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Pina · 2020年06月02日

问一道题：NO.PZ2015120204000016

  1. CFA II
  2. Quantitative

问题如下：

Selected ANOVA Results for Hansen’s Regression

The most appropriate interpretation of the multiple R-squared for Hansen’s model is that:

选项：

A.

unexplained variation in the dependent variable is 36 percent of total variation.

B.

correlation between predicted and actual values of the dependent variable is 0.36.

C.

correlation between predicted and actual values of the dependent variable is 0.60.

解释：

C is correct.

The multiple R-squared for the regression is 0.36; thus, the model explains 36 percent of the variation in the dependent variable. The correlation between the predicted and actual values of the dependent variable is the square root of the R-squared or0.36\sqrt{0.36}= 0.60.

老师好， 这里的术语中这样理解对吗? multiple R squared = R squared = coefficient determination ; multiple R = R = correlation between actual Y and the predicted Y under multiple regression = correlation between actual X and the predicted Y under single regression， 正负号取决于slope b1. 谢谢。

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星星_品职助教 · 2020年06月02日

同学你好，基本都对，做了略微调整

multiple R squared = R squared = coefficient of determination ; （√）

multiple R = R squared 开方后取绝对值（没有“R”这个术语） = correlation between actual Y and the predicted Y （这个关系是定义式，无论在一元还是多元下都成立，actual Y and the predicted Y一定是正相关，此时不需要考虑符号）

仅在一元回归下时，以上关系还等于 correlation between X and ACTUAL Y  ，由于X和Y的关系不一定是正相关，所以此时还需要判断符号，正负号取决于slope b1。这条关系需要注意的是在方程中代入X得到的就是predicted Y，所以可以把这俩理解成同一个东西。所以需要求的是X和actual Y的相关系数，最终也是在求predicted Y和actual Y 的相关系数，符合定义式

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