- CFA Exams
- CFA Exam: Level II 2021
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 2. Interpreting a regression coefficient

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**CFA Practice Question**

Which of the following is (are) true of the slope of the least-squares regression line?

II. the square of the slope equals the fraction of the variation in the dependent variable that is explained by the independent variable.

III. It is unitless.

I. It has the same sign as the correlation coefficient.

II. the square of the slope equals the fraction of the variation in the dependent variable that is explained by the independent variable.

III. It is unitless.

Correct Answer: I only

II: It is the square of the correlation coefficient that equals the fraction of the variation in the dependent variable that is explained by the independent variable. While the slope and the correlation coefficient have the same sign, their numerical values and other properties are different.

III: the unit of slope is units of y divided by units of x. The correlation coefficient is unitless, not the slope.

I is correct since b = r s

_{y}/s_{x}, where b is the slope, r is the correlation coefficient, and the ratio of the standard deviations, s_{y}/s_{x}, is always positive.II: It is the square of the correlation coefficient that equals the fraction of the variation in the dependent variable that is explained by the independent variable. While the slope and the correlation coefficient have the same sign, their numerical values and other properties are different.

III: the unit of slope is units of y divided by units of x. The correlation coefficient is unitless, not the slope.

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**User Contributed Comments**
2

User |
Comment |
---|---|

Sandy69 |
Since information is non - material hence can be used |

danlan |
Do not be confused by correlation coefficient and slope of the regression line. Correlation coefficient is the geometric average of two slopes (exchange dependant and independant variables), and has same sign as each slope, but the value can be different. |