Chapter 6 starts with the description of multiple regression. Even if it is unlikely for multiple regression to be used as the primary method for multivariate biomarker discovery based on high-dimensional data, presenting this classical method provides the necessary background for regression analysis and highlights the weaknesses of multiple regression, which will be addressed by the subsequently presented methods. This chapter also presents partial least squares regression (PLSR), which by performing supervised dimensionality reduction addresses some weaknesses of multiple regression; however, by not performing any feature selection, PLSR does not reduce noise that is typically abundant in high-dimensional data.