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Breusch-Pagan Test The Breusch-Pagan test is a statistical tool used to assess heteroscedasticity in a linear regression model. Heteroscedasticity occurs when the variation of one variable is larger at certain values of another variable. This can result in bias in ordinary least squares (OLS) estimates, which the Breusch-Pagan test is designed to detect. The Breusch-Pagan test is a statistical method used to determine if a linear regression model has heteroscedasticity, which is the presence of non-constant variance in the errors. This test is commonly used in econometrics to verify assumptions made by statistical models.

### Working of Breusch-Pagan Test

The Breusch-Pagan test works by calculating an F-statistic, which measures the variability of residuals compared to the independent variables. If this F-statistic is statistically significant, then it indicates that heteroscedasticity exists within the dataset and OLS estimates may be biased. In other words, if the F-statistic is high enough, then you can reject the null hypothesis that there is no heteroscedasticity present in the dataset. To calculate the Breusch-Pagan statistic, you first need to calculate a measure of variance heterogeneity called White’s Generalized Variance Ratio (GV). GV measures how much of the variance comes from differences among groups rather than from within group variability.

To calculate GV, we take a squared residual from our linear regression model and divide it by its degrees of freedom. Next, we multiply this value by a factor that takes into account how many groups are present in our data and how large each group is relative to our sample size. The product of these two numbers gives us our GV value, which should be compared against an appropriate critical value from a chi-squared distribution with degrees of freedom equal to 1 plus twice the number of independent variables in our model (this number will also depend on whether or not a constant term was included). If we find that this GV statistic exceeds our critical value, then we can conclude that there is evidence for heteroscedasticity present in our data and OLS estimates may be biased as a result.

We can also use this statistic to quantify how serious this issue might be; normally distributed errors are assumed when running any sort of regression analysis so if GV values are particularly high, then it could indicate serious problems with underlying assumptions related to your data set.