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小王爱学习 · 2022年01月28日

老师，，你看我这么理解对吗？

  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.

那0.07和0.06与F test的0.045对比。画一个F分布，是右驱，0.07和0.06都在0.045的右边，所以拒绝

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1 个答案

品职答疑小助手雍 · 2022年01月28日

同学你好，不对。

多元回归对系数的检验只需要用F-test就可以了，本题中说的对单个系数的t检验是误导项，因为F检验的p-value=0.045，处于尾部的0.05的范围（对应95%的confidence level）内，所以拒绝原假设。

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