Jarque-Bera test
The Jarque-Bera test checks whether regression residuals are normally distributed by comparing their sample skewness and kurtosis to the values expected under normality, producing a statistic compared to a chi-square distribution.
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A regression's 100 residuals show a sample skewness of 0.3 and kurtosis of 3.6, close to the normal benchmarks of 0 and 3. The Jarque-Bera statistic, (100 ÷ 6) × [0.3² + 0.6² ÷ 4], works out to 3.00, comfortably below the 5.99 chi-square critical value, so there is no strong evidence against normality.
Where it fits
SubjectData Analysis & StatisticsAdvancedTopicRegression Diagnostics & ProblemsAdvanced
The formula
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Variables
- Number of residuals
- Sample skewness of the residuals
- Sample kurtosis of the residuals
Tests whether residuals' skewness and kurtosis are consistent with a normal distribution; compared to a chi-square distribution with 2 degrees of freedom.