Question

a) Please explain what the Durbin-Watson statistic tests for and how it is used.

b) Please explain how to perform both the Bruesch-Pagan and White tests (STATA can do both tests automatically, but this question is asking you to explain what is going on.)

c) What is ρ in the study of serial correlation, and what is its role in Generalized Least Squares?

Answer 1

a) Durbin-Watson statistic test is used for testing the auto correlation present in residual and regression analysis .

It is a specific type of auto correlation . Auto correlation means it works as lagged correlation between variable's current value and variable's past value .

During the use of this test some assumptions are followed :

• Errors are normally distributed with mean 0
• Errors are stationary .

Now, the Test statistic is calculated with the formula :

Here, = Residuals and T is the number of observations .

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b) The test statistic for Bruesch-Pagan test = with k degree of freedom .

Here, Sample size,

Coefficient of determination of the regression of squared residuals .

The statistic follows chi-square distribution

Some assumptions are as followed :

• Null hypothesis for this test is that the error variances are equal .
• Alternative hypothesis are that error variances are not equal .

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White Test : To testing the constant variance just take a regression model from original regression model onto a set of regressors so that it contains along with the squared and cross product.

then the test statistics is calculated using formula: .

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c) In the study of serial correlation , is the correlation coefficient between between variables .

Generalized Least Squares is used in estimating the unknown parameters in the linear regression model for the correlation () between the residuals in a regression model.