R Statistics Cookbook

Testing homoscedasticity

The ordinary least squares algorithm generates estimates that are unbiased (the expected values are equal to the true values), consistent (converge in probability to the true estimates), and with the minimal variance among unbiased estimates (when we get more data, the estimates don't change much, compared to other techniques). Also, the estimates are distributed according to a Gaussian distribution. But all of this occurs when certain conditions are met, in particular the following ones:

• The residuals should be homoscedastic (same variance).
• The residuals should not be correlated, which generally occurs with temporal data.
• There is no perfect correlation between variables (or linear combinations of variables). ...