A **moderating variable** is a type of variable that affects the relationship between a dependent variable and an independent variable.

When performing regression analysis, we’re often interested in understanding how changes in an independent variable affect a dependent variable. However, sometimes a moderating variable can affect this relationship.

For example, suppose we want to fit a regression model in which we use the independent variable *hours spent exercising each week* to predict the dependent variable *resting heart rate*.

We suspect that more hours spent exercising is associated with a lower resting heart rate. However, this relationship could be affected by a moderating variable such as **gender**.

It’s possible that each extra hour of exercise causes resting heart rate to drop more for men compared to women.

Another example of a moderating variable could be **age**. It’s likely that each extra hour of exercise causes resting heart rate to drop more for younger people compared to older people.

**Properties of Moderating Variables**

Moderating variables have the following properties:

**1. Moderating variables can be qualitative or quantitative**.

Qualitative variables are variables that take on names or labels. Examples include:

- Gender (Male or Female)
- Education Level (High School Degree, Bachelor’s Degree, Master’s Degree, etc.)
- Marital Status (Single, Married, Divorced)

Quantitative variables are variables that take on numerical values. Examples include:

- Age
- Height
- Square Footage
- Population Size

In the previous examples, **gender** was a qualitative variable that could affect the relationship between hours studied and resting heart rate while **age** was a quantitative variable that could potentially affect the relationship.

**2. Moderating variables can affect the relationship between an independent and dependent variable in a variety of ways.**

Moderating variables can have the following effects:

- Strengthen the relationship between two variables.
- Weaken the relationship between two variables.
- Negate the relationship between two variables.

Depending on the situation, a moderating variable can *moderate* the relationship between two variables in many different ways.

**How to Test for Moderating Variables**

If X is an independent variable (sometimes called a “predictor” variable) and *Y* is a dependent variable (sometimes called a “response” variable), then we could write a regression equation to describe the relationship between the two variables as follows:

*Y* = β_{0} + β_{1}*X*

If we suspect that some other variable, *Z*, is a moderator variable, then we could fit the following regression model:

*Y* = β_{0} + β_{1}*X*_{1}+ β_{2}*Z*_{ }+ β_{3}*XZ*

In this equation, the term *XZ* is known as an **interaction term**.

If the p-value for the coefficient of *XZ* in the regression output is statistically significant, then this indicates that there is a significant interaction between *X* and *Z* and *Z* should be included in the regression model as a moderator variable.

We would write the final model as:

*Y* = β_{0} + β_{1}*X*+ β_{2}*Z*_{ }+ β_{3}*XZ*

If the p-value for the coefficient of *XZ* in the regression output is not statistically significant, then *Z* is not a moderator variable.

However it’s possible that the coefficient for *Z* could still be statistically significant. In this case, we would simply include *Z* as another independent variable in the regression model.

We would then write the final model as:

*Y* = β_{0} + β_{1}*X*+ β_{2}*Z*

**Additional Resources**

How to Read and Interpret a Regression Table

How to Use Dummy Variables in Regression Analysis

Introduction to Confounding Variables