Ananalyst in interested in predicting annual sales for XYZ Company, a maker ofpaper products. The following table reports a regression of the annual salesfor XYZ against paper product industry sales.

Regression Output

Thecorrelation between company and industry sales is 0.9757. The regression wasbased on 5 observations.

Which ofthe following is closest to thevalue and reports the most likely interpretation of the R² for thisregression? The R² is:

1.  0.048, indicating that thevariability of industry sales explains about 4.8% of the variability of companysales.

2. 0.952, indicating that thevariability of industry sales explains about 95.2% of the variability ofcompany sales.

3. 0.952, indicating that thevariability of company sales explains about 95.2% of the variability ofindustry sales.

Correct Answer: B

【解析】

本题主要考察了对R²的计算与理解。

(1)   R²对应的全称为coefficientof determination (判定系数)，R²指的是因变量(dependent variables)变化能由自变量(independentvariables)解释的部分。

(2)   计算R²有两种方法：

• 平方法：将因变量与自变量之间的相关系数(correlation coefficient)取平方。该方法一般用于只有一个自变量的情况，该方法的缺点也就是如果有多个自变量存在时，该方法失效。

• 其中;该方法适用于多元回归情况，也是我们常用的方法。

从本题给出的条件来看，分析师预测XYZ的销售情况，因而XYZ是因变量，使用行业的销售情况对其进行回归估计，因此行业的销售情况是自变量。题目中给出了两者的相关系数为0.9757，根据平方法：R²=(0.9757)²=0.952.所以答案为B, 判定系数为0.952，表示XYZ公司销售变化的95.2%能由行业销售量解释。

来自：Finance365CFA