Q16. For the case of simple linear regression with one independent variable, which of the following statements about the correlation coefficient is least accurate?

A)   If the correlation coefficient is negative, it indicates that the regression line has a negative slope coefficient.

B)   The correlation coefficient can vary between −1 and +1.

C)   If the regression line is flat and the observations are dispersed uniformly about the line, the correlation coefficient will be +1.

Q17. The Y variable is regressed against the X variable resulting in a regression line that is flat with the plot of the paired observations widely dispersed about the regression line. Based on this information, which statement is most accurate?

A)   The R² of this regression is close to 100%.

B)   X is perfectly positively correlated to Y.

C)   The correlation between X and Y is close to zero.

Q18. Which of the following statements about linear regression is least accurate?

A)   The independent variable is uncorrelated with the residuals (or disturbance term).

B)   The correlation coefficient, ρ, of two assets x and y = (covariance_x,y) × standard deviation_x × standard deviation_y.

C)   R2 = RSS / SST.

Q19. Suppose the covariance between Y and X is 12, the variance of Y is 25, and the variance of X is 36. What is the correlation coefficient (r), between Y and X?

A)   0.160.

B)   0.013.

C)   0.400.

答案和详解如下：

Q16. For the case of simple linear regression with one independent variable, which of the following statements about the correlation coefficient is least accurate?

A)   If the correlation coefficient is negative, it indicates that the regression line has a negative slope coefficient.

B)   The correlation coefficient can vary between −1 and +1.

C)   If the regression line is flat and the observations are dispersed uniformly about the line, the correlation coefficient will be +1.

Correct answer is C)

Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables. The measure of this relationship is called the coefficient of correlation.

If the regression line is flat and the observations are dispersed uniformly about the line,there is no linear relationship between the two variables and the correlation coefficient will be zero.

Both of the other choices are TRUE.

Q17. The Y variable is regressed against the X variable resulting in a regression line that is flat with the plot of the paired observations widely dispersed about the regression line. Based on this information, which statement is most accurate?

A)   The R² of this regression is close to 100%.

B)   X is perfectly positively correlated to Y.

C)   The correlation between X and Y is close to zero.

Correct answer is C)

Perfect correlation means that the observations fall on the regression line. An R² of 100%, means perfect correlation. When there is no correlation, the regression line is flat and the residual standard error equals the standard deviation of Y.

Q18. Which of the following statements about linear regression is least accurate?

A)   The independent variable is uncorrelated with the residuals (or disturbance term).

B)   The correlation coefficient, ρ, of two assets x and y = (covariance_x,y) × standard deviation_x × standard deviation_y.

C)   R2 = RSS / SST.

Correct answer is B)

The correlation coefficient, ρ, of two assets x and y = (covariance_x,y) divided by (standard deviation_x × standard deviation_y). The other statements are true. For the examination, memorize the assumptions underlying linear regression!

Q19. Suppose the covariance between Y and X is 12, the variance of Y is 25, and the variance of X is 36. What is the correlation coefficient (r), between Y and X?

A)   0.160.

B)   0.013.

C)   0.400.

Correct answer is C)

The correlation coefficient is: r = 12 / (5)(6) = 0.40

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