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Aimee🌸 · 2022年08月10日

关于multiple R-squared的疑问

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.

讲义中的R-squared和此处的multiple R-squared是相等的吗?

那么为什么讲义上说R2 of 0.9 indicates that the model,as a whole,explains 90% of the variation in the dependent variable,此处multiple R-squared=0.36,指的不就是整个方程可以解释36%的Y吗?但A选项不是说的是未被解释的占36%?非常疑惑。

虽然错误的选择了B,看了解释之后理解B错在是说correlation,但不明白A为什么是对的。

2 个答案

星星_品职助教 · 2022年11月05日

@愤怒的鱼蛋 开根号的原因是在一元回归中,(Multiple)R-squared=correlation的平方。

星星_品职助教 · 2022年08月10日

同学你好,

1)R-squared和此处的multiple R-squared是相等的。

2)本题A描述是错误的。答案选择C。

愤怒的鱼蛋 · 2022年11月04日

如果R-square和这里的multiple R-squared是相等的,为什么还要开根号呀,还是不是很理解需要开根号的原因

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