Question

1. Carefully go through each statement. Answer true or false with explanation (only answers with an explanation will gain credit). (a) In a regression model, a stochastic regressor is an explanatory variable that has a random component (4 marks] (b) When a stochastic regressor is used in a regression model, OLS regression estimates will be biased. [4 marks] (c) Heteroscedasticity occurs when the disturbance term in a regression model is correlated with one of the explanatory variables. [4 marks] (d) In the presence of heteroscedasticity, ordinary least squares (OLS) is an inefficient estimation technique and this causes / tests and F tests to be invalid. [4 marks] (e) Heteroscedasticity can be detected by comparing the residuals from a regression using half of the observations with those from a regression using the other half and see if there is a significant difference. [4 marks]

Answer 1

1. False, In regression model we assume regressor or the explanatory variable constant. This is necessary for finding out conditional value of the regressand.
2. False, If the regressors are stochastic then the OLS regression estimates will be random may not be biased.
3. False. Heteroscedasticity occurs when variability in the error term as define by explanatory variable is not constant.
4. True. The estimators will have high variances and standard error, thus making t and F statistically insignificant and allows to accept the Nulls that could have been rejected.
5. False. We first must omit the some values from centre, so that the difference become more pronounced and then check the standard errors or variation in the two groups.