Indonesian Actuarial Analytics Short Course

Regression analysis is a statistical method that is widely used in many fields of study, with actuarial science being no exception. This chapter introduces the role of the normal distribution in regression and the use of logarithmic transformations in specifying regression relationships.

This chapter considers regression in the case of only one explanatory variable. Despite this seeming simplicity, many deep ideas of regression can be developed in this framework. By limiting ourselves to the one variable case, we can illustrate the relationships between two variables graphically. Graphical tools prove to be important for developing a link between the data and a predictive model.

This chapter introduces linear regression in the case of several explanatory variables, known as multiple linear regression (MLR). Many basic linear regression concepts extend directly, including goodness of fit measures such as the coefficient of determination and inference using t-statistics. Multiple linear regression models provide a framework for summarizing highly complex, multivariate data. Because this framework requires only linearity in the parameters, we are able to fit models that are nonlinear functions of the explanatory variables, thus providing a wide scope of potential applications.

This chapter describes tools and techniques to help you select variables to enter into a linear regression model, beginning with an iterative model selection process. In applications with many potential explanatory variables, automatic variable selection procedures are available that will help you quickly evaluate many models. Nonetheless, automatic procedures have serious limitations including the inability to account properly for nonlinearities such as the impact of unusual points; this chapter expands upon the Chapter 2 discussion of unusual points. It also describes collinearity, a common feature of regression data where explanatory variables are linearly related to one another. Other topics that impact variable selection, including out-of-sample validation, are also introduced.

An application, determining an individual's characteristics that influence its health expenditures, illustrates the regression modeling process from start to finish. Subsequently, the chapter summarizes what we learn from the modeling process, underscoring the importance of variable selection.