Final answer:
Pure heteroscedasticity occurs when the variance of the error terms in a regression model is related to the predicted values, while impure heteroscedasticity occurs when the variance is also related to other factors not included in the model.
Step-by-step explanation:
Pure heteroscedasticity occurs when the variance of the error terms in a regression model is related to the predicted values. This means that as the predicted values change, the variance of the residuals also changes.
On the other hand, impure heteroscedasticity occurs when the variance of the error terms is not only related to the predicted values, but also to other factors that are not included in the model. These other factors could be omitted variables or misspecified functional forms.
For example, let’s say you are analyzing a housing market dataset to predict housing prices.
If pure heteroscedasticity is present, the scatter plot of the residuals against the predicted values would show a consistent pattern such as a cone shape, indicating that the variance of the residuals increases or decreases systematically with the predicted values.
However, if impure heteroscedasticity is present, the scatter plot of the residuals against the predicted values would show a more scattered pattern with no clear systematic relationship.