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🍥 · 2020年05月25日

问一道题：NO.PZ2018122801000062 [ FRM I ]

  1. FRM I
  2. Quantitative

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.

可以详细解释一下吗？不是很懂

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1 个答案

品职答疑小助手雍 · 2020年05月25日

嗨，努力学习的PZer你好：


首先要注意的是这一句You wish to test the joint null hypothesis that at the 95% confidence level.

所以要判断这个回归能不能被接受是要通过F检验的p value来判断的。因为这题给的F检验的p value是0.045，小于了5%，所以拒绝原假设，也就是回归是成立的。

而前两个beta的p value是检验两个系数是不是显著等于0的，和回归线性关系成立不成立是两回事。


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