Models and Regression

A model is said to be linear if the partial derivatives with respect to any of the model parameters are independent of the other parameters. All models of the form 

The purpose of a model is to explain the behavior of a system and/or to predict current or future observations. Let 

It should be noted that for notation purposes, the symbol s will be used interchangeably with the symbol e, although technically e is an estimator of e.  

The goal is to find the best line through the data and consequently find the best estimators for 0. One method is to find the set of Y. v that are closest to the observed Y based on some type of minimization criterion or objective function. Thus, 

Applying the derivatives, the following pair of equations is obtained 

---

Figure 1-1. Mathematical modeling and regression analysis. By permission, A. Constantinides, Applied Numerical Methods With Personal Computers, McGraw-Hill Book Co., 1987.

This chapter discusses two-way models and serves as a introduction for the chapters to come. A distinction is made between component models and regression models. 

---