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小王爱学习 · 2022年01月16日

没太看懂

  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.

没太看懂这道题考什么。然后每个值表什么 怎么运用。可以画图讲解吗？ 同时 joint hypothesis是什么意思

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1 个答案

DD仔_品职助教 · 2022年01月16日

嗨，从没放弃的小努力你好：


同学你好，这道题不需要画图理解哦，只需要理解p-value越小越拒绝原假设即可。

那么我们下面来看提咋说的，第一段不用看，从第二段开始：题目说你希望joint的原假设在95%的置信区间下是显著的，joint假设代表的是同时对系数β1和β2来进行检验。β1的p-value是0.07，β2的p-value是0.06，F-test的p value是0.045。在这里我们是想做joint的假设检验，那么就要选取F test的p value来进行判断。不可以单单选取β1或者是β2的p value。

那么我们的结论是p value越小越拒绝原假设，这个原假设就是joint 假设的原假设，及系数β1和β2都等于0(我们把想要拒绝的放在原假设里，这里想要拒绝系数同时等于0，因为如果系数同时等于0，就代表这个回归白做了，没有任何解释力度)。F test的p value=0.045小于题目给出的置信区间5%，那么我们就要拒绝joint的原假设，拒绝原假设则代表这个检验在95%的置信区间下是significant的，那么我们就选择c。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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