Linear Regression Models

In earlier chapters, we were primarily concerned about inferences on population parameters. In this chapter, we examine the relationship between one or more variables and create a model that can be used for predictive purposes. For example, consider the question “Is there statistical evidence to conclude that the countries with the highest average blood-cholesterol levels have the greatest incidence of heart disease?” It is important to answer this if we want to make appropriate lifestyle and medical choices. The process of finding a mathematical equation that best fits the noisy data is known as regression analysis. Our aim is to create a model and study inferential procedures when one dependent and several independent variables are present. In his book Natural Inheritance, Sir Francis Galton introduced the word regression in 1889 to describe certain genetic relationships. The technique of regression is one of the most popular statistical tools to study the dependence of one variable with respect to another. There are different forms of regression: simple linear, nonlinear, multiple, and others. The primary use of a regression model is prediction.