Data Exploration Using Non-Spatial Methods: The Linear Model
Richard E. Plant · 2018
This chapter provides an introduction to multiple linear regression and develops the approach to model selection. It aims to develop a procedure for using model selection as an exploratory tool to help determine potential explanatory variables for ecological processes. The bifunctional relationship between Yield and the explanatory variables makes it impossible to construct a meaningful regression model that describes yield response over the entire field without including interaction terms. The bad effects of multicollinearity, as well as the difficulty of identifying influential data records, are part of what makes the process of selecting explanatory variables to include in a multiple regression model so difficult and dangerous. The process of selecting which explanatory variables to retain and which to eliminate from a multiple linear regression model can be viewed as a search for balance in the bias-variance trade-off . The impact of multicollinearity can be assessed by means of added variable plots, which are also called partial regression plots.