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JillTian · 2024年09月24日

R^2的解释

NO.PZ2023040502000011

问题如下:


Pres party dummy is equal to 1 if the US President is a member of the Democratic Party and 0 if a member of the Republican Party.


Is the regression model as a whole significant at the 0.05 level?

选项:

A.

No, because the calculated F-statistic is less than the critical value for F.

B.

Yes, because the calculated F-statistic is greater than the critical value for F.

C.

Yes, because the calculated χ2 statistic is greater than the critical value for χ2.

解释:

The F-test is used to determine if the regression model as a whole is significant.

F = Mean square regression (MSR) ÷ Mean squared error (MSE)

MSE = SSE/[n – (k + 1)] = 19,048 ÷ 427 = 44.60

MSR = SSR/k = 1071 ÷ 3 = 357

F = 357 ÷ 44.60 = 8.004

The critical value for degrees of freedom of 3 and 427 with (one-tail) is F = 2.63. The calculated F is greater than the critical value, and you should reject the null hypothesis that all regression coefficients are equal to zero.

这道题算数我可以算懂,但从R^2的来看,本题大部分SS都是error,很少被regression capture到,为啥最后算出来是significant。

1 个答案

品职助教_七七 · 2024年09月24日

嗨,努力学习的PZer你好:


R方和F检验没有直接的关联关系。R方大小不能说明F检验的结果。反之,F显著也可能R方很小。

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