify outliers and discuss in detailsthe problems that occur in case of autocorrelation, multicollinearity and heteroscedasticity.We use a numerical example to illustrate in detail all calculations anduse this numerical example to outline the problems that occur in case of endogeneity