heteroscedasticitás

Heteroscedasticity refers to a situation in statistical modeling, particularly in regression analysis, where the variance of the errors (or residuals) is not constant across all levels of the independent variables. In simpler terms, the spread of the data points around the regression line is not uniform. This is the opposite of homoscedasticity, where the error variance is constant.

The presence of heteroscedasticity can have significant implications for statistical inference. While ordinary least squares (OLS) estimators remain unbiased and consistent in the presence of heteroscedasticity, they are no longer the most efficient. More importantly, the standard errors of the regression coefficients are estimated incorrectly, leading to invalid hypothesis tests (t-tests, F-tests) and confidence intervals. This means that conclusions drawn about the significance of independent variables might be misleading.

Common causes of heteroscedasticity include omitted variables that are related to the variance of the error term, incorrect functional form of the model, and outliers. Visual inspection of residual plots, such as plotting residuals against predicted values or independent variables, is a common method for detecting heteroscedasticity. Statistical tests like the Breusch-Pagan test or the White test can also be used to formally assess its presence.

If heteroscedasticity is detected, several approaches can be taken to address it. These include transforming the dependent variable (e.g., using a logarithm), using weighted least squares (WLS) regression where observations with higher variance are given less weight, or employing robust standard errors that are designed to be valid even in the presence of heteroscedasticity.