开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

Shawnxz · 2020年07月02日

问一道题:NO.PZ2015120204000003

问题如下:

The independent variable is the ratio of net income to sales for restaurants with a market cap of more than $100 million and the dependent variable is the ratio of cash flow from operations to sales for those restaurants.

  

What is the correlation between X and Y?

选项:

A.

-0.7436.

B.

0.7436.

C.

0.8623.

解释:

C is correct.

For a regression with one independent variable, the correlation is the same as the Multiple R with the sign of the slope coefficient. Because the slope coefficient is positive, the correlation is 0.8623.

请问coefficient和correlation有什么区别?就是R2和mutiple R如何区分呢

1 个答案
已采纳答案

星星_品职助教 · 2020年07月02日

同学你好,

coefficient是回归方程中的系数,就是第二张表的“Coefficients”那一列对应的数字。根据这个系数可以写出来方程为Y cap=0.077+0.826X

R-squared是真实的数据Yi,和方程预测的Y cap之间的相关系数(correlation)的平方。由于本题是一元回归方程,所以这个Yi和Y cap之间的相关系数也等于Yi和X之间的相关系数,即题目要求的correlation between X and Y。

所以将R-squared开方就可以得到correlation between X and Y的绝对值,即|correlation between X and Y|=+√0.7436=0.8623。

这个相关系数的正负号取决于X和Y的关系,这就回到了coefficient上,由于X的系数是0.826大于0,所以X和Y是正相关关系。

所以本题的correlation between X and Y就是+0.8623,选择C选项。

multiple R就是R-squared开方后取绝对值。由于本题中X和Y是正相关关系,所以本题的multiple R=correlation between X and Y=0.8623