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中了张 · 2020年03月16日

问一道题:NO.PZ2015120204000022

问题如下:

lExcess stock market returnt=a0+a1Default spreadt1 +a2Term spreadt1 +a3Pres party dummyt1 +e{l}Excess\text{ }stock\text{ }market\text{ }return_t\\=a_0+a_1Default\text{ }spread_{t-1}\text{ }+a_2Term\text{ }spread_{t-1}\text{ }+a_3Pres\text{ }party\text{ }dummy_{t-1}\text{ }+e

Default spread is equal to the yield on Baa bonds minus the yield on Aaa bonds. Term spread is equal to the yield on a 10-year constant-maturity US Treasury index minus the yield on a 1-year constant-maturity US Treasury index. Pres party dummy is equal to 1 if the US President is a member of the Democratic Party and 0 if a member of the Republican Party.

The regression is estimated with 431 observations.

Exhibit 1.Multiple Regression Output

Exhibit 2. Table of the Student’s t-Distribution (One-Tailed Probabilities for df = )

The 95 percent confidence interval for the regression coefficient for the default spread is closest to:

选项:

A.

0.13 to 5.95.

B.

1.72 to 4.36.

C.

1.93 to 4.15.

解释:

B is correct.

The confidence interval is computed as a1±s(a1)×(95%,)a_1\pm s(a_1)\times(95\%,\infty). From Exhibit 1, a1 = 3.04 and t(a1) = 4.52, resulting in a standard error of a1 = s(a1) = 3.04/4.52 = 0.673. The critical value for t from Exhibit 3 is 1.96 for p = 0.025. The confidence interval for a1 is 3.04 ± 0.673 × 1.96 = 3.04 ± 1.31908 or from 1.72092 to 4.35908.

老师您好,有两个问题麻烦解答一下:1、题目中给了单尾的表,实际上本题的检验是双尾的呢?2、关于单尾和双尾检验,我理解跟您在前几个问题答复中解释的恰好是反的。。。单尾检验的话,拒绝域在一个尾巴上的话,中间面积95%,那查表时不应该是使用α按照5%来查表的么,因为只有一个尾巴。而相反双尾的话,中间区域面积是95%,查表时用α/2按照2.5%来查。麻烦您帮捋一下,感谢🙏

1 个答案

星星_品职助教 · 2020年03月17日

同学你好,

1. 本题是求置信区间,而不是假设检验。置信区间是跟双尾的t值直接对应的,但双尾的t临界值和单尾的t临界值是有对应关系的,双尾5%的临界值就相当于单尾2.5%的临界值

2. 单尾检验不存在“中间面积”的概念,例如右尾5%,一定是左侧(包括左尾在内)所有的面积一共是95%,不可能单出来一个中间面积,这个时候左尾不是空出来的。如果是置信区间,则一定是个“中间面积”的概念,即左右都有尾巴(拒绝域)

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NO.PZ2015120204000022 1.72 to 4.36. 1.93 to 4.15. B is correct. The confinintervis computea1±s(a1)×(95%,∞)a_1\pm s(a_1)\times(95\%,\infty)a1​±s(a1​)×(95%,∞). From Exhibit 1, = 3.04 ant(a1) = 4.52, resulting in a stanrerror of = s(a1) = 3.04/4.52 = 0.673. The criticvalue for t from Exhibit 3 is 1.96 for p = 0.025. The confinintervfor is 3.04 ± 0.673 × 1.96 = 3.04 ± 1.31908 or from 1.72092 to 4.35908.老师请问stanrerror为什么是3.04\4.52 ? 谢谢

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