Advanced Regression Models

This chapter describes the simple linear regression concepts. The first quite natural idea is building a linear regression model involving more than one regressor. Finding the parameters by ordinary least squares (OLS) is a rather straightforward exercise. What is much less straightforward is the statistical side of the coin, since the presence of multiple variables introduces some new issues. The chapter discusses the problems of testing a multiple regression model, selecting regressor variables, and assessing forecasting uncertainty. The chapter does so for the simpler case of nonstochastic regressors and under restrictive assumptions about the errors, that is, independence, homoskedasticity, and normality. The chapter also describes logistic regression, a possible approach to cope with a categorical regressed variable, based on a nonlinear transformation of the output of a linear regression model. There are many settings in which nonlinearity in data must be explicitly recognized, leading to nonlinear regression. Controlled Vocabulary Terms forecasting; linear regression; logistic regression; nonlinear regression; ordinary least squares; polynomial regression