MODULE8_INCOME_SAVINGS_SYNTHETIC
Simulating Heteroskedasticity
Generate and visualize changing variance.
Module 8
Heteroskedasticity
Learn how changing error variance affects regression inference, how to use heteroskedasticity-robust standard errors and tests, how to diagnose heteroskedasticity, and when weighted least squares or feasible GLS may improve estimation.
20 lessons9 to 13 hoursIntermediate to Advanced Intermediate
Skills
Define homoskedasticity and heteroskedasticity using conditional error variance.Distinguish coefficient validity from inference validity when errors have changing variance.Compute and interpret heteroskedasticity-robust standard errors, t tests, confidence intervals, and joint tests.Use residual plots, Breusch-Pagan tests, and White tests as diagnostics without overclaiming what they prove.Explain weighted least squares, known-form heteroskedasticity, group-size weighting, and feasible GLS.Compare OLS, robust OLS, WLS, and robust WLS results in professional applied language.Explain why the linear probability model is heteroskedastic and why robust inference is usually the safe starting point.Produce a diagnostic report that separates practical importance, statistical evidence, and model limitations.
Progress tracking
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Module resources
20 quiz checks22 datasets12 notebooks
Lessons
1What Is Heteroskedasticity?How can regression uncertainty change across values of x?Open lesson2What Heteroskedasticity Does and Does Not BreakWhich OLS claims survive changing error variance, and which inference claims need repair?Open lesson3Visual Signs of HeteroskedasticityWhat can residual plots suggest before formal tests?Open lesson4Robust Standard ErrorsHow can we keep OLS coefficients but repair the covariance estimate?Open lesson5Robust t Tests and Confidence IntervalsHow do robust standard errors change tests and intervals?Open lesson6Robust Joint TestsHow do we test several restrictions when conventional F tests are not reliable?Open lesson7The Logic of Robust LM TestsWhy can a restricted model still tell us about excluded regressors?Open lesson8The Breusch-Pagan TestHow does an auxiliary regression of squared residuals detect changing variance?Open lesson9The White TestHow can squares and interactions detect flexible variance patterns?Open lesson10Special White Test Using Fitted ValuesHow can fitted values give a compact White-style diagnostic?Open lesson11Interpreting Heteroskedasticity Tests CarefullyWhat should we do after a significant diagnostic test?Open lesson12Log Transformations and Variance StabilizationWhen can logging a positive outcome make error spread easier to model?Open lesson13Weighted Least Squares IntuitionWhy should noisier observations sometimes receive less weight?Open lesson14Known-Form HeteroskedasticityWhat if the shape of the variance function is known up to scale?Open lesson15Group Means, Population Weights, and Aggregated DataWhy do larger groups usually produce more precise means?Open lesson16Feasible GLSHow can we estimate weights when the variance function is unknown?Open lesson17What If the WLS Variance Model Is Wrong?Why should WLS results still be checked with robust standard errors?Open lesson18Prediction under HeteroskedasticityWhy can prediction intervals widen at high-variance x values?Open lesson19The Linear Probability Model RevisitedWhy is a binary dependent variable necessarily heteroskedastic?Open lesson20Module 8 Capstone: Diagnose and Correct HeteroskedasticityHow do we produce a professional heteroskedasticity diagnostic report?Open lesson
Notebook labs
MODULE8_ROBUST_SE_DEMO
Conventional versus Robust Standard Errors
Compare conventional, HC0, HC1, HC2, and HC3 standard errors.
MODULE8_INCOME_SAVINGS_SYNTHETIC
Breusch-Pagan Test
Run and manually audit the Breusch-Pagan workflow.
MODULE8_HOUSING_VARIANCE_SYNTHETIC
White Test
Use full and fitted-value White diagnostics.
MODULE8_ROBUST_SE_DEMO
Robust Joint Tests
Test multiple restrictions with robust covariance.
MODULE8_INCOME_SAVINGS_SYNTHETIC
Weighted Least Squares
Choose inverse-variance weights and compare OLS with WLS.
MODULE8_WLS_GROUP_MEANS
Population and Group-Size Weights
Use group size as a precision weight.
MODULE8_FGLS_DEMO
Feasible GLS
Estimate a variance function and fit FGLS.
MODULE8_FGLS_DEMO
Robust Standard Errors after WLS
Compare WLS conventional and robust standard errors.
MODULE8_HOUSING_VARIANCE_SYNTHETIC
Prediction Intervals with Changing Variance
Plot prediction intervals under changing variance.
MODULE8_BINARY_OUTCOME_LPM
LPM Robust Inference
Estimate a linear probability model with HC1 robust standard errors.
MODULE8_INCOME_SAVINGS_SYNTHETIC
Module 8 Capstone
Complete a full diagnostic and correction workflow.