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Cooljas · 2022年06月25日

为啥回归变量是正相关的，coefficient就是一正一负；回归变量如果是负相关的，coefficient就是一正一负啊？

  1. FRM I
  2. Quantitative

NO.PZ2020010801000020

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.




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品职答疑小助手雍 · 2022年06月25日

同学你好，首先这题不建议深究，深究也没意义。

举个例子，如果两个回归变量是正相关的话，现在F检验说明俩系数至少一个不为零，t检验则表示俩系数都不能显著不等于0（相当于两个检验的结论矛盾），那系数如果要变化只能一增一减，否则因变量Y会被两个同时增加的变量，和同时增加的系数弄得很大和原值不符。只有一增一减才可以抵消使Y值稳定。实在看不懂可以算了，也没见考过。

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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

请问一下highly correlate什么可以呢

2020-02-25 12:04 1 · 回答

可以这么理解吗？ ρ=Corr[b1X1,b2X2] 属于(-1,0)？

2020-02-24 22:37 2 · 回答

不理解

2020-01-30 23:59 3 · 回答