### Terminology:
**Regression, ANOVA, ANCOVA**

In every field, it's essential to use the proper terminology in order
to be understood and to inspire confidence. In
statistics, some analyses can be described correctly in different ways.
This can be viewed as liberating or as evidence of a sinister plot
according to one's general outlook on life.

An example of this overlap in nomenclature occurs with

**regression**, **analysis of variance (ANOVA)**, and
**analysis of covariance (ANCOVA)**.

These methods are used
to model a numerical response variable (such as cholesterol level) in
terms of predictor variables. The name of the method depends on whether
the predictors are numerical, categorical (for example, rice oil/canola
oil/peanet oil), or both.
One simple rule states that

- if all predictors are numerical
(quantitative), the analysis is called
**regression**; - if all
predictors are categorical (qualitative), the analysis is called
**analysis of variance**; - if there are both qualitative and
quantitative predictors, the analysis is called
**analysis of
covariance**.

*Sometimes* additional criteria are applied when both qualitative
and quantitative predictors are used.

- If the focus is on the
**quantitative predictors**, the analysis is often called
**regression**. - If the focus is on the
**qualitative
predictors**, the analysis is almost always called **ANCOVA** and
the quantitative predictors are called **covariates**.

Most analysts would say the name ANCOVA should be used only when the
model does **not** include interactions between the covariates and the
factor of interest. Thus, a strict ANCOVA model is a **"parallel
slopes" model**, so that the regression coefficients for the
covariates are the same for all factor levels. When an author says that
an ANCOVA model was fitted, assume no allowance was made for an
interaction between the factor and covariates unless there is a statement
to the contrary.

The name of the analysis is not always the the name of the computer
program that performs it. Any ANOVA or ANCOVA can be performed by using
an ordinary regression package if one is clever about constructing the
proper sets of indicator variables. One can and should report that an
ANOVA or ANCOVA was performed even when a regression program is used to
do it.