## Durbin-Watson Test

### Purpose

The Durbin-Watson test assesses whether or not there is autocorrelation among the residuals of time series data.

### Definition

The Durbin-Watson test statistic, DW, is

$DW=\frac{\sum _{i=1}^{n-1}{\left({r}_{i+1}-{r}_{i}\right)}^{2}}{\sum _{i=1}^{n}{r}_{i}^{2}},$

where ri is the ith raw residual, and n is the number of observations.

### How To

After obtaining a fitted model, say, mdl, using fitlm or stepwiselm, you can perform the Durbin-Watson test using

dwtest(mdl)
For details, see the dwtest method of the LinearModel class.

### Test for Autocorrelation Among Residuals

This example shows how to test for autocorrelation among the residuals of a linear regression model.

Load the sample data and fit a linear regression model.

mdl = fitlm(ingredients,heat);

Perform a two-sided Durbin-Watson test to determine if there is any autocorrelation among the residuals of the linear model, mdl.

[p,DW] = dwtest(mdl,'exact','both')
p = 0.8421
DW = 2.0526

The value of the Durbin-Watson test statistic is 2.0526. The $p$-value of 0.8421 suggests that the residuals are not autocorrelated.