(Solved): Consider a simple linear regression model with nonstochastic regressor: \( Y_{i}=\beta_{1}+\beta_{2 ...

Consider a simple linear regression model with nonstochastic regressor: \( Y_{i}=\beta_{1}+\beta_{2} X_{i}+u_{i} \). 1. [3 points] What are the assumptions of this model so that the OLS estimators are BLUE (best linear unbiased estimates)? 2. [3 points] Given that \( \hat{\beta}_{2}=\beta_{2}+\sum \frac{\left(X_{i}-\bar{X}\right) u_{i}}{\sum\left(X_{i}-\bar{X}\right)^{2}} \), show that \( \hat{\beta}_{2} \) is an unbiased estimator of \( \beta_{2} \).