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临江仙 · 2020年02月08日

问一道题: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.

这里第四问怎么计算的,答案都看不懂

1 个答案

orange品职答疑助手 · 2020年02月08日

本题看的是Z分布的标准正态分布表,双尾95%对应的分位点是±1.96 。之所以是±2倍的残差标准差,是因为,在这里本题为了计算方便采用了近似处理的办法。(虽然误差不大,但正式考试中应该不用这样或者额外说明,否则还是精确点保险)。


然后置信区间里,之所以要用残差的标准差,是因为这里求的就是预测值的置信区间,所以就应该用SER。SER就是残差项的标准差。同学你可以看一下截图部分。

XP · 2020年04月29日

晕死,上图中的这个知识点都还没有学到,这个题目不应该放在这里啊

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