What does the assumption of homoscedasticity in linear regression refer to?

The assumption of homoscedasticity in linear regression refers to the assumption that the variance of the errors (or residuals) is constant across all levels of the independent variables. In other words, it means that the spread of the residuals is the same for all values of the predictors.

To check for homoscedasticity, you can plot the residuals against the predicted values or the independent variables. If the spread of the residuals appears to be consistent across the range of predicted values or independent variables, then the assumption of homoscedasticity is likely met. On the other hand, if the spread of the residuals is not consistent and shows a pattern (such as a funnel shape or increasing/decreasing spread), then the assumption of homoscedasticity may be violated.

If the assumption of homoscedasticity is violated, it can lead to biased and inefficient estimates of the regression coefficients. In such cases, you may need to consider using alternative regression models or applying transformations to the variables to achieve homoscedasticity.