110年 - 110 國立中央大學_碩士班招生考試_經濟學系/不分組(一般生):統計學#105320

(a) (6 points) Find E(Y|X + Y = 4).

(a) (5 points) Find the method of moments estimator

(b) (S points) Let

(c) (10 points) Consider the following hypotheses:
 Now consider a test that rejects the null hypothesis when X(n) ≤ 2.5 is observed, where Find the probability of type I error and the power function, K(θ), of this test.

(a) (8 points) Please derive the OLS estimators,

(c) (8 points) Please test H₀ :β=0 and then interpret the economic meaning of (0.12)

(b) (12 points) If the assumption of classical linear regression model,does not hold.
 i. (4 points) What problem the OLS estimation suffers?
 ii. (4 points) Assuming,the Durbin-Watson d test can be used to test this problem. Please show the Durbin-Watson d statistic.

 iii. (4 points) If we find d=3.5. Please comment on the test result.