Goldfeld Quandt Test
- Splits the sample into two equal-sized subsamples, fits the regression separately on each, and compares the residual variances.
- A significant difference in variances indicates heteroscedasticity; similar variances indicate homoscedasticity.
- The test assumes normally distributed residuals and may be limited when only two subsamples are used.
Definition
Section titled “Definition”The Goldfeld-Quandt test is a statistical test used to determine whether a regression model is heteroscedastic or homoscedastic. Heteroscedasticity occurs when the variance of the residuals is not constant across different values of the independent variables, while homoscedasticity occurs when the variance of the residuals is constant.
Explanation
Section titled “Explanation”To perform the Goldfeld-Quandt test, the sample is divided into two equal-sized subsamples, and the regression is run separately on each subsample. If the variance of the residuals is significantly different between the two subsamples, then the model is considered heteroscedastic. The test therefore compares the residual variances from the two subsamples to assess whether the variance of the residuals is constant across values of the independent variables.
Examples
Section titled “Examples”Housing prices example
Section titled “Housing prices example”Suppose we have a regression model predicting housing prices based on the size of the house and the number of bedrooms. We divide the sample into two equal-sized subsamples, and run the regression on each subsample. If the variance of the residuals is significantly different between the two subsamples, then this indicates that the variance of the residuals is not constant across different values of the independent variables, and the model is heteroscedastic.
Stock returns example
Section titled “Stock returns example”A regression model predicting stock returns based on the stock’s market capitalization and its beta can be tested similarly: divide the sample into two equal-sized subsamples and run the regression on each. If the variance of the residuals is significantly different between the two subsamples, then this indicates heteroscedasticity.
Use cases
Section titled “Use cases”- Detecting whether the variance of regression residuals is constant or not, which informs correct interpretation of regression results.
- Applied in practical regression analyses where residual variance behavior affects inference and model diagnostics.
Notes or pitfalls
Section titled “Notes or pitfalls”- The test only divides the sample into two subsamples, which may not always be sufficient to accurately detect heteroscedasticity; in some cases it may be necessary to divide the sample into more than two subsamples.
- The Goldfeld-Quandt test assumes that the residuals are normally distributed; when residuals are not normally distributed, the test may not be appropriate.
Related terms
Section titled “Related terms”- Heteroscedasticity
- Homoscedasticity
- Residuals
- Regression model