Lesson 15

Introduction to F Tests

Big question

Why do we need a joint test?

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain introduction to f tests in plain language.
  • Use linear restriction correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

An F test evaluates several restrictions at the same time instead of running separate t tests.

Key terms

linear restriction
A hypothesis that imposes a linear equation on regression parameters.
F statistic
A statistic used to test several linear restrictions jointly.
R-squared F form
An F statistic shortcut based on restricted and unrestricted R-squared values.

Core formula

H0:qrestrictionsholdjointlyH0: q restrictions hold jointly

Use plain-language interpretation before algebra.

Example

BWGHT gives students a real-data setting for introduction to f tests. The lesson emphasizes inference mechanics and interpretation, not memorized output.

Interactive visual

RestrictedUnrestrictedModelBuilder

Original Module 4 visual for Introduction to F Tests.

wage_sample.csv

y variable

wage

The dependent variable. It is the outcome students want to explain.

x variable

education

The explanatory variable. It is used to describe changes in wage.

Live Python

Introduction to F Tests Python example

Introduction to F Tests Python example

Stdout

Run Python to see results here.

Status / stderr

Ready to run Python in your browser.

Line-by-line guide

  1. Line 1Load a Python library needed for data work or regression.
  2. Line 2Load a Python library needed for data work or regression.
  3. Line 3Load a Python library needed for data work or regression.
  4. Line 5Load the dataset into a pandas DataFrame.
  5. Line 6Create or update a Python object used in the analysis.
  6. Line 7Add an intercept column to the regression design matrix.
  7. Line 8Add an intercept column to the regression design matrix.
  8. Line 9Create or update a Python object used in the analysis.
  9. Line 10Create or update a Python object used in the analysis.
  10. Line 11Create or update a Python object used in the analysis.
  11. Line 12Display a result so students can inspect the output.
  12. Line 13Display a result so students can inspect the output.

Python walkthrough

  1. 1Load the real dataset and keep the variables needed for both models.
  2. 2Estimate unrestricted and restricted models or use statsmodels f_test.
  3. 3Compute or read the F statistic and p-value.
  4. 4Interpret the test as a joint statement about population parameters.

Live notebook

Run this lesson as a notebook

Open an editable notebook cell-by-cell, run Python in the browser, and download the `.ipynb` file for later.

Open live notebookDownload .ipynbDownload .py

Related dataset

WAGE1

Estimated time

25 to 40 min

Packages

pandas, numpy, statsmodels, patsy

Expected output

A regression or inference table with coefficients, uncertainty, and short interpretation notes.

Learning goals

  • Load and inspect WAGE1.
  • Run the Python cells connected to Testing a Single Coefficient Against Zero.
  • Interpret the output using t tests and WAGE1.

Common errors

  • File not found: check that WAGE1.DTA is installed or use the course data folder.
  • Package import error: use the browser notebook first, then download for local Jupyter if your local packages differ.
  • Column name error: compare your variable names with the dataset variables listed for this notebook.

Dataset path helper

import pandas as pd

df = pd.read_stata("/data/WAGE1.DTA")
df.head()

Interactive activity

RestrictedUnrestrictedModelBuilder

Identify restricted and unrestricted models

Choose which variables are removed under the joint null.

BWGHT

Inputs

Try it yourself

Write one plain-English sentence explaining the main idea from this lesson.

Common mistakes

Check these before you move on.

A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.

Quick quiz

What is the safest inference focus in Introduction to F Tests?

Quick quiz

Which reporting habit is most important in Introduction to F Tests?

Quick quiz

Why is LAWSCH85 a reasonable practice dataset here?

Key takeaway

Introduction to F Tests turns regression output into evidence only when the hypothesis, assumptions, and magnitude are stated clearly.

Download dataDownload resultsDownload interpretation