4. Consider the simple regression y_i = α + β x_i + _iAnd suppose population parameter β = 2 and least square estimator β = 2.3. Now consider the regression (x_i - y_i) = α^* + β^* x_i + u_i.What is the value of β? (A) 1 (B)-1 (C)-1.3 (D)-0.3 (E) 0.3

5. Consider the linear model with intercept: $y_t = \alpha + \beta x_t + u_t$ If the $A = \sum_{i=1}^{n} (x_i - \bar{x})^2$ is positive definite and $E(u_i \mid x_i) = 0, \forall t = 1, 2, \dots, T$, which statement is true under sample size $T \to \infty$. (A) $ \hat{\beta} $ is consistent, but we cannot judge whether $ \hat{\beta} $ is efficiency (B) $ \hat{\beta} $ is unbiased and efficiency (C) $ \hat{\beta} $ is consistent and efficiency (D) $ \hat{\beta} $ is, but we cannot judge whether $ \hat{\beta} $ is efficiency (E) $ \hat{\beta} $ is unbiased and consistent.

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