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ZF Everyday · 2021年05月02日

A为什么不对？

  1. FRM I
  2. Quantitative

NO.PZ2018122801000062

问题如下：

For a sample of 400 firms, the relationship between corporate revenue (Yi) and the average years of experience per employee (Xi) is modeled as follows:

Y i = β 1 + β 2 X i + ε i ,i=1,2,...,400  

You wish to test the joint null hypothesis that at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07, and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?

选项：

A.

You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.

B.

You cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level.

C.

You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.

D.

You cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.

解释：

C is correct.

考点 ： Regression Coefficient Confidence Interval and Significance test

解析 ： The T-test would not be sufficient to test the joint hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus, the null can be rejected.

You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.

经典题解释中，何老师说，贝塔不是跟0做对比，所以AB错误？那是跟谁对比呢？

题目的答案中说的是联合检验，不用t test AB所以 错误

A B的检验，单独拿出来看，p 值很小，拒绝，为什么不对呢


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小刘_品职助教 · 2021年05月02日

同学你好，

这是两个维度的概念，题目的开始就说了You wish to test the joint null hypothesis that at the 95% confidence level. 即本身这个线性回归成不成立，所以要用F检验。

在单独检验A和B的时候前提假设是A和B本身的p值是否很小，而不是用β本身的绝对值去比较，所以正如何老师说的那样，不能用β跟0去比较，所以A和B是错误的。 你单独说 B的检验，单独拿出来看，p 值很小，拒绝，得到的结论是这个贝塔的系数确实不等于0（即假设检验是β=0）和线性回归是否成立的假设检验是不一致。

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