When dealing with heteroscedasticity, which statistical effect is affected?

When dealing with heteroscedasticity, the effect most significantly impacted is the reliability of the adjusted R-squared value. Heteroscedasticity refers to the situation in regression analysis where the variance of the residuals (errors) is not constant across all levels of the independent variable(s). This non-constant variance can lead to unreliable estimates of the coefficients.

In a standard linear regression model, one of the assumptions is that the residuals should have a constant variance (homoscedasticity). If this assumption is violated, as it is with heteroscedasticity, the ordinary least squares (OLS) estimates remain unbiased, but their statistical properties are compromised. Specifically, the standard errors of the coefficients can become inaccurate. This implies that the tests of the significance of the predictors are invalidated, leading to misleading conclusions regarding the strength of relationships.

The adjusted R-squared statistic evaluates the proportion of variance explained by the model while accounting for the number of predictors. When heteroscedasticity is present, the estimates of variance become unreliable, which in turn affects the adjusted R-squared calculations. Therefore, the adjusted R-squared cannot be trusted to accurately reflect the goodness of fit of the model under these conditions, making it unreliable