Lesson 14

Testing Intercept and Slope Differences

Big question

How do we test whether groups differ in more than one way?

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain testing intercept and slope differences in plain language.
  • Use dummy variable correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Use t tests for one coefficient and F tests for several restrictions together.

Key terms

Dummy variable
A binary regressor used to represent qualitative information in a regression.
Interaction term
A regressor formed by multiplying variables so one effect can depend on another variable.
Self-selection
A situation where people choose treatment or participation based on factors related to outcomes.

Core formula

H0:δ0=δ1=δ2=0H_0: \delta_0=\delta_1=\delta_2=0

Use plain-language interpretation before algebra.

Example

MODULE7_WAGE_GROUPS_SYNTHETIC is an original Ceteris Lab synthetic teaching dataset for testing intercept and slope differences. It lets students practice joint test without presenting fabricated real-world empirical findings.

Interactive visual

GroupDifferenceHypothesisBuilder: use the controls to code a group, choose a base group, and write one correct interpretation.

Original Module 7 visual for Testing Intercept and Slope Differences.

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

Testing Intercept and Slope Differences Python example

Testing Intercept and Slope Differences 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 4Load the dataset into a pandas DataFrame.
  4. Line 5Create or update a Python object used in the analysis.
  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 8Display a result so students can inspect the output.

Python walkthrough

  1. 1Load pandas and statsmodels so the workflow is reproducible.
  2. 2Read the installed Ceteris Lab synthetic CSV from the public data folder.
  3. 3Create or inspect dummy variables before estimating the model.
  4. 4Estimate OLS with an intercept and the selected regressors.
  5. 5Print coefficients or summaries, then interpret them as associations unless the design supports causality.

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

MODULE7_WAGE_GROUPS_SYNTHETIC

Estimated time

25 to 40 min

Packages

pandas, numpy, statsmodels, patsy

Expected output

Printed Python results that can be compared with the lesson explanation.

Learning goals

  • Load and inspect MODULE7_WAGE_GROUPS_SYNTHETIC.
  • Run the Python cells connected to Full Regression Differences Across Groups.
  • Interpret the output using dummy variables and qualitative information.

Common errors

  • File not found: check that module7_wage_groups_synthetic.csv 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_csv("/data/module-7/module7_wage_groups_synthetic.csv")
df.head()

Interactive activity

GroupDifferenceHypothesisBuilder

Testing Intercept and Slope Differences

GroupDifferenceHypothesisBuilder: choose the coding rule, base group, or probability interpretation before reading the coefficient.

MODULE7_WAGE_GROUPS_SYNTHETIC

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 should students check before trusting the result in Testing Intercept and Slope Differences?

Quick quiz

What should students check before trusting the result in Testing Intercept and Slope Differences?

Quick quiz

Why is MLB1 a reasonable practice dataset here?

Key takeaway

Testing Intercept and Slope Differences helps students convert qualitative information into transparent, testable regression comparisons.

Download dataDownload resultsDownload interpretation