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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:

**H _{0}Â (null hypothesis):Â **There is no correlation among the residuals.

**H _{A}Â (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**e**The t_{t}:^{th}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:

How to Perform a Durbin-Watson Test in R

How to Perform a Durbin-Watson Test in Python

How to Perform a Durbin-Watson Test in Excel