Statistics in a Nutshell

Chapter 12. Introduction to the General Linear Model

In Chapter 9, you learned to describe the association between two variables by using a simple graphical technique in a two-dimensional (x, y) plane. You also learned to quantify the bivariate relationship by computing a correlation coefficient. You may have been surprised by how easy it was to relate the mathematical relationship between two variables, especially for simple cases such as r = 1.00, where a perfect correlation can be graphically described by a straight line, with a specific slope and intercept.

It is possible to take the relationship one step further and use characteristics, such as the slope and intercept, to build a functional mathematical model, and determine the precise deviation from the model for observed data. In this approach, the correlation coefficient and the coefficient of determination still have an important role to play; however, the use of linear regression to test the goodness of fit of observed data to a theoretical model goes one step further in being able to characterize existing data, and predict values of dependent variables from independent variables. This process occurs literally by simple algebraic operations, such as substitution.

Linear regression is an extremely valuable technique, which is often used for prediction in models where no experimental control has been applied to the collection of data. For example, you may want to determine the relationship between training and performance ...