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:

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
  • βi: The coefficients for the regressors
  • xi: 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

Additional Resources

How to Interpret Regression Coefficients
How to Test the Significance of a Regression Slope
How to Read and Interpret a Regression Table

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