In the presence of heteroscedasticity, which statistic becomes unreliable?

In the context of heteroscedasticity, the adjusted R² statistic can indeed become unreliable. Heteroscedasticity refers to the situation in regression analysis where the variance of the errors is not constant across all levels of the independent variable(s). This violation of the assumption of constant variance can distort the validity of standard statistical measures, including adjusted R².

Adjusted R² is designed to provide a better measure of the goodness-of-fit for regression models, particularly when different numbers of predictors are used. However, when heteroscedasticity is present, the calculations that underpin adjusted R² may be influenced by the variability in the error terms. As a result, adjusted R² may not accurately reflect the true explanatory power of the model, as it is sensitive to the scale of the residuals.

In contrast, while measures like the variance inflation factor (VIF) and the F test are also affected by violations of the assumptions underlying linear regression, the adjusted R² tends to be more directly distorted by the presence of heteroscedasticity. Therefore, it is the most clear-cut response regarding which statistic becomes less reliable under these conditions.