还是没有看懂这个解释，t检验和f检验有什么关系和区别啊？

NO.PZ2020010801000021

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.

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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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DD仔_品职助教 · 2022年06月26日

嗨，从没放弃的小努力你好：

你可以直接忽略掉这个图，对理解没帮助，并且还是一个很偏的点。

在多元回归中，t检验是用于检测单个系数的有效性的，也就是b1是否=0或者b2是否等于0,或者b3是否=0等等，都是只针对一个系数。

f检验是站在总体的角度，做的联合检验，也就是说所有的系数作为一个整体是否有效，此时检验的原假设就是b1=b2=b3=等等=0。

t检验和f检验都是独立的，也就是说通过了t检验不代表也可以通过f检验，通过了f检验，不一定可以通过t检验。

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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.t=1为什么上正相关，t=1为什么拒绝h0

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看不懂这个figure

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2020-01-31 00:04 1 · 回答

还是没有看懂这个解释，t检验和f检验有什么关系和区别啊？

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