# Calculates the Durbin-Watson statistic

In such a case, the regression line has one parameter only, which is its slope: The requirement of having zero intercept has major impact of inferential statistic of the estimated model, that is, one cannot apply any test of hypothesis or construct confidence interval.

## Calculates the Durbin-Watson statistic

### using the Durbin–Watson statistic and the estimated variance

Understand that the distribution of p-values under null hypothesis H is uniform, and thus does not depend on a particular form of the statistical test.

### This statistic is then used for testing the above null hypothesis.

For the fixed-sample size, when the number of realizations is decided in advance, the distribution of p is uniform, assuming the null hypothesis is true.

## Durbin-Watson Table for values of alpha = .01 and .05

1 Durbin Watson Test The Durbin-Watson statistic is a simple numerical method for checking serial dependence. Let rk be the residuals sorted into time order.

## Statistical hypothesis testing - Wikipedia

where is the number of observations. Note that if one has a lengthy sample, then this can be linearly mapped to the Pearson correlation of the time-series data with its lags.^{} Since is approximately equal to 2(1 − ), where is the sample autocorrelation of the residuals,^{} = 2 indicates no autocorrelation. The value of 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 indicate successive error terms are, on average, close in value to one another, or positively correlated. If > 2, successive error terms are, on average, much different in value from one another, i.e., negatively correlated. In regressions, this can imply an underestimation of the level of .

## Durbin_Watson - The Durbin-Watson test statistic tests …

In , the **Durbin–Watson statistic** is a used to detect the presence of at lag 1 in the (prediction errors) from a . It is named after and . The distribution of this ratio was derived by (von Neumann, 1941). Durbin and Watson (1950, 1951) applied this statistic to the residuals from regressions, and developed bounds tests for the that the errors are serially uncorrelated against the alternative that they follow a first order process. Later, and developed several von Neumann–Durbin–Watson type test statistics for the null hypothesis that the errors on a regression model follow a process with a against the alternative hypothesis that the errors follow a stationary first order (Sargan and Bhargava, 1983). Note that the distribution of this test statistic does not depend on the estimated regression coefficients and the variance of the errors.^{}