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Shuangshuang · 2020年01月31日

问一道题：NO.PZ2020010801000021

  1. FRM I
  2. Quantitative

问题如下：

Suppose you fit a model where both t-statistics are exactly +1.0. Could an F-statistic lead to rejection in this circumstance? Use a diagram to help explain why or why not.

选项：

解释：

Yes. When the regressors are very positively correlated, then this can happen. The t-stats are small because the variables are highly co-linear, so that the variation in the left-hand-side variable cannot be uniquely attributed to either. However, the F-stat is a joint test and so if there is an effect in at least one, the F can reject even if the t-stats do not. See the image below that shows the region where the F would fail to reject, and the two t-stats.


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品职答疑小助手雍 · 2020年02月06日

这里的条件说的是t检验等于1，在t检验里是大于不了critical value的，也就是t检验里无法拒绝原假设（原假设是b1=0 b2=0）。但是此时整体的回归依旧是有可能成立的，也就是存在t检验通不过，但是F检验可以通过的可能。这个可以当结论记一下~

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NO.PZ2020010801000021 问题如下 Suppose you fit a mol where both t-statistiare exactly +1.0. CoulF-statistic leto rejection in this circumstance? Use a agrto help explain why or why not. Yes. When the regressors are very positively correlate then this chappen. The t-stats are small because the variables are highly co-linear, so ththe variation in the left-hansi variable cannot uniquely attributeto either. However, the F-stis a joint test anso if there is effein least one, the F crejeeven if the t-stats not. See the image below thshows the region where the F woulfail to reject, anthe two t-stats.

2022-06-25 18:23 1 · 回答

看不懂这个figure

2020-02-24 22:44 1 · 回答