Introduction

In the realm of regression analysis, it’s crucial to ensure the validity of the assumptions underlying your model. One of these assumptions is homoskedasticity, which implies that the variance of the error terms is constant across all levels of the independent variables. However, in practice, this assumption may not hold true, leading to heteroskedasticity. This chapter delves into the methods for testing whether a regression is affected by heteroskedasticity and understanding its implications.

Testing for Heteroskedasticity

Heteroskedasticity, often characterized by increasing or decreasing variability in the error terms as the values of the independent variables change, can undermine the reliability of your regression results. To test for heteroskedasticity, one commonly used method is the White Test (also known as the White heteroskedasticity-consistent estimator).

White Test

The White Test involves regressing the squared residuals from your initial regression model against the independent variables. Mathematically, the model can be represented as:

$$\text{Squared Residuals} =\beta_0+\beta_1 X_1+\beta_2 X_2+\ldots+\beta_k X_k+\epsilon$$

Here, $X_1$, $X_2$, $\ldots$, $X_k$ are the independent variables, $\beta_0$, $\beta_1$, $\ldots$, $\beta_k$ are the coefficients, and $\epsilon$ represents the error term. If the coefficients in this auxiliary regression are statistically significant, it suggests the presence of heteroskedasticity.

Interpretation

A statistically significant relationship between the squared residuals and the independent variables indicates the likelihood of heteroskedasticity in the original regression. In simpler terms, if the variability of the residuals systematically changes as the values of the independent variables change, it indicates heteroskedasticity.

Example: Suppose you’re analyzing a regression model to predict housing prices based on factors like size, location, and amenities. After conducting the White Test, you find that the coefficients in the squared residuals regression are significant. This suggests that the variability of the housing price residuals changes as the size, location, and amenities vary, potentially indicating heteroskedasticity.