Q6. Rafael Garza, CFA, is considering the purchase of ABC stock for a client’s portfolio. His analysis includes calculating the covariance between the returns of ABC stock and the equity market index. Which of the following statements regarding Garza’s analysis is most accurate?

A)   The covariance measures the strength of the linear relationship between two variables.

B)   A covariance of +1 indicates a perfect positive covariance between the two variables.

C)   The actual value of the covariance is not very meaningful because the measurement is very sensitive to the scale of the two variables.

Q7. Consider the case when the Y variable is in U.S. dollars and the X variable is in U.S. dollars. The 'units' of the covariance between Y and X are:

A)  a range of values from −1 to +1.

B)  squared U.S. dollars.

C)  U.S. dollars.

Q8. Which of the following statements about covariance and correlation is least accurate?

A)     The covariance and correlation are always the same sign, positive or negative.

B)     There is no relation between the sign of the covariance and the correlation.

C)     A zero covariance implies a zero correlation.

Q9. Which of the following statements regarding the coefficient of determination is least accurate? The coefficient of determination:

A)     cannot decrease as independent variables are added to the model.

B)     is the percentage of the total variation in the dependent variable that is explained by the independent variable.

C)     may range from −1 to +1.

Q10. A simple linear regression equation had a coefficient of determination (R²) of 0.8. What is the correlation coefficient between the dependent and independent variables and what is the covariance between the two variables if the variance of the independent variable is 4 and the variance of the dependent variable is 9?

       Correlation coefficient        Covariance

A)         0.91                               4.80

B)         0.89                              5.34

C)         0.89                              4.80

答案和详解如下：

Q6. Rafael Garza, CFA, is considering the purchase of ABC stock for a client’s portfolio. His analysis includes calculating the covariance between the returns of ABC stock and the equity market index. Which of the following statements regarding Garza’s analysis is most accurate?

A)   The covariance measures the strength of the linear relationship between two variables.

B)   A covariance of +1 indicates a perfect positive covariance between the two variables.

C)   The actual value of the covariance is not very meaningful because the measurement is very sensitive to the scale of the two variables.

Correct answer is C)

Covariance is a statistical measure of the linear relationship of two random variables, but the actual value is not meaningful because the measure is extremely sensitive to the scale of the two variables. Covariance can range from negative to positive infinity.

Q7. Consider the case when the Y variable is in U.S. dollars and the X variable is in U.S. dollars. The 'units' of the covariance between Y and X are:

A)  a range of values from −1 to +1.

B)  squared U.S. dollars.

C)  U.S. dollars.

Correct answer is B)

The covariance is in terms of the product of the units of Y and X. It is defined as the average value of the product of the deviations of observations of two variables from their means. The correlation coefficient is a standardized version of the covariance, ranges from −1 to +1, and is much easier to interpret than the covariance.

Q8. Which of the following statements about covariance and correlation is least accurate?

A)     The covariance and correlation are always the same sign, positive or negative.

B)     There is no relation between the sign of the covariance and the correlation.

C)     A zero covariance implies a zero correlation.

Correct answer is B)

The correlation is the ratio of the covariance to the product of the standard deviations of the two variables. Therefore, the covariance and the correlation have the same sign.

Q9. Which of the following statements regarding the coefficient of determination is least accurate? The coefficient of determination:

A)     cannot decrease as independent variables are added to the model.

B)     is the percentage of the total variation in the dependent variable that is explained by the independent variable.

C)     may range from −1 to +1.

Correct answer is C)

In a simple regression, the coefficient of determination is calculated as the correlation coefficient squared and ranges from 0 to +1.

Q10. A simple linear regression equation had a coefficient of determination (R²) of 0.8. What is the correlation coefficient between the dependent and independent variables and what is the covariance between the two variables if the variance of the independent variable is 4 and the variance of the dependent variable is 9?

       Correlation coefficient        Covariance

A)         0.91                               4.80

B)         0.89                              5.34

C)         0.89                              4.80

Correct answer is B)

The correlation coefficient is the square root of the R², r = 0.89.

To calculate the covariance multiply the correlation coefficient by the product of the standard deviations of the two variables:

COV = 0.89 × √4 × √9 = 5.34

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