Lesson 12

Binary by Continuous Interactions

Big question

How can a slope differ across groups?

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain binary by continuous interactions in plain language.
  • Use categorical variable correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Multiplying a dummy by a continuous variable lets the slope on that variable differ for the D=1 group.

Key terms

Categorical variable
A variable whose values name groups rather than measure amounts.
Dummy-variable trap
Perfect collinearity caused by including an intercept and every category indicator.
Linear probability model
An OLS model with a binary dependent variable interpreted as a probability.

Core formula

yi=β0+δ0Di+β1xi+δ1Dixi+uiy_i = \beta_0 + \delta_0D_i + \beta_1x_i + \delta_1D_ix_i + u_i

Use plain-language interpretation before algebra.

Example

MODULE7_WAGE_GROUPS_SYNTHETIC is an original Ceteris Lab synthetic teaching dataset for binary by continuous interactions. It lets students practice group slope without presenting fabricated real-world empirical findings.

Interactive visual

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

Original Module 7 visual for Binary by Continuous Interactions.

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

Binary by Continuous Interactions Python example

Binary by Continuous Interactions 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 6Add an intercept column to the regression design matrix.
  6. Line 7Display a result so students can inspect the output.
  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 Binary by Continuous Interactions.
  • 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

GroupSlopeExplorer

Binary by Continuous Interactions

GroupSlopeExplorer: 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 Binary by Continuous Interactions?

Quick quiz

What should students check before trusting the result in Binary by Continuous Interactions?

Quick quiz

Why is HPRICE1 a reasonable practice dataset here?

Key takeaway

Binary by Continuous Interactions helps students convert qualitative information into transparent, testable regression comparisons.

Download dataDownload resultsDownload interpretation