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中了张 · 2020年03月16日

问一道题:NO.PZ2015120204000019

问题如下:

Excess stock market returnt=a0+a1Default spreadt-1+a2Term spreadt-1+a3Pres party dummyt-1+et

Default spread is equal to the yield on Baa bonds minus the yield on Aaa bonds. Term spread is equal to the yield on a 10-year constant-maturity US Treasury index minus the yield on a 1-year constant-maturity US Treasury index. 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.

The regression is estimated with 431 observations.

Exhibit 1.Multiple Regression Output

Exhibit 2. Table of the F-Distribution (Critical Values for Right-Hand Tail Area Equal to 0.05) Numerator: df1 and Denominator: df2

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:

B is correct.

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 α=0.05 (one-tail) is F = 2.63 from Exhibit 2. The calculated F is greater than the critical value, and Chiesa should reject the null hypothesis that all regression coefficients are equal to zero.

老师麻烦给解释下F检验查表,df1和df2哪个指k,哪个指n-k-1,为啥题目中给的f表中提到分子分母?

1 个答案

星星_品职助教 · 2020年03月17日

同学你好,

查F表需要两个自由度,这和F-statistics=MSR/MSE=(SSR/k)/(SSE/n-k-1)是对应的,分子的自由度就是k,也就是df1=3,分母的自由度就是n-k-1,也就是df2=427

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