65. 茶葉之發酵主要係靠：
(A)酵母菌
(B)乳酸菌
(C)自身酵素
(D)環境中存在的微生物

66. 低酸性食品的定義是指食品的酸鹼值要在多少以上？ (A)7.0 (B)6.0 (C)4.6 (D)3.5

1. Jack use OLS method to estimate the parameters of linear model with intercept: $y_t = \alpha + \beta x_t + \varepsilon_t.$ If the heteroskedasticity ($Var(\varepsilon_t | x_t) = \sigma^2_x x_t$) exits in the errors but other Gauss-Markov conditions satisfy, which statement is true?      (1)      (A). The estimated parameter, \( \hat{\beta} \), is biased, and variance of \( \hat{\beta}_1 \) obtained by OLS method is incorrect. (B). The estimated parameter, \( \hat{\beta} \), is biased, and variance of \( \hat{\beta}_1 \) obtained by OLS method is accurate. (C). The estimated parameter, \( \hat{\beta} \), is unbiased, and variance of \( \hat{\beta}_1 \) obtained by White heteroskedasticity-robust method is accurate. (D). The estimated parameter, \( \hat{\beta}_1 \), is unbiased and efficiency. (E). Jack cannot use OLS to estimate parameters because of inefficiency.

2. Consider the simple linear regression model: $y_t = \beta y_{t-1} + \varepsilon_t,$with the error structure as below: $\varepsilon_t = \rho \varepsilon_{t-1} + u_t,$ where $u_t \sim i.i.d(0, \sigma^2)$. What is the probability limit ($\rho$ lim) of OLS estimator $\hat{\beta}$?      (2)      (A). \( \frac{\beta}{1 + \beta\rho} \) (B). \( \beta \) (C). \( \frac{\beta + \rho}{1 + \beta\rho} \) (D). \( \frac{\rho}{1 + \beta\rho} \) (E). \( \frac{1}{1 + \beta\rho} \)

3. Consider the model: $y_t = \alpha + \rho x_t + \varepsilon_t,$ where $t = 1, \dots, T$. If we want to obtain consistent estimator $\hat{\rho}$ for the large sample, which necessary condition it must be have?      (3)      (A). \( \operatorname{cov}(\varepsilon_t x_t) = 0 \) (B). \( Var(\varepsilon_t \mid 1, x_t) = \sigma^2 \) (C). \( E(\varepsilon_t \mid 1, x_t) = 0 \) (D). \( E(\varepsilon_t \mid x_t) = 0 \) (E). \( E(\varepsilon_t\varepsilon_s|x_t,x_s) = 0 \)

4. An economist uses data to estimate the linear model with intercept $y_t = \alpha + \beta_1 x_{1t} + \varepsilon_t,$ but the true population model is as below: $y_t = \alpha + \beta_1 x_{1t} + \beta_2 x_{2t} + u_t.$ Under which condition satisfied, the OLS estimator $\hat{\beta}_1$ is still consistent?      (4)      (A). \( E(x_{2t}u_t) = 0 \) (B). \( \alpha = 0 \) (C). \( E(x_{2t}\varepsilon_t) = 0 \) (D). \( E(x_{2t}|x_{1t}) = 0 \) (E). \( E(x_{1t}u_t) = 0 \)

5. Suppose that there is an exact relationship between two scalar random variable y and x: $y = \beta x + v$However, $y$ is not known and unobserved. A variable $x^*$ is observed, such that $$x^* = x + u$$ Under which condition satisfied, the OLS estimator $\hat{\beta}_1$ is still consistent? (5) (A). \( E(y\alpha^{*}) = 0 \) (B). \( E(x^{*}u) = 0 \) (C). \( E(xu) = 0 \) (D). \( E(xv) = 0 \) (E). \( E(uv) = 0 \)

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