Detect autocorrelation in residuals

In linear and nonlinear regression, it is assumed that the residuals are independent of (not correlated with) each other. If the independence assumption is violated, some model fitting results might not be reliable. For example, positive correlation between error terms tends to inflate the t-values for coefficients, making predictors seem significant when they might not be.

Minitab provides two ways to determine whether residuals are correlated:

  • Use a graph of residuals versus data order (1, 2, 3, 4, n) to visually inspect residuals for autocorrelation.

    A positive autocorrelation is identified by a clustering of residuals with the same sign. A negative autocorrelation is identified by fast changes in the signs of consecutive residuals.

  • Use the Durbin-Watson statistic to test for the presence of autocorrelation.

    The test is based on 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 get 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.
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