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CC · 2023年09月23日

能把每个选项都解释下吗?

NO.PZ2022062760000011

问题如下:

A risk manager has estimated a regression of a firm’s monthly portfolio returns against the returns of three US domestic equity indexes: the Russell 1000 Index, the Russell 2000 Index, and the Russell 3000 Index. The results are shown below:


Based on the regression results, which statement is correct?

选项:

A.

The estimated coefficient of 0.3533 indicates that the returns of the Russell 3000 Index are more statistically significant in determining the portfolio returns than the other two indexes.

B.

The high adjusted R2 indicates that the estimated coefficients on the Russell 1000, Russell 2000, and Russell 3000 Indexes are statistically significant.

C.

The high p-value of 0.9452 indicates that the regression coefficient of the returns of the Russell 1000 Index is more statistically significant than the other two indexes.

D.

The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.

解释:

中文解析:

这是多重共线性的一个例子,当其中一个回归变量与其他回归变量高度相关时,就会出现这种情况。在这种情况下,所有三个回归变量都高度相关,因此这三个回归变量之间存在多重共线性。由于变量之间并不完全相关,这是一个不完美的情况,而不是完美的多重共线性。

This is an example of multicollinearity, which arises when one of the regressors is very highly correlated with the other regressors. In this case, all three regressors are highly correlated with each other, so multicollinearity exists between all three. Since the variables are not perfectly correlated with each other this is a case of imperfect, rather than perfect, multicollinearity.

麻烦老师把每个选项都解答下,方便找一下差异点,谢谢

1 个答案

pzqa27 · 2023年09月25日

嗨,爱思考的PZer你好:


A说:0.3533 的估计系数表明,罗素 3000 指数的收益在决定投资组合收益方面比其他两个指数更具统计意义。

这个不对,因为有没有意义不看系数,看的是R方

B说:调整后的高 R2 表明,罗素 1000、罗素 2000 和罗素 3000 指数的估计系数在统计意义上是显著的。

显著不显著不看R方,看的是P值。

C说:0.9452 的高 p 值表明,罗素 1000 指数收益率的回归系数比其他两个指数更具有统计意义。

高的P值会接受原假设,所以应该是更没有统计意义才对。

D说:每对指数收益率之间的高相关性表明,回归中的变量之间存在多重共线性。

这个是对的

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