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Amy_ywh · 2024年06月14日

请问可以解释一下这里df1 和df2怎么判断么

  1. CFA II
  2. Quantitative

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.

是不是f test 的df1 都指的是k 然后df2 是n呢？ 谢谢！

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品职助教_七七 · 2024年06月14日

嗨，从没放弃的小努力你好：


df1是k，df2为n-k-1。这是根据检验“regression model as a whole”时的F统计量公式确定的：

df1是分子（numerator）对应的自由度，从下方公式中，可见分子上调整的自由度就是k；

df2是分母（denominator）对应的自由度，从下方公式中，可见分子上调整的自由度就是n-k-1；

所以本题有三个自变量（红框），k=3，这就是df1；同时n=431（蓝框），n-k-1=431-3-1=427，这就是df2.

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NO.PZ2023040502000011 问题如下 Pres party mmy is equto 1 if the US Presint is a member of the mocratic Party an0 if a member of the RepublicParty.Is the regression mol a whole significant the0.05 level? A.No, because the calculateF-statistic is less thanthe criticvalue for F. B.Yes, because the calculateF-statistic is greaterththe criticvalue for F. C.Yes, because the calculateχ2 statistic is greaterththe criticvalue for χ2. The F-test is useto termine if theregression mol a whole is significant.F = Mesquare regression (MSR) ÷ Mesquarerror (MSE)MSE = SSE/[n – (k + 1)] = 19,048 ÷427 = 44.60MSR = SSR/k = 1071 ÷ 3 =357F = 357 ÷ 44.60 = 8.004The criticvalue forgrees of freem of 3 an427 with (one-tail) is F= 2.63. The calculateF is greater ththe criticvalue, anyoushoulrejethe null hypothesis thall regression coefficients are equtozero. 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。

2024-09-24 11:26 1 · 回答