# Durbin-Watson test

The Durbin-Watson test checks if there is autocorrelation among the residuals of a linear regression. It is available in Excel using the XLSTAT software.

## Durbin Watson test definition

Developed by J.Durbin and G.Watson (1950,1951), the Durbin-Watson test is used to **detect the autocorrelation** in the **residuals** from a **linear regression**.

In practice, the errors are often autocorrelated, it leads to undesirable consequences such as sub-optimal least-squares estimates.

Assume that the error terms (epsilon) are stationary and normally distributed with mean 0. The null and alternative hypotheses of the Durbin-Watson test are:

- H0: The errors are uncorrelated
- H1: The errors are AR(1)

And the test statistic D is:

In the context of the Durbin-Watson test, the main problem is the evaluation of the p-values. In XLSTAT the Imhof procedure (1961) is used to solve this problem.

## Options of the Durbin-Watson test in XLSTAT

**Significance level (%):** Enter the significance level for the test (default value: 5%)

**Order:** Enter the order, i.e. the number of lags for the residuals (default value: 1)

**Do not accept missing data:** Activate this option so that XLSTAT does not continue calculations if missing values have been detected.

**Remove observations:** Activate this option to remove the observations which include missing data.

**Replace by the average of the previous and next values:** Activate this option to estimate the missing data by the mean of the first preceding non missing value and of the first next non missing value.

**Ignore missing data:** Activate this option to ignore missing data.

**Descriptive statistics**: Activate this option to display descriptive statistics for the residuals.

## Results of the Durbin-Watson test in XLSTAT

In XLSTAT, the results of the Durbin-Watson test are the following:

The tables of descriptive statistics show the simple statistics for the residuals. The number of observations, missing values, the number of non-missing values, the mean and the standard deviation (unbiased) are displayed.

The value of the statistic D and the p-value of the Durbin-Watson test. A short interpretation is also displayed.

## Example

A tutorial on the Durbin-Watson test is available on our helpcenter.

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