Detecting Autocorrelation in Residuals
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In linear and nonlinear regression, it is assumed that the residuals are independent of (not correlated with) one another. If the independence assumption is violated, some model fitting results may be questionable. For example, positive correlation between error terms tends to inflate the t-values for coefficients, making predictors appear significant when they may not be.

Minitab provides two methods to determine if residuals are correlated:

·    A graph of residuals versus data order (1 2 3 4... n) can provides a means to visually inspect residuals for autocorrelation. A positive correlation is indicated by a clustering of residuals with the same sign. A negative correlation is indicated by rapid changes in the signs of consecutive residuals.

·    For linear regression, the Durbin-Watson statistic tests for the presence of autocorrelation in regression residuals by determining whether or not the correlation between two adjacent error terms is zero. The test is based upon an assumption that errors are generated by a first-order autoregressive process. If there are missing observations, these are omitted from the calculations, and only the nonmissing observations are used.

To reach a conclusion from the test, you will need to compare the displayed statistic with lower and upper bounds in a table. If D > upper bound, no correlation exists; if D < lower bound, positive correlation exists; if D is in between the two bounds, the test is inconclusive. For additional information, see [8], [35].