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The independence of errors assumption in regression analysis states that residuals (errors) should not be correlated with one another.
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This means that the value of one residual should not provide information about the value of another. Violating this assumption, particularly in time-series data or spatial data, can lead to misleading statistical inferences, such as underestimated standard errors and inflated significance levels. When errors are correlated (autocorrelated), the model may not capture all underlying patterns in the data, indicating a need for adjustments.
One of the ways to check for independence of errors is through a residual plot, where residuals should appear randomly scattered without any visible pattern.
Additionally, in time-series analysis, autocorrelation can be assessed using the Durbin-Watson test, where a value close to 2 suggests little to no autocorrelation, while values closer to 0 or 4 indicate positive or negative correlation, respectively. We’ll cover this later in the module.
If errors are found to be dependent, several remedies can be applied. In time-series data, using an ARIMA model or Generalised Least Squares (GLS) can help account for autocorrelation. In cases of spatial correlation, models such as spatial regression or mixed-effects models might be more appropriate.
Another approach is to include missing explanatory variables that could be responsible for the observed dependency.
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