Breusch-Pagan or White's tests are used to detect what in regression analysis?

Breusch-Pagan or White's tests are used to detect what in regression analysis?

• A. Autocorrelation
• B. Normality of residuals
• C. Linearity of relationship
• D. Heteroscedasticity

Answer: (D)

Heteroscedasticity is what these tests look for. In ordinary least squares regression we assume that the spread of the errors is constant across all levels of the independent variable(s). If the residuals fan out or funnel in as X changes, the standard errors and test statistics can be biased. The Breusch-Pagan test checks this by taking the squared residuals from the main regression and regressing them on the original predictors (and sometimes their squares or cross-products). A significant relationship indicates that the variance of the errors depends on the predictors, i.e., heteroscedasticity. White’s test goes a step further and regresses the squared residuals on the predictors, their squares, and cross-products, capturing a wider range of possible patterns of changing variance without assuming a specific form. A significant result again points to heteroscedasticity. These tests don’t assess autocorrelation, normality of residuals, or the linearity of the relationship; those require different checks. If heteroscedasticity is present, you’d typically use robust standard errors or other remedies, since the coefficient estimates from OLS remain unbiased for the mean structure, but the usual standard errors need adjustment.

Heteroscedasticity is what these tests look for. In ordinary least squares regression we assume that the spread of the errors is constant across all levels of the independent variable(s). If the residuals fan out or funnel in as X changes, the standard errors and test statistics can be biased. The Breusch-Pagan test checks this by taking the squared residuals from the main regression and regressing them on the original predictors (and sometimes their squares or cross-products). A significant relationship indicates that the variance of the errors depends on the predictors, i.e., heteroscedasticity. White’s test goes a step further and regresses the squared residuals on the predictors, their squares, and cross-products, capturing a wider range of possible patterns of changing variance without assuming a specific form. A significant result again points to heteroscedasticity. These tests don’t assess autocorrelation, normality of residuals, or the linearity of the relationship; those require different checks. If heteroscedasticity is present, you’d typically use robust standard errors or other remedies, since the coefficient estimates from OLS remain unbiased for the mean structure, but the usual standard errors need adjustment.