4. Consider the simple regression y_i = α + β x_i + _i And 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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