Solved – Breusch-Pagan test

heteroscedasticityhypothesis testinginterpretation

I want an interpretation of this BP test result:

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of envdisc

         chi2(1)      =     0.02
         Prob > chi2  =   0.8829

Best Answer

Take your OLS regression of $y_i$ against your independent variables to get fitted values of $\hat{y}_i$

Find your residuals $u_i=y_i-\hat{y}_i$. You want to know whether the variance of the residuals is constant

So regress the squares of the residuals $u_i^2$ against the same independent variables and find the $R^2$. Under the null hypothesis of homoscedasticity, this should be close to zero

Under the null hypothesis $nR^2$ is asymptotically distributed as $\chi^2_1$: your (Stata?) run gives $0.02$, so find the probability of this or a higher value on that distribution, which is about $0.8829$

Since this presumably is greater than your personal significance level ($0.05$?), you cannot reject the null hypothesis of homoscedasticity on the basis of this data and test

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