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FRM一级每日一题【风险管理基础42-定量分析】一元线性回归

来源：高顿网校 2015-03-04

　　习题：

　　Exercise:

　　An analyst is given the data in the following table for a regression of the annual sales for Company XYZ, a maker of paper products, on paper product industry sales.

Parameters	Coefficient	Standard Error of the Coefficient
Intercept	-94.88	32.97
Slope (industry sales)	0.2796	0.0363

　　The correlation between company and industry sales is 0.9757. Which of the following is closest to the value and reports the most likely interpretation of the R2?

　　A 0.048, indicating that the variability of industry sales explains about 4.8% of the variability of company sales.

　　B 0.048, indicating that the variability of company sales explains about 4.8% of the variability of industry sales.

　　C 0.952, indicating that the variability of industry sales explains about 95.2% of the variability of company sales.

　　D 0.952, indicating that the variability of company sales explains about 95.2% of the variability of industry sales.

　　解析：

　　Answer: C

　　Explanation: The R2 is computed as the correlation squared: (0.9757)2 = 0.952. The interpretation of this R2 is that 95.2% of the variation in Company XYZ’s sales is explained by the variation in industry sales.

　　知识点：

　　Coefficient of Determination

　　The R2 can be written as the ratio of the explained sum of squares to the total sum of squares or in terms of the fraction of the variance of Yi not explained by Xi.

　　l The explained sum of squares (ESS) is the sum of squared deviations of the predicted values of Yi from their average.

　　l The total sum of squares (TSS) is the sum of squared deviations of Yi from its average.

　　l The sum of squared residuals (SSR) is the sum of the squared residuals.

　　Also, the R2 of the regression of Y on the single regressor X is the square of the correlation coefficient between Y and X.

　　An R2 near 1 indicates that the regressor is good at predicting Yi, while an R2 near 0 indicates the regressor is not very good at predicting Yi.
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