Use VOTEl for this exercise.
(i) Estimate a model with voteA as the dependent variable and prystrA, democA, log(expendA),
and log(expendB) as independent variables. Obtain the OLS residuals, $\hat{u}_{i},$ and regress these on
all of the independent variables. Explain why you obtain $R^{2}=0$ .
(ii) Now, compute the Breusch-Pagan test for heteroskedasticity. Use the $F$ statistic version and
report the $p$ -value.
(iii) Compute the special case of the White test for heteroskedasticity, again using the $F$ statistic
form. How strong is the evidence for heteroskedasticity now?

Answer

i. This is the goal of OLS. ii. BP unable to reject null (homoskedasticity) at 5%. iii. White test gives similar conclusion.

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Video Transcript

this is the regression result. The art square of the regression is 0.8 and there are 173 observations in the sample. I have the beta estimates in blue and they're centered errors in green. So given this regression, now you can get the residuals from the regression and then regrets the residual under right hand side variables. Again, you may find that your are square would be almost zero. This happens due to the outcome of their old ls the purpose of the l s. So ls chooses beta head such that they are uncorrelated with their residuals or the error terms and error terms will also have a zero sample Simple mean. Also, we have a very well defined, uh, model. If we run into problems such as admitted variables, then it's likely that the regression of the residual on their right hand side variables will not produce. A zero are square for Part B and C. We're going to test whether there is hetero Scholastic City. The null hypothesis in both B and C is and no had terrorists. Galatis City or there is home. Most get elasticity in Part B. We will do a BP test in the BP test, we will regret they're square residual on the independent variables. In part one, the EFS test the F statistic with four and 168 degrees of freedom ISS about 2.33 with a P value of 0.58 And it means that we are are unable to reject the null hypotheses at the 5% level. For policy, we do a white test. A white test, um, is conducted by regressing The square residuals on there fitted value of their outcome variable and fitted Value square actually vote a head and vote a head square. And what a hat. Are there old aesthetic values from Part one? Yeah, the F start with two and 1 70 degrees of freedom. It's about 2.79 with a p value of pointing 065 Oh, and we have a similar conclusion to part B. In short. For both part, there is some evidence of hetero Scholastic city, but not quite at the 5% level.

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