What is Heteroscedasticity?

Heteroscedasticity in regression is a common issue that affects the accuracy of statistical models. It occurs when the variance of errors is not constant across all levels of the independent variables. In simpler terms, the spread or “scatter” of the residuals (errors) changes as the value of the independent variable(s) changes.

In contrast, when the variance of the errors is constant, we refer to it as homoscedasticity, which is one of the key assumptions of the Classical Linear Regression Model (CLRM).

Why is Heteroscedasticity a Problem?

Heteroscedasticity does not bias the coefficient estimates themselves, but it causes the standard errors to be incorrect. This leads to:

• Inefficient estimates: Ordinary Least Squares (OLS) is no longer the Best Linear Unbiased Estimator (BLUE).

• Unreliable hypothesis tests: t-tests and F-tests may give misleading results.

• Wider or narrower confidence intervals, depending on the pattern of variance.

As a result, heteroscedasticity can lead to incorrect conclusions about the significance of predictor variables.

Common Causes of Heteroscedasticity

• Omitted variables that influence the variance of the dependent variable.

• Incorrect functional form of the regression model.

• Presence of outliers or skewed data.

• Data combining groups with different variances (e.g., large vs. small firms).

• How to Detect Heteroscedasticity

  Several methods are commonly used to identify heteroscedasticity:

  1. Graphical Method:

  • Plot the residuals against the fitted values.

  • A funnel or cone-shaped pattern indicates heteroscedasticity.

  2. Breusch-Pagan Test:

  A formal statistical test that checks whether the variance of the residuals depends on the values of the independent variables.

  3. White’s Test:

  More general than Breusch-Pagan, it can detect more complex forms of heteroscedasticity.

  4. Goldfeld–Quandt Test:

  Compares the variance of residuals across two subgroups of data.

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  How to Fix or Correct Heteroscedasticity

  1. Log or Square Root Transformation:

  Applying a transformation to the dependent variable often stabilizes the variance.

  2. Use Weighted Least Squares (WLS):

  WLS gives less weight to observations with higher variance, correcting the inefficiency in OLS.

  3. Use Robust Standard Errors:

  Also called heteroscedasticity-consistent standard errors, these correct the standard errors while keeping the OLS estimates.

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  Conclusion

  Heteroscedasticity is a critical issue in regression analysis that can distort statistical inference. While it doesn’t bias the regression coefficients, it does affect their precision and reliability. Therefore, detecting and correcting heteroscedasticity ensures that your regression results are valid, interpretable, and robust.

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