Excel: How to Interpret P-Values in Regression Output

Multiple linear regression is used to quantify the relationship between two or more predictor variables and a response variable.

Whenever we perform multiple linear regression, we’re always interested in the p-values in the output to determine if the relationship between the predictor variables and the response variable is statistically significant.

This tutorial explains how to interpret the p-values in the output of a multiple linear regression model in Excel.

Example: Interpreting P-values in Regression Output in Excel

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 perform multiple linear regression using hours studied and prep exams taken as predictor variables and exam score as a response variable.

The following screenshot shows the regression output of this model in Excel:

There are three p-values that we should look at in the output:

• P-value of the overall model
• P-value of the first predictor variable (hours)
• P-value of the second predictor variable (prep exams)

Here is how to interpret each p-value:

P-Value of the Overall Model

The p-value of the overall model can be found under the column called Significance F in the output.

We can see that this p-value is 0.00.

Since this value is less than .05, we can conclude that the regression model as a whole is statistically significant.

In other words, the combination of hours studied and prep exams taken has a statistically significant relationship with final exam score.

P-value of the first predictor variable (hours)

The p-value for the first predictor variable, hours, is 0.00.

Since this value is less than .05, we can conclude that hours studied is statistically significant.

In other words, the number of hours that a student studies has a statistically significant relationship with the final exam score that a student receives.

P-value of the second predictor variable (prep exams)

The p-value for the second predictor variable, prep exams , is 0.52.

Since this value is not less than .05, we can conclude that number of prep exams taken is not statistically significant.

In other words, the number of prep exams that a student takes does not have a statistically significant relationship with the final exam score that a student receives.

Since this variable is not statistically significant, we may decide to remove it from the model because it doesn’t add any significant improvement to the overall model.

In this case, we could perform simple linear regression using only hours studied as the predictor variable.