What is a Regressor? (Definition & Examples)

In statistics, a regressor is the name given to any variable in a regression model that is used to predict a response variable.

A regressor is also referred to as:

An explanatory variable
An independent variable
A manipulated variable
A predictor variable
A feature

All of these terms are used interchangeably depending on the type of field you’re working in: statistics, machine learning, econometrics, biology, etc.

Note: Sometimes a response variable is called a “regressand.”

Regressors in Regression Models

Most regression models take the following form:

Y = β₀ + B₁x₁+ B₂x₂ + B₃x₃ + ε

where:

Y: The response variable
β_i: The coefficients for the regressors
x_i: The regressors
ε: The error term

The whole point of building a regression model is to understand how changes in a regressor lead to changes in a response variable (or “regressand”).

Note that regression models can have one or more regressors.

When there is only one regressor, the model is referred to as a simple linear regression model and when there are multiple regressors, the model is referred to as a multiple linear regression model to indicate that there are multiple regressors.

The following examples illustrate how to interpret regressors in different regression models.

Example 1: Crop Yield

Suppose a farmer is interested in understanding the factors that affect total crop yield (in pounds). He collects data and builds the following regression model:

Crop Yield = 154.34 + 3.56*(Pounds of Fertilizer) + 1.89*(Pounds of Soil)

This model has two regressors: Fertilizer and Soil.

Here’s how to interpret these two regressors:

Fertilizer: For each additional pound of fertilizer used, crop yield increases by an average of 3.56 pounds, assuming the amount of soil is held constant.
Soil: For each additional pound of soil used, crop yield increases by an average of 1.89 pounds, assuming the amount of fertilizer is held constant.

Example of a regressor

Example 2: Exam Scores

Suppose a professor is interested in understanding how the amount of hours studied affects exam scores. He collects data and builds the following regression model:

Exam Score = 68.34 + 3.44*(Hours Studied)

This model has one regressor: Hours studied. We interpret the coefficient for this regressor to mean that for each additional hour studied, exam score increases by an average of 3.44 points.

Regressor vs. regressand