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pengyaning · 2023年10月19日

关于线性回归

NO.PZ2023091601000123

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:


You wish to test the joint null hypothesis that at the 95% confidence level. The p-value for the t-statistic for β1is 0.07, and the p-value for the t-statistic forβ2is 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 neitherβis 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:

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

1.此题为一元线性回归,为什么用f检验?而不是t检验?

2.原题目解析中“which in this case is statistically significant at the 95% confidence level‘’是怎么判断的?

1 个答案

DD仔_品职助教 · 2023年10月20日

嗨,从没放弃的小努力你好:


同学你好,

1,t检验是单个检验,只检验单一系数,这个题涉及到多个系数的检验,我们称之为联合检验,所以要用Ftest

2,f检验的p value是0.045,小于1-95%,p value越小越拒绝,所以是拒绝原假设

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努力的时光都是限量版,加油!