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jacqie · 2022年01月10日

为什么不是按照公式算出来加入两个变量后的R大于加入前的R就能验证需要加入两个变量？

  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?

选项：

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.


我用这个公式算加入两个变量后的R是68.69%>加入前的68.53%,为什么不能这么做，而需要用假设检验？

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1 个答案

李坏_品职助教 · 2022年01月10日

嗨，从没放弃的小努力你好：


判断是否可以加入两个解释变量，不能只看R^2大小，因为算出来的新的R^2比加入前的68.53%大的那一点，必须符合统计学意义才行（必须拒绝F检验的原假设才有统计意义）。


结果发现无法拒绝H0，也就是算出来的大的这一点R^2，还不够大，不具备统计意义。

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