Lesson 15

Multicollinearity and VIF

Big question

Why can highly related regressors make estimates imprecise?

Lesson progress

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain multicollinearity and vif in plain language.
  • Use ceteris paribus correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Multicollinearity means explanatory variables share information. VIF summarizes how much the variance of a coefficient is inflated by that shared information.

Key terms

ceteris paribus
Other included factors held fixed for interpretation.
multicollinearity
Strong but not perfect relationships among explanatory variables.
residual
The sample prediction error y minus fitted y.

Core formula

VIFj=1/(1−Rj2)VIF_j = 1 / (1 - R_j^2)

Use plain-language interpretation before algebra.

Example

A high VIF is a warning about precision, not automatic proof that a model is invalid or that a control should be removed.

Interactive visual

VIF calculator and multicollinearity visualizer

Original Module 3 visual for Multicollinearity and VIF.

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

Multicollinearity and VIF Python example

Multicollinearity and VIF 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 6Keep rows that have the variables required for this model.
  6. Line 7Add an intercept column to the regression design matrix.
  7. Line 8Create or update a Python object used in the analysis.
  8. Line 9Run this Python instruction as part of the lesson workflow.
  9. Line 10Run this Python instruction as part of the lesson workflow.
  10. Line 11Run this Python instruction as part of the lesson workflow.
  11. Line 12Display a result so students can inspect the output.

Python walkthrough

  1. 1Load the dataset and keep only variables needed for the current model.
  2. 2Construct the dependent variable and explanatory-variable matrix.
  3. 3Add a constant so the regression includes an intercept.
  4. 4Fit OLS and interpret coefficients with the controls held fixed.

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

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

Learning goals

  • Load and inspect WAGE1.
  • Run the Python cells connected to Multicollinearity and VIF.
  • Interpret the output using VIF and multicollinearity.

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

MulticollinearityVisualizer

Calculate VIF

Translate shared variation among regressors into a precision warning.

DISCRIM

Controlled prediction

Simple prediction2.12
Multiple-regression prediction1.76
Absolute residual signal0.25

Interpretation sentence

Holding experience and tenure fixed, one more year of education changes predicted log wage by about 0.075 in this teaching setup.

Residual sketch

Variable role check

In a wage model with education as the focal x, classify experience.

Precision check

Larger samples tighten estimates. Under the Gauss-Markov assumptions, OLS has the smallest variance among linear unbiased estimators.

VIF calculator

VIF: 2.22

SE index: 0.136

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 interpretation focus in Multicollinearity and VIF?

Quick quiz

Which interpretation habit is most important in Multicollinearity and VIF?

Quick quiz

Why is HTV a reasonable practice dataset here?

Key takeaway

Multicollinearity and VIF helps turn multiple regression output into a careful ceteris paribus interpretation.

Download dataDownload resultsDownload interpretation