Lesson 10

Interactions between Continuous Variables

Big question

How can the effect of one variable depend on another variable?

Lesson progress

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain interactions between continuous variables in plain language.
  • Use adjusted r-squared correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

An interaction lets the slope for x change with z. The coefficient on x alone is the slope when z equals zero, so it may not be the most useful number to report.

Key terms

Adjusted R-squared
A fit measure that penalizes adding regressors.
Smearing factor
A retransformation adjustment for predicting y from a log(y) regression.
Elasticity
The approximate percent change in y associated with a one percent change in x.

Core formula

partialy/partialx=beta1+beta3zpartial y / partial x = beta_1 + beta_3 z

Use plain-language interpretation before algebra.

Example

M6_SALES_ADVERTISING is a synthetic teaching dataset for interactions between continuous variables. It is designed to practice continuous interactions without presenting fabricated real-world empirical findings.

Interactive visual

Choose values of z and compute the implied slope for x, then write a sentence that avoids treating beta_1 as the whole effect.

Original Module 6 visual for Interactions between Continuous Variables.

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

Interactions between Continuous Variables Python example

Interactions between Continuous Variables 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 7Run this Python instruction as part of the lesson workflow.
  7. Line 8Create or update a Python object used in the analysis.
  8. Line 9Display a result so students can inspect the output.

Python walkthrough

  1. 1Load the synthetic teaching dataset from the Module 6 public data folder.
  2. 2Create transformed variables only after checking their meaning and valid support.
  3. 3Fit a regression that matches the lesson's interpretation target.
  4. 4Print coefficient or prediction summaries that students can connect to the formula.
  5. 5Use comments and output labels so no empirical result is presented without context.

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

M6_GPA_INTERACTIONS

Estimated time

25 to 40 min

Packages

pandas, numpy

Expected output

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

Learning goals

  • Load and inspect M6_GPA_INTERACTIONS.
  • Run the Python cells connected to Interactions between Continuous Variables.
  • Interpret the output using interactions and dummy variables.

Common errors

  • File not found: check that M6_GPA_INTERACTIONS.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-6/M6_GPA_INTERACTIONS.csv")
df.head()

Interactive activity

ContinuousInteractionSurface

Read an interaction slope

Choose a value of z and compute the implied slope for x.

M6_SALES_ADVERTISING

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 main mistake to avoid in Interactions between Continuous Variables?

Quick quiz

What is the main mistake to avoid in Interactions between Continuous Variables?

Quick quiz

Why is M6_SALES_ADVERTISING a reasonable practice dataset here?

Key takeaway

Interactions between Continuous Variables helps students make multiple regression more flexible while keeping interpretation precise and honest.

Download dataDownload resultsDownload interpretation