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🍑(o^^o)Fay 🙃 · 2023年01月08日

不明白 这个correlation 指的是什么。 为什么会跟multiple R^2 有关系。

NO.PZ2015120204000016

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.

不明白这个correlation 就是 R-square 开平方 的结论是哪儿来的。

1 个答案

星星_品职助教 · 2023年01月09日

同学你好,

correlation为Y的实际值Yi,和方程预测出的Y cap之间的相关系数,即“correlation between predicted and actual values of the dependent variable”。

这个相关系数r在数学上可以证明:r的平方=(multiple)R-squared,证明过程教材并没有讲,直接给出的结论。两边开方即有|r|=R方开方。

上面对于correlation的描述是同时适用于一元和多元回归的。此外,仅在一元回归里,由于Y cap(predicted dependent variable)只是由单一的一个X决定的,所以此时相关系数也等于实际值Yi和X之间的相关系数。

上述关系目前的教材里提到的很少,了解即可。

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