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Ella · 2024年05月11日

这个知识点在新考纲范围内吗

NO.PZ2020010801000036

问题如下:

In a model with two explanatory variables, Yi=α+β1X1i+β2X2i+ϵiY_i = \alpha + \beta_1X_{1i} +\beta_2X_{2i} + \epsilon_i, what does the correlation need to be between the two regressors, X1 and X2, for the variance inflation factor to be above 10?

选项:

解释:

The variance inflation factor is 11Rj2\frac{1}{1-R_j^2}, where Rj2R_j^2 measures how well variable j is explained by the other variables in the model. Here there are two variables, and so Rj2=ρX1X22R_j^2=\rho_{X_1X_2}^2. The variance inflation factor of 10 solves 10=1/(1ρX1X22)10 = 1/(1 - \rho_{X_1X_2}^2 ), so that 1/(1ρX1X22)=1/101/(1 - \rho_{X_1X_2}^2 ) = 1/10 or ρX1X22=11/10=0.9\rho_{X_1X_2}^2=1-1/10=0.9.

Correlations greater than (in absolute value) 0.90.948\sqrt 0.9 ≈ 0.948 would produce values above 10.

这个知识点在新考纲范围内吗

1 个答案
已采纳答案

pzqa39 · 2024年05月11日

嗨,爱思考的PZer你好:


在的,这个知识点在数量基础班section6 serial correlation 小节 一倍速7min35s左右的位置。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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NO.PZ2020010801000036 问题如下 In a mol with two explanatory variables, Yi=α+β1X1i+β2X2i+ϵiY_i = \alpha + \beta_1X_{1i} +\beta_2X_{2i} + \epsilon_iYi​=α+β1​X1i​+β2​X2i​+ϵi​, whes the correlation neeto between the two regressors, X1 anX2, for the varianinflation factor to above 10? The varianinflation factor is 11−Rj2\frac{1}{1-R_j^2}1−Rj2​1​, where Rj2R_j^2Rj2​ measures how well variable j is explainethe other variables in the mol. Here there are two variables, anso Rj2=ρX1X22R_j^2=\rho_{X_1X_2}^2Rj2​=ρX1​X2​2​. The varianinflation factor of 10 solves 10=1/(1−ρX1X22)10 = 1/(1 - \rho_{X_1X_2}^2 )10=1/(1−ρX1​X2​2​), so th1/(1−ρX1X22)=1/101/(1 - \rho_{X_1X_2}^2 ) = 1/101/(1−ρX1​X2​2​)=1/10 or ρX1X22=1−1/10=0.9\rho_{X_1X_2}^2=1-1/10=0.9ρX1​X2​2​=1−1/10=0.9. Correlations greater th(in absolute value) 0.9≈0.948\sqrt 0.9 ≈ 0.9480​.9≈0.948 woulprovalues above 10. 在课程中讲到,在多元回归方程中,R SQUARE等于CORRELATION 的平方是不成立的,这是多元和一元回归的一个区别。因此,在本题目中,对于CORRELATION 没有任何思路,只计算出一个0.9,然后再也无法继续下去了。还麻烦请详细讲讲 R SQUARE 到底是否等于 CORRELATION 的平方,非常感谢!

2023-02-05 04:43 1 · 回答

NO.PZ2020010801000036

2022-01-10 01:02 1 · 回答

NO.PZ2020010801000036 考察的是哪个知识点呢?谢谢!

2021-09-21 08:28 2 · 回答

 varianinflation factor这个知识点在基础班哪里提到的呀?一点印象也没有了。谢谢老师

2020-08-29 18:04 1 · 回答