Perform a White test for heteroskedasticity using auxiliary regressions. Attach your results, and write out the form of the test as well as the value of the statistic and its interpretation.
Answer: Sometimes the researcher wish to verify if more than one variable is proportionality factor in the heteroscedasticity process: in these situations it is preferable to consider the Breush Pagan test or the White test. The White test has the advantage that it does not assume a specic form of heteroscedasticity.
It is based on a auxiliary regression with suqred residuals as dependent variable and regressors given by: the regressors of the initial model,, their squares and their cross-products. The White test procedure is as follows:
1 - we estimate the regression model throught OLS obtaining the OLS residuals, ei. For instance we estimate: ^yi = b0 + b1x1i + b2x2i, then ei = yi y^i;
2 - we estimate an auxiliary regression model with e2i as dependent variable and initial regressors, their squares and cross-products as covariates. For instance, we estimate:e2i =0 +1x1i + 2x2i + 3x21i +4x22i +5x1ix2i.3 - we verify the signicance of the auxiliary regression throught the test nR2, which, under the null hypothesis (omoscedasticity) has 2(q), where the degrees of freedom q are equal to the number of regressors in the auxiliary model. In the example q = 5.4 - if the sample value of the 2(q) is greater than the critical one we reject the null hypothesis of omoscedasticity.