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# The Durbin-Watson Test: Definition & Example

One of the main assumptions in linear regression is that there is no correlation between consecutive residuals. In other words, itâ€™s assumed that the residuals are independent.

When this assumption is violated, the standard errors of the coefficients in a regression model are likely to be underestimated which means predictor variables are more likely to be deemed statistically significant when theyâ€™re actually not.

One way to determine if this assumption is met is to perform aÂ Durbin-WatsonÂ test, which is used to detect the presence of autocorrelation in the residuals of a regression.

### Steps to Perform a Durbin-Watson Test

The Durbin-Watson test uses the following hypotheses:

H0Â (null hypothesis):Â There is no correlation among the residuals.

HAÂ (alternative hypothesis):Â The residuals are autocorrelated.

The test statistic for the Durbin-Watson test, typically denoted d, is calculated as follows:

where:

• T: The total number of observations
• et: The tth residual from the regression model

The test statistic always ranges from 0 to 4 where:

• d = 2 indicates no autocorrelation
• d
• d > 2 indicates negative serial correlation

In general, ifÂ d is less than 1.5 or greater than 2.5 then there is potentially a serious autocorrelation problem. Otherwise, if d is between 1.5 and 2.5 then autocorrelation is likely not a cause for concern.

To determine if a Durbin-Watson test statistic is significantly significant at a certain alpha level, you can refer to this table of critical values.

If the absolute value of the Durbin-Watson test statistic is greater than the value found in the table, then you can reject the null hypothesis of the test and conclude thatÂ  autocorrelation is present.

### What to Do if Autocorrelation is Detected

If you reject the null hypothesis of the Durbin-Watson test and conclude that autocorrelation is present in the residuals, then you have a few different options to correct this problem if you deem it to be serious enough:

• For positive serial correlation, consider adding lags of the dependent and/or independent variable to the model.
• For negative serial correlation, check to make sure that none of your variables areÂ overdifferenced.
• For seasonal correlation, consider adding seasonal dummy variables to the model.

These strategies are typically sufficient to remove the problem of autocorrelation.

### Examples of Performing a Durbin-Watson Test

For step-by-step examples of Durbin-Watson tests, refer to these tutorials that explain how to perform the test using different statistical software: