Please define the notations clearly to answer the questions below:

1. How to test the existence of Heteroskedasticity in the linear regression model? State the Breusch-Pagan test and White test.
2. How to obtain the feasible generalized least square estimator?
3. Explain what the RESET does and how to implement the test.
4. What are the conditions that a proxy variable should satisfy to provide consistent estimator for the parameter of interest?
5. What is the difference-in-difference estimator? How to use this estimator to perform policy evaluation?
6. In a two period panel data fixed effect model, how to obtain the least squares estimator for the key parameter of interest using the differenced equation?
7. What is the with-in estimator for the fixed effect panel data model?
8. What is the random effect estimator for the panel data model? What is the key difference between random effect and fixed effect?
9. What is endogeneity in linear regression model? What are the conditions for a valid instrumental variable? How to obtain the instrumental variable estimator?
10. How to obtain the two-stage least squares estimator in a multiple linear regression in which one regressor is endogenous?