Question
Brief description: 1) (5) Please briefly describe what heteroskedasticity is 2) (5) Please briefly state what Gauss-Markov theorem is 1) (2)f the regression errors either have different variances (heteroskedasticity) or ar 2) (2)The adjusted R(R2) always increases even if we added some irrelevant variables i 3) Tell "true" or "False" on the following statements correlated with one another (autocorrelation), then OLS is unbiased but is no longer the best estimator. The best estimator is GLS the regression. (2)The distribution of the OLS estimator under classical assumptions takes t forma is N (' he followin B)Suppose you want to carry out a F-test test 1-2-0 in the sample regre hich obeys the classical assumption. ease write down the steps and detail about this F-test, including the hypothesis, restricted d unrestricted model, F-stat, and how to draw conclusion based on F-stat. e simple linear regression model is given by sume that the classical assumptions hold. 1) (3)Consider an estimator for : is this an unbiased estimator for ? (4)Calculate var(). (4)compare with the OLS estimator from the previous parts of the question to discuss which estimator you think is best Hint: To simplify the derivations, you may use the following result: 2) 3) Use the concept of efficiency and your results
Explanation / Answer
1. Heteroscedasticity, also spelled heteroskedasticity, refers to a situation in statistics in which the variability of a dependent variable is not equal across the entire range of values of the predictor variable. The scatter plot of the variable showing heteroscedasticity will have a cone-like shape as the variability of the dependent variable becomes wide or narrow with an increase in the value of the predictor variable. Homoscedasticity is the opposite of homoscedasticity, which means that the variability of the dependent variable is same across all values of the independent variable.
