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杰西西 · 2022年03月12日

单尾与双尾判断

  1. CFA II
  2. Quantitative

NO.PZ2015120204000022

问题如下：

lExcess stock market returnt=a0+a1Default spreadt−1 +a2Term spreadt−1 +a3Pres party dummyt−1 +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，请问有什么好一点的办法判断什么时候用单尾，什么时候用双尾吗？做题的时候纠结了一下该用5%（单尾）还是2.5%（双尾）对应的critical value

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1 个答案

星星_品职助教 · 2022年03月12日

同学你好，

数量科目里，所有的confidence interval的拒绝域都在两边，即你说的“双尾”情况。

所以95%的置信区间相当于两侧双尾拒绝域一共为5%，单侧即为2.5%。


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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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