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