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小王爱学习 · 2022年01月28日

这道题为什么不用t分布呢?

NO.PZ2016062402000023

问题如下:

Which of the following statements about the linear regression of the return of a portfolio over the return of its benchmark presented below are correct?

I. The correlation is 0.71.

II. About 34% of the variation in the portfolio return is explained by variation in the benchmark return.

III. The portfolio is the dependent variable.

IV. For an estimated portfolio return of 12%, the confidence interval at 95% is (7.16%-16.84%).

选项:

A.

II and IV

B.

Ill and IV

C.

I, II, and III

D.

II,IIIand IV

解释:

The correlation is given by 0.66=0.81\sqrt{0.66}=0.81 so answer I is incorrect. Next,66% of the variation in Y is explained by the benchmark, so answer II. is incorrect. The portfolio return is indeed the dependent variable Y, so answer III. is correct. Finally, to find the 95 % two-tailed confidence interval, we use a from a normal distribution, which covers 95% within plus or minus 1.96, close to 2.00. The interval is theny2SD(e),  y+2SD(e)y-2SD{(e)},\;y+2SD{(e)} or (7.16 -16.84). So answers III. and IV. are correct.

1、这道题我算出来了,但是我很疑惑为什么不用t分布,总体方差不知道,用t,这里并不知道总体的方差吧 ?还是说standard error就是总体方差,所以我们可以直接用1。96.



2、 请问Ttable,df=2, 95%conident interval,双尾,是不是= 4.3?

2 个答案

李坏_品职助教 · 2022年02月04日

嗨,努力学习的PZer你好:


是的,t值是近似等于4.3

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努力的时光都是限量版,加油!

李坏_品职助教 · 2022年01月28日

嗨,努力学习的PZer你好:


t分布的自由度是n-1,其中n是样本数量,这道题我们不知道n是多少,也就无法使用t分布来计算了。


另外,当样本数量足够大的时候,t值和正态分布的Z值是很接近的,也就是在95%的置信度下,双尾,近似为1.96。

----------------------------------------------
努力的时光都是限量版,加油!

小王爱学习 · 2022年01月29日

2、 请问T table,df=2, 95%confident interval,双尾,t-value是不是= 4.3?

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