If you have only one independent variable, it’s often designated by X, and the dependent

variable is designated by Y. If you have more than one independent variable, variables are usually

designated by letters toward the end of the alphabet (W, X, Y, Z). Parameters are often designated

by letters toward the beginning of the alphabet (a, b, c, d). There’s no consistent rule regarding

uppercase versus lowercase letters.

Sometimes a collection of predictor variables is designated by a subscripted variable (

and so

on) and the corresponding coefficients by another subscripted variable (

, and so on).

In mathematical texts, you may see a regression model with three predictors written in one of several

ways, such as

(different letters for each variable and parameter)

(using a general subscript-variable notation)

In practical work, using the actual names of the variables from your data and using meaningful

terms for parameters is easiest to understand and least error-prone. For example, consider the

equation for the first-order elimination of an injected drug from the blood,

. This form, with its short but meaningful names for the two variables,

Conc (blood concentration) and Time (time after injection), and the two parameters,

(concentration at Time

) and

(elimination rate constant), would probably be more

meaningful to a reader than

.

Classifying different kinds of regression

You can classify regression on the basis of

How many predictors or independent variables appear in the model

The type of data of the outcome variable

What mathematical form to which the data appear to conform

There are different terms for different types of regression. In this book, we refer to regression models

with one predictor in the model as simple regression, or univariate regression. We refer to regression

models with multiple predictors as multivariate regression.

In the next section, we explain how the type of outcome variable determines which regression to

select, and after that, we explain how the mathematical form of the data influences the type of

regression you choose.

Examining the outcome variable’s type of data

Here are the different regressions we cover in this book by type of outcome variable:

Ordinary regression (also called linear regression) is used when the outcome is a continuous