Multiple Regression

Abstract

One of the major applications in statistics is the prediction of one or more characteristics of individuals on the basis of knowledge about related characteristics. For example, common-sense observation has taught most of us that the amount of time we practice learning something is somewhat predictive of how well we perform on that thing we are trying to master. Our bowling score tends to improve (up to a point) in relationship to the amount of time we spend practicing bowling. In the social sciences however, we are often interested in predicting less obvious outcomes. For example, we may be interested in predicting how much a person might be expected to use a computer on the basis of a possible relationship between computer usage and other characteristics such as anxiety in using machines, mathematics aptitude, spatial visualization skills, etc. Often we have not even observed the relationships but instead must simply hypothesize that a relationship exists. In addition, we must hypothesize or assume the type of relationship between our variables of interest. Is the relationship a linear one? Is it a curvilinear one?

This chapter develops the theory and applications of Multiple Linear Regression Analysis. The multiple regression methods are frequently used (and misused.) It also forms the heart of several other analytic methods including Path Analysis, Structural Equation Modeling and Factor Analysis.