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A **partial regression coefficient** is the name given to the regression coefficients in a multiple linear regression model.

This is in contrast to a plain old “regression coefficient”, which is the name given to the regression coefficient in a simple linear regression model.

The way to interpret a partial regression coefficient is: The average change in the response variable associated with a one unit increase in a given predictor variable, assuming all other predictor variables are held constant.

The following example explains how to identify and interpret partial regression coefficients in a multiple linear regression model.

**Example: Interpreting Partial Regression Coefficients**

Suppose we want to know if the number of hours spent studying and the number of prep exams taken affects the score that a student receives on a certain college entrance exam.

To explore this relationship, we can fit a multiple linear regression model using **hours studied** and **prep exams taken **as predictor variables and **exam score **as a response variable.

The following regression table shows the output of the model:

Here is how to interpret the partial regression coefficients:

**Hours:** For each additional hour spent studying, exam score increases by an average of **5.56** points, assuming the number of prep exams is held constant.

Here’s another way to think about this: If student A and student B both take the same amount of prep exams but student A studies for one hour more, then student A is expected to earn a score that is 5.56 points higher than student B.

**Prep Exams:** For each additional prep exam taken, exam score decreases by an average of **0.60** points, assuming the number of hours studied is held constant.

Another way to think about this: If student A and student B both study for the same number of hours but student A takes one additional prep exam, then student A is expected to earn a score that is 0.60 points lower than student B.

Using the coefficients from the regression output, we can write the estimated multiple linear regression equation:

Exam score = 67.67 + 5.56*(hours) – 0.60*(prep exams)

We can use this estimated regression equation to calculate the expected exam score for a student, based on the number of hours they study and the number of prep exams they take.

For example, a student who studies for three hours and takes one prep exam is expected to receive a score of **83.75**:

Exam score = 67.67 + 5.56*(3) – 0.60*(1) = 83.75

**Additional Resources**

Introduction to Simple Linear Regression

Introduction to Multiple Linear Regression

How to Read and Interpret a Regression Table