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m糖分w · 2020年02月23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,这道题目是问整个回归是否成立,我理解是只要有一个自变量系数不等于0即成立,在表一中看到三个自变量的P-value都非常小,是不是可以直接判断回归是有意义的,不用再算一遍F-test了吧?(当然算F-test没错哈,我只是说我这样理解是否可以)

1 个答案

星星_品职助教 · 2020年02月23日

同学你好,

在多元回归里,t检验的结果和F检验不一定一致。所以不能只看t而不做F。不过这个超范围了,从考试的角度讲,只要看到方程整体就直接选F去检验就行。

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NO.PZ2015120204000019问题如下Excess stomarket returnt=a0+a1fault sprea-1+a2Term sprea-1+a3Pres party mmyt-1+etfault spreis equto the yielon Bbon minus the yielon Abon. Term spreis equto the yielon a 10-yeconstant-maturity US Treasury inx minus the yielon a 1-yeconstant-maturity US Treasury inx. Pres party mmy is equto 1 if the US Presint is a member of the mocratic Party an0 if a member of the RepublicParty.The regression is estimatewith 431 observations.Exhibit 1.Multiple Regression OutputExhibit 2. Table of the F-stribution (CriticValues for Right-HanTail Area Equto 0.05) Numerator: 1 annominator: 2 Is the regression mol a whole significant the 0.05 level?A.No, because the calculateF-statistic is less ththe criticvalue for F.B.Yes, because the calculateF-statistic is greater ththe criticvalue for F.C.Yes, because the calculateχ2 statistic is greater ththe criticvalue for χ2. B is correct.The F-test is useto termine if the regression mol a whole is significant.F = Mesquare regression (MSR) ÷ Mesquareerror (MSE)MSE = SSE/[n – (k + 1)] = 19,048 ÷ 427 = 44.60MSR = SSR/k = 1071 ÷ 3 = 357F = 357 ÷ 44.60 = 8.004The criticvalue for grees of freem of 3 an427 with α=0.05 (one-tail) is F = 2.63 from Exhibit 2. The calculateF is greater ththe criticvalue, anChiesa shoulrejethe null hypothesis thall regression coefficients are equto zero. 题目表格中的T统计是做什么用的?是怎样计算出来的?谢谢!

2024-06-24 14:14 1 · 回答

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2023-02-02 13:47 1 · 回答

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2021-05-04 15:17 1 · 回答