- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 4. The Standard Error of Estimate in Multiple Linear Regression Model

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**CFA Practice Question**

Which of the following statements is (are) true with respect to the coefficient of determination of a multiple regression?

II. The coefficient of determination expresses the proportion of the total volatility in the dependent variable that is explained by the regression model.

III. As the regression sum of squares increases relative to the sum of squares of the error terms, the coefficient of determination will decrease.

IV. If the dependent variable moves in opposite direction to the independent variables, then the coefficient of determination will be a negative number.

I. The coefficient of determination and the correlation coefficient must always have the same algebraic sign.

II. The coefficient of determination expresses the proportion of the total volatility in the dependent variable that is explained by the regression model.

III. As the regression sum of squares increases relative to the sum of squares of the error terms, the coefficient of determination will decrease.

IV. If the dependent variable moves in opposite direction to the independent variables, then the coefficient of determination will be a negative number.

A. I and II

B. III and IV

C. II only

**Explanation:**Coefficient of Determination (R

^{2}) = Regression Sum of Squares / Total Sum of Squares = (Total Sum of Squares - Sum of the Squares of the Errors) / Total Sum of Squares.

III is incorrect because as the regression sum of squares increases relative to the sum of squares of the error terms, the coefficient of determination will also increase.

IV is incorrect because coefficient of determination can be no greater than 1 and no less than zero. Therefore, I is also incorrect because a dependent variable can have a negative correlation coefficient with the independent variable even if the coefficient of determination is a high positive figure.

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