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What is the Breusch-Pagan Test? The Breusch-Pagan test is used to determine whether or not heteroscedasticity is present in a regression model. The test uses the following null and alternative hypotheses: Null Hypothesis (H0): Homoscedasticity is present (the residuals are distributed with equal variance)
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We shall introduce beta-score LM tests for heteroscedasticity in linear regression models, which trades-off the degree of robustness and efficiency is through a tuning parameter beta>=0, being beta =0 the classical Breusch-Pagan test-statistic, the most efficient one under absence of outliers.
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Step 2: Perform a Breusch-Pagan Test. Next, we will perform a Breusch-Pagan Test to determine if heteroscedasticity is present. The test statistic is 4.0861 and the corresponding p-value is 0.1296. Since the p-value is not less than 0.05, we fail to reject the null hypothesis. We do not have sufficient evidence to say that heteroscedasticity is.
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Procedure Under the classical assumptions, ordinary least squares is the best linear unbiased estimator (BLUE), i.e., it is unbiased and efficient. It remains unbiased under heteroskedasticity, but efficiency is lost. Before deciding upon an estimation method, one may conduct the Breusch-Pagan test to examine the presence of heteroskedasticity.
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The Breusch-Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these. The null hypothesis is that there is no serial correlation of any order up to p. [3]
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Running the Test. The test statistic for the Breusch-Pagan-Godfrey test is: N * R2 (with k degrees of freedom) Where: n = sample size. R 2 = R 2 ( Coefficient of Determination) of the regression of squared residuals from the original regression. k = number of independent variables. The test statistic approximately follows a chi-square distribution.
