Heteroscedasticity

As explained in Machine Learning System Design

Heteroscedasticity is the condition in which regression-error variance changes across predictor or fitted-value levels.

Heteroscedasticity occurs when regression-error variance is not constant across predictor or fitted-value levels. In demand forecasting, higher fitted values can show greater residual variance. section 9.2.2

Check for heteroscedasticity during regression error analysis:

• Use a scale-location plot to assess whether residual variance remains homogeneous. section 9.2.2
• Treat a horizontal pattern with evenly dispersed points as evidence of homoscedasticity; increasing spread at higher fitted values signals a problem. section 9.2.2
• Compare the result with residuals-versus-fitted, Q-Q, and leverage plots to distinguish variance problems from other assumption failures or influential cases. section 9.2.2

Figure 9.11 Four diagnostic plots for linear regression’s residual analysis in both cases (Case 2: Assumptions are not met)

Compare diagnostic plots where regression assumptions hold with plots showing assumption failures, including changing residual variance. section 9.2.2

How Machine Learning System Design covers it

How deep it goes

Explains changing residual variance and identifies it through scale-location and related diagnostic plots.

Examples

Uses demand forecasting and a scale-location plot where higher fitted values have higher residual variance.

What it assumes

Assumes familiarity with linear regression, predictors, fitted values, residuals, and basic regression assumptions.

What you can do after

Diagnose/debug regression assumptions by reading residual, scale-location, Q-Q, and leverage plots.

How it connects

Connects heteroscedasticity with linear regression, residuals, homoscedasticity, diagnostic plots, normality, and outliers.

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Also explained in

• 

  liveBookmanning.com
  Effective Data AnalysisHeteroscedasticity is the condition in which the spread of residuals varies across the range of predicted or explanatory values.
• 

  liveBookmanning.com
  Grokking StatisticsHeteroscedasticity is the condition in which the variance of a response changes across the values of an independent variable.
• 

  liveBookmanning.com
  Statistics Every Programmer NeedsHeteroscedasticity is the condition that the variance of regression residuals changes systematically across levels of the predictors.

Compare how 4 books explain heteroscedasticity →

Related concepts

• homoscedasticitycontrasts with · Homoscedasticity is the statistical condition in which regression-error or response variance remains approximately constant across predictor or fitted-value levels.
• Pearson correlation coefficientcontrasts with · The Pearson correlation coefficient measures the strength and direction of the linear relationship between two numerical variables.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning System Design. The section links point to the parts of the book it draws on.