*53*

An F-test produces an F-statistic. To find the p-value associated with an F-statistic in Excel, you can use the following command:

**=F.DIST.RT(x, degree_freedom1, degree_freedom2)**

where:

**x:**Â the value of the F-statistic**degree_freedom1:**Â numerator degrees of freedom**degree_freedom2:**Â denominator degrees of freedom

For example, here is how to find the p-value associated with an F-statistic of 5.4, with numerator degrees of freedom = 2 and denominator degrees of freedom = 9:

The p-value isÂ **0.02878**.

One of the most common uses of an F-test is for testing the overall significance of a regression model. In the following example, we show how to calculate the p-value of the F-statistic for a regression model.

**Example: Calculating p-value from F-statistic**

Suppose we have a dataset that shows the total number of hours studied, total prep exams taken, and final exam score received for 12 different students:

If we fit a linear regression model to this data usingÂ **study_hoursÂ **andÂ **prep_exams Â **as the explanatory variables and

**scoreÂ**as the response variable, we will get the following output:

The F-statistic for the overall regression model is **5.0905**. This F-statistic has 2 degrees of freedom for the numerator and 9 degrees of freedom for the denominator.

Excel automatically calculates that the p-value for this F-statistic is** 0.0332**:

In order to calculate this p-value ourselves, we could use the following code:

Notice that we get the same p-value as the linear regression output.