The general linear model assumes independence What does inde

The general linear model assumes independence. What does independence mean? Provide an example of violating the assumption of independence.

Solution

An important independence assumption is that the error of the mean has to be independent from the independent variables.

Violations of independence are potentially very serious in time series regression models

serial correlation in the errors (i.e., correlation between consecutive errors or errors separated by some other number of periods) means that there is room for improvement in the model, and extreme serial correlation is often a result of a badly mis-specified model. Serial correlation (also called as autocorrelation”) is sometimes a byproduct of a violation of the linearity assumption, as in the case of a simple (straight) trend line fitted to data which are growing exponentially over time.

Independence can also be violated in non-time-series models if errors tend to always have the same sign under particular conditions, i.e., if the model systematically underpredicts or overpredicts what will happen when the independent variables have a particular configuration.