Question

What is the null hypothesis for the Durban Watson Test?

Answer 1

The null hypothesis for the Durbin-Watson test is that there is no first-order serial correlation in the residuals of a regression model.

Step-by-step explanation:

The Durbin-Watson test is used to detect the presence of first-order serial correlation in the residuals of a regression analysis. Serial correlation occurs when the error terms of a regression model are correlated with each other. The null hypothesis (H0) for the Durbin-Watson test asserts that there is no such serial correlation in the residuals, meaning that the errors are independent.

Mathematically, the null hypothesis can be expressed as follows:

`\[H_0: \rho = 0\]`

Here, \(\rho\) represents the first-order autocorrelation coefficient. If the test statistic, denoted as (d), is close to 2, it indicates no serial correlation, supporting the null hypothesis. On the other hand, values significantly different from 2 suggest the presence of serial correlation, leading to the rejection of the null hypothesis.

The test statistic is calculated using the formula:

`\[d = (\sum_(t=2)^(n) (e_t - e_(t-1))^2)/(\sum_(t=1)^(n) e_t^2)\]`

Where
`\(e_t\)` represents the residuals. If
`\(d\)` is approximately 2, the null hypothesis is not rejected. If
`\(d\)` deviates significantly from 2, it provides evidence against the null hypothesis.

In summary, the null hypothesis for the Durbin-Watson test asserts that there is no first-order autocorrelation in the residuals, and the test is conducted to examine whether this assumption holds in the regression model.