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claireteng · 2022年06月23日

请问standard deviation of error是指的什么

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.

是指残差的标准差吗?如果是残差的标准差,那就不是因变量Y的标准差吧,为什么用它来求置信区间?

2 个答案

李坏_品职助教 · 2022年06月23日

嗨,爱思考的PZer你好:


题目最后一小问给的12%是estimated portfolio return,也就是预期的收益率,实际上是一个点估计值。置信区间是在点估计的基础上,± Z * 标准误。这个公式参考我的第二个截图。


题目给的standard deviation of error是点估计(就是mean)的标准误差,我们需要用这个数结合Z值才能知道置信区间。题目给的这个数据不用去考虑自变量还是因变量,因为线性回归中的SD(e)都指的是因变量Y的

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

李坏_品职助教 · 2022年06月23日

嗨,从没放弃的小努力你好:


SD(e)中文意思是“估计标准误”, 也就是均值(mean)的标准差。可以参考讲义P125:

这道题是利用SD(e)这个数据来计算置信区间的,计算方法参考讲义P137:


同学,建议你还是多翻一下基础班讲义,这些都是讲义写过的公式

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努力的时光都是限量版,加油!

claireteng · 2022年06月23日

老师,标准误我知道,但我不懂为什么这里要用标准误,这个标准误是自变量的还是因变量的没有说,另外这里为什么用标准误我也不明白,算置信区间用的是均值吗?应该不是吧,那为什么加减z*标准差要用标准误?

claireteng · 2022年06月23日

12%不是porfolio的均值吧?那为什么后面对应的要用标准误而不是porfolio的标准差

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