Overall F-test of a regression

Models and regression · reference distribution: F(k, n−k−1)

When to use it

Test whether the regression model as a whole explains anything, or whether all coefficients may be zero.

Null hypothesis

All coefficients (except the intercept) are zero.

Assumptions

The same as linear regression

Test statistic

F = \dfrac{R^2 / k}{(1 - R^2) / (n - k - 1)}

Effect size

Cohen’s f². Benchmarks: 0.02, 0.15 and 0.35.

f^2 = \dfrac{R^2}{1 - R^2}

How to report it

F(2, 47) = 9.4, p < .001, R² = .29

In R and Python

summary(lm(y ~ x1 + x2, data = df))  # the F is on the last line

Python

import statsmodels.formula.api as smf
m = smf.ols("y ~ x1 + x2", data=df).fit()
m.fvalue, m.f_pvalue

In Python, stats is scipy.stats and np is numpy.

Variants and alternatives

Partial F, to compare nested models

Where it sits in the catalog

Models and regression. Tests run inside a fitted model: whether a coefficient matters, whether the model explains anything and whether the residuals meet the assumptions.

In the decision tree

What do you want to do? Test a regression model
What do you want to test? Whether the model as a whole explains anything

Open the decision tree

F table Simple Linear Regression See it in the catalog table