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Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
In the JMP output, the "Durbin-Watson" value gives the test statistic (d), which is testing whether the residuals have first-order positive autocorrelation. You can get the p-value associated with this test by clicking on the section red triangle menu and selecting the "Significance P-Value" option (note that the computation of this exact probability can be memory and time-intensive if there are many observations). A significant p-value (based on your chosen significance level, commonly 0.05) allows you to reject the null hypothesis that the residuals are independent and conclude that there is first-order positive autocorrelation.
The value under AutoCorrelation simply displays the calculated autocorrelation of the residuals.
Rules of thumb regarding the value of d are discussed in the Durbin–Watson statistic Wikipedia article: Since d is approximately equal to 2(1 − r), where r is the sample autocorrelation of the residuals, d = 2 indicates no autocorrelation. The value of d always lies between 0 and 4. If the Durbin–Watson statistic is substantially less than 2, there is evidence of positive serial correlation. As a rough rule of thumb, if Durbin–Watson is less than 1.0, there may be cause for alarm. Small values of d indicate successive error terms are positively correlated. If d > 2, successive error terms are negatively correlated.