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Clare · 2022年01月23日

可以这样理解吗？由joint判断F检验，但是95%是不是对应双尾，然后0.045落在2.5%外的接受域啊？

  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.

可以这样理解吗？由joint判断F检验，但是95%是不是对应双尾，然后0.045落在2.5%外的接受域啊？

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DD仔_品职助教 · 2022年01月23日

嗨，努力学习的PZer你好：


同学你好，不是这样的

在用p value进行判断的时候不需要考虑单尾或者是双尾，只需要知道“p value越小越拒绝原假设”。

0.045这个p value，小于5%，拒绝原假设：β1=β2=0。说明这个F检验在95%的置信区间下显著。

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