homoskedastisia

Homoskedasticia is a statistical concept that arises in the analysis of multiple linear regression models with multiple independent variables. It refers to the situation where the residual variance is assumed to be the same across different levels of the independent variables, a key assumption of linear regression.

In a multiple linear regression model, the residuals are the differences between the observed response values and the predicted values. The assumption of homoskedasticia implies that the variance of these residuals is consistent across different values of the independent variables. This is an important assumption because many statistical tests, such as t-tests and F-tests, rely on it.

If homoskedasticia is violated, the variance of the residuals is not constant across different levels of the independent variables. This type of heteroskedasticia can lead to incorrect conclusions when using statistical tests, particularly those that assume equal variances across groups. It is often detected by visual inspection of a residual plot or by using specific statistical tests, such as the Breusch-Pagan test or the White test.

If homoskedasticia is violated, modifications to the model, such as transformation of the independent variables or the response variable, can be made to meet the assumption. Using robust standard errors or employing techniques, such as weighted least squares or generalized least squares, can also address the issue. Correcting for homoskedasticia is essential to ensure the validity of the statistical inferences drawn from a multiple linear regression model.