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🍑(o^^o)Fay 🙃 · 2024年04月09日

  r^2

NO.PZ2019040801000076

问题如下:

An analyst gathers the following data for a regression of the annual sales for Company Bridge, a maker of oil products, on oil product industry sales.

The regression was based on six observations and the correlation between company and industry sales is 0.9126.

Which of the following is closest to the value and is the most likely interpretation of the R^2 ? The R^2 is:

选项:

A.

0.1672, indicating that the variability of industry sales explains about 16.72% of the variability of company sales.

B.

0.1672, indicating that the variability of company sales explains about 16.72% of the variability of industry sales.

C.

0.8328, indicating that the variability of oil industry sales explains about 83.28% of the variability of company sales.

D.

0.8328, indicating that the variability of company sales explains about 83.28% of the variability of oil  industry sales.

解释:

C is correct.

考点:Linear Regression with One Regressor

解析:R^2 = 0.9126^2 =0.8328

自变量的变动可以解释R^2比例的因变量的变动。因此本题选C;答案D说反了。

题目中 描述   The correlation between company sales and industry=0.9**,   此处考察 multiple r = r^2   以及r^2  的解释。 multiple r 是 correlation between actual y  & forecast y.      感觉的题目描述有问题

2 个答案

李坏_品职助教 · 2024年04月09日

嗨,爱思考的PZer你好:


参考讲义ANOVA table里面的Coefficient Determination (R2)这部分内容:


对于一元线性回归来说,R^2 = ρ^2 (squared correlation coefficient意思是相关系数的平方)

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李坏_品职助教 · 2024年04月09日

嗨,努力学习的PZer你好:


题目问你R^2是什么含义,并且等于多少?

由于相关系数ρ=0.9126,并且这是一元线性回归,只有一个X,所以R^2 = ρ^2 = 0.8328.


R^2的含义是:X可以解释多少比例的Y的波动。

本题表格里告诉我们industry sales是X(在表格括号里的是X),而Y是company sales,也就是这个回归模型是用行业销售额(自变量X)来解释公司的销售额(因变量Y)。R^2 = 0.8328表示行业销售额可以有效解释83.28%的公司销售额,所以选C。


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🍑(o^^o)Fay 🙃 · 2024年04月09日

我明白 r^2是x对于y的解释力度。我想问的是为什么 x&y 的相关系数 和  r^2有关系。 为什么  x&y 的correlatio = r ^2.  

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相关问题

NO.PZ2019040801000076问题如下analyst gathers the following ta for a regression of the annusales for Company Brie, a maker of oil procts, on oil proinstry sales.The regression wbaseon six observations anthe correlation between company aninstry sales is 0.9126. Whiof the following is closest to the value anis the most likely interpretation of the R^2 ? The R^2 is:A.0.1672, incating ththe variability of instry sales explains about 16.72% of the variability of company sales.B.0.1672, incating ththe variability of company sales explains about 16.72% of the variability of instry sales.C.0.8328, incating ththe variability of oil instry sales explains about 83.28% of the variability of company sales.0.8328, incating ththe variability of company sales explains about 83.28% of the variability of oil instry sales.C is correct.考点LineRegression with One Regressor解析R^2 = 0.9126^2 =0.8328自变量的变动可以R^2比例的因变量的变动。因此本题选C;答案反了。怎么知道哪个是自变量哪个是因变量啊

2024-05-06 19:47 1 · 回答

NO.PZ2019040801000076 0.1672, incating ththe variability of company sales explains about 16.72% of the variability of instry sales. 0.8328, incating ththe variability of oil instry sales explains about 83.28% of the variability of company sales. 0.8328, incating ththe variability of company sales explains about 83.28% of the variability of oil  instry sales. C is correct. 考点LineRegression with One Regressor 解析R^2 = 0.9126^2 =0.8328 自变量的变动可以R^2比例的因变量的变动。因此本题选C;答案反了。表格里的数字有什么用处

2021-08-22 14:30 1 · 回答

0.9126是什么?怎么求出来的?

2019-11-06 23:20 1 · 回答

     老师你好,请问这道题的因变量和自变量是怎么判断的?谢谢

2019-08-11 19:19 1 · 回答