请问这道题考点是多重共线性吗？|r|>0.7 是吗？-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

请问这道题考点是多重共线性吗？|r|>0.7 是吗？

NO.PZ2020010801000020

问题如下：

You estimate a regression model $Y_i = \alpha + \beta_1X_{1i} + \beta_2X_{2i} + \epsilon_i$ .

Using the F-stat of the model, you reject the null $H_0:\beta_1 = \beta_2 = 0$ but fail to reject either of the nulls $H_0:\beta_1 = 0 or H_0:\beta_2 = 0$ using the t-stat of the coefficient. Which values of $\rho = Corr[X_1, X_2]$ make this scenario more likely?

选项：

解释：

This is most likely to occur when the regressors are highly correlated. If the regressors are positively correlated, then the parameter estimators of the coefficients will be negatively correlated. If both values are positive, this would lead to rejection by the F-test. Similarly, if the regressors were negatively correlated, then the estimators are positively correlated and the F will reject if one t is positive and the other is negative. The figure below shows the case for positively correlated regressors. The shaded region is the area where the F would fail to reject. The t-stats are outside this area even though neither is individually significant.

请问这道题考点是多重共线性吗？|r|>0.7 是吗？是讲义P231的内容吗？

嗨，努力学习的PZer你好：

这道题是原版书当中非常偏的知识点，讲义中没有涉及。

这道题目考的是一个结论：当F检验拒绝原假设（β至少有一个不为0），但是t检验又拒绝不了原假设（β=0 ）时：如果回归变量是正相关的，那么他们的coefficient就是一正一负；回归变量是负相关的，那么coefficient就是同正负。

图显示的是当X1和X2正相关时，coefficient的点和F检验的拒绝域。

不用太纠结这道题，因为至今还没有考过，有时间的话看看结论就好。

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请问这道题考点是多重共线性吗？|r|>0.7 是吗？

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