Independence of Error Term Observations

Correlation in observations

The Gauss-Markov theorem assumes that the observations of the error term are independent and uncorrelated. However, observations that are collected over time or across regions are likely to be correlated over time or within a region. If the temporal or spatial dependence isn’t modeled explicitly, the residuals will be correlated over time or spatially, causing standard error estimates to be biased. Since our focus in this course is the cross-sectional design, we won’t explore the time dependence, usually referred to as autocorrelation in the residuals. The dataset final.85v2 does have a spatial dimension. So, we’ll explore whether there’s any systematic pattern in the residuals that are correlated with regions. The figure below plots residuals versus fitted values by continent, a variable for regions.