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🌊 梅根 · 2020年02月24日

问一道题：NO.PZ2020010801000020

  1. FRM I
  2. Quantitative

问题如下：

You estimate a regression model Yi=α+β1X1i+β2X2i+ϵiY_i = \alpha + \beta_1X_{1i} + \beta_2X_{2i} + \epsilon_i.

Using the F-stat of the model, you reject the null H0:β1=β2=0H_0:\beta_1 = \beta_2 = 0 but fail to reject either of the nulls H0:β1=0orH0:β2=0H_0:\beta_1 = 0 or H_0:\beta_2 = 0 using the t-stat of the coefficient. Which values of ρ=Corr[X1,X2]\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.


可以这么理解吗？

ρ=Corr[b1X1,b2X2] 属于(-1,0)？

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2 个答案

DD仔_品职助教 · 2021年12月30日

嗨，努力学习的PZer你好：


同学你好，讲义里没有涉及，原版书的知识点，这个点比较偏，学有余力可以记一下结论，没必要深究性价比低，以讲义里的知识为重。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

orange品职答疑助手 · 2020年02月25日

同学你好，本题解析的意思是说：

当F检验拒绝原假设时候，也就是这些b里面至少一个不等于零，但是t检验又拒绝不了原假设（bi=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。


这题来自原版书，考的有点偏，学有余力记个结论就可以了

he123456 · 2021年12月30日

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。这个结论是怎么来的？讲义里好像没学到

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NO.PZ2020010801000020 问题如下 You estimate a regression mol Yi=α+β1X1i+β2X2i+ϵiY_i = \alpha + \beta_1X_{1i} + \beta_2X_{2i} + \epsilon_iYi​=α+β1​X1i​+β2​X2i​+ϵi​. Using the F-stof the mol, you rejethe null H0:β1=β2=0H_0:\beta_1 = \beta_2 = 0H0​:β1​=β2​=0 but fail to rejeeither of the nulls H0:β1=0orH0:β2=0H_0:\beta_1 = 0 or H_0:\beta_2 = 0H0​:β1​=0orH0​:β2​=0 using the t-stof the coefficient. Whivalues of ρ=Corr[X1,X2]\rho = Corr[X_1, X_2]ρ=Corr[X1​,X2​] make this scenario more likely? This is most likely to occur when the regressors are highly correlate If the regressors are positively correlate then the parameter estimators of the coefficients will negatively correlate If both values are positive, this woulleto rejection the F-test. Similarly, if the regressors were negatively correlate then the estimators are positively correlateanthe F will rejeif one t is positive anthe other is negative. The figure below shows the case for positively correlateregressors. The sharegion is the area where the F woulfail to reject. The t-stats are outsi this area even though neither is invially 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？

2024-01-28 18:04 1 · 回答

NO.PZ2020010801000020 问题如下 You estimate a regression mol Yi=α+β1X1i+β2X2i+ϵiY_i = \alpha + \beta_1X_{1i} + \beta_2X_{2i} + \epsilon_iYi​=α+β1​X1i​+β2​X2i​+ϵi​. Using the F-stof the mol, you rejethe null H0:β1=β2=0H_0:\beta_1 = \beta_2 = 0H0​:β1​=β2​=0 but fail to rejeeither of the nulls H0:β1=0orH0:β2=0H_0:\beta_1 = 0 or H_0:\beta_2 = 0H0​:β1​=0orH0​:β2​=0 using the t-stof the coefficient. Whivalues of ρ=Corr[X1,X2]\rho = Corr[X_1, X_2]ρ=Corr[X1​,X2​] make this scenario more likely? This is most likely to occur when the regressors are highly correlate If the regressors are positively correlate then the parameter estimators of the coefficients will negatively correlate If both values are positive, this woulleto rejection the F-test. Similarly, if the regressors were negatively correlate then the estimators are positively correlateanthe F will rejeif one t is positive anthe other is negative. The figure below shows the case for positively correlateregressors. The sharegion is the area where the F woulfail to reject. The t-stats are outsi this area even though neither is invially significant.

2022-06-25 11:38 1 · 回答

请问一下highly correlate什么可以呢

2020-02-25 12:04 1 · 回答

不理解

2020-01-30 23:59 3 · 回答