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亚利 · 2023年05月20日

这个F检验在实际考试中会怎么考，直接让计算统计量？

  1. FRM I
  2. Quantitative

NO.PZ2020010801000037

问题如下：

You are interested in understanding the determinants of the yield spread of corporate bonds above a maturity matched sovereign bond. You include three explanatory variables: the leverage defined as the ratio of long-term debt to the book value of assets, a dummy variable for high yield, and a measure of the volatility of the profitability of the issuer. You are interested in testing whether there are nonlinear effects of some of these variables, and so use a RESET test including both the squared and cubic term. The R2R^2 of the original model is 68.6%, and the R2R^2 from the model that includes both additional terms is 68.9%. You have 456 observations. What do you conclude about the specification of the model?

解释：

The RESET test examines whether the two additional explanatory variables that squared and cubed fitted values have zero coefficients. It is implemented using an F-test:

(0.689−0.6862)/(1−0.689456−6) F2,450(\frac{0.689-0.686}{2})/(\frac{1-0.689}{456-6})~F_{2,450}

The F-test examines the difference between the R2R^2 in the two models. The critical value for an F2,450F_{2,450} is 3.01 (F.INV. RT(0.05,2,450) in Excel). The value of the test statistic is 2.17, which is less than the critical value, and so the null that the coefficient on the squared and cubic terms is 0 is not rejected.

这个F检验在实际考试中会怎么考，直接让计算统计量？

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1 个答案

李坏_品职助教 · 2023年05月20日

嗨，努力学习的PZer你好：


要么是给出p值然后让你判断结论是否拒绝原假设，要么就是自己计算F值。


公式要记住：


原模型的回归方程可以写为：y=a+β1*X1+β2*X2+β3*X3

包含两个附加项的新模型可以写为：y=a+β1*X1+β2*X2+β3*X3+β4*X4+β5*X5


所以新的模型（加了俩自变量的）是unrestricted

原来的模型是restricted

Ru是unrestricted的R^2，Rr是restricted的R^2.


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