小王爱学习 · 2022年01月17日
NO.PZ2020010801000024
问题如下：
Suppose Yi and Xi followed a bivariate normal so that:
What is the in a model that regresses Y on X? What would the be in a model that regressed X on Y?
选项：
解释：
Because this is a regression with a single explanatory variable, the is the squared correlation. The correlation is and so the . The is the same in both regressions because it only depends on the correlation between the variables.
后面的矩阵是有固定的格式吗？为什么右斜边是方差？
NO.PZ2020010801000024 问题如下 Suppose Yi anXi followea bivariate normso that: [YiXi]∼ii([00],[10.90.93])\begin{bmatrix}Y_i\\X_i\enbmatrix}\overset{ii\sim N\left(\begin{bmatrix}0\\0\enbmatrix},\begin{bmatrix}1 0.9\\0.9 3\enbmatrix}\right)[YiXi]∼ii([00],[10.90.93])Whis the R2R^2R2 in a mol thregresses Y on X? Whwoulthe R2R^2R2 in a mol thregresseX on Y? Because this is a regression with a single explanatory variable, the R2R^2R2 is the squarecorrelation. The correlation is 0.9/3=.5190.9/\sqrt 3 = .5190.9/3=.519 anso the R2=0.27R^2 = 0.27R2=0.27. The R2R^2R2 is the same in both regressions because it only pen on the correlation between the variables. 本题给的公式没有看懂，为什么3代表n呢？为什么要除以根号3呢。
NO.PZ2020010801000024 问题如下 Suppose Yi anXi followea bivariate normso that: [YiXi]∼ii([00],[10.90.93])\begin{bmatrix}Y_i\\X_i\enbmatrix}\overset{ii\sim N\left(\begin{bmatrix}0\\0\enbmatrix},\begin{bmatrix}1 0.9\\0.9 3\enbmatrix}\right)[YiXi]∼ii([00],[10.90.93])Whis the R2R^2R2 in a mol thregresses Y on X? Whwoulthe R2R^2R2 in a mol thregresseX on Y? Because this is a regression with a single explanatory variable, the R2R^2R2 is the squarecorrelation. The correlation is 0.9/3=.5190.9/\sqrt 3 = .5190.9/3=.519 anso the R2=0.27R^2 = 0.27R2=0.27. The R2R^2R2 is the same in both regressions because it only pen on the correlation between the variables. 您好，我看了以前的问答，但是还是想问这道题。因为在讲义中讲了这个矩阵，但是没细讲，但是题目中是有的，因此，还请把这道题讲清楚。另外，讲义中说了解的问题，其实不是不考，反而经常出现在题目里。因此，麻烦请详细解答下该题，作为案例记下来。谢谢
NO.PZ2020010801000024 请老师下这道题的题目和答案，题目的矩阵应该怎么看？谢谢！
请老师详细下这套题的分析过程
