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🌊 梅根 · 2020年02月24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.


看不懂这个figure

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1 个答案

orange品职答疑助手 · 2020年02月25日

同学你好，学有余力的话可以把以下当成结论补充记忆一下，这个考的太偏了

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）。但是此时整体的假设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

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