Determine and interpret the correlation coefficient for the two variables X and Y. The standard deviation of X is 0.05, the standard deviation of Y is 0.08, and their covariance is ?0.003.

A) +0.75 and the two variables are positively associated.

B) ?0.75 and the two variables are negatively associated.

C) ?1.33 and the two variables are negatively associated

Determine and interpret the correlation coefficient for the two variables X and Y. The standard deviation of X is 0.05, the standard deviation of Y is 0.08, and their covariance is ?0.003.

A) +0.75 and the two variables are positively associated.

B) ?0.75 and the two variables are negatively associated.

C) ?1.33 and the two variables are negatively associated.

Unlike the coefficient of determination, the coefficient of correlation:

A) indicates whether the slope of the regression line is positive or negative.

B) indicates the percentage of variation explained by a regression model.

C) measures the strength of association between the two variables more exactly.

Unlike the coefficient of determination, the coefficient of correlation:

A) indicates whether the slope of the regression line is positive or negative.

B) indicates the percentage of variation explained by a regression model.

C) measures the strength of association between the two variables more exactly.

In order to have a negative correlation between two variables, which of the following is most accurate?

A) Either the covariance or one of the standard deviations must be negative.

B) The covariance must be negative.

C) The covariance can never be negative.

In order to have a negative correlation between two variables, which of the following is most accurate?

A) Either the covariance or one of the standard deviations must be negative.

B) The covariance must be negative.

C) The covariance can never be negative.

Which of the following statements regarding a correlation coefficient of 0.60 for two variables Y and X is least accurate? This correlation:

A) indicates a positive covariance between the two variables.

B) indicates a positive linear relation between the two variables.

C) is significantly different from zero.

Which of the following statements regarding a correlation coefficient of 0.60 for two variables Y and X is least accurate? This correlation:

A) indicates a positive covariance between the two variables.

B) indicates a positive linear relation between the two variables.

C) is significantly different from zero.

Which model does not lend itself to correlation coefficient analysis?

A) Y = X + 2.

B) Y = X3.

C) X = Y × 2.

Which model does not lend itself to correlation coefficient analysis?

A) Y = X + 2.

B) Y = X3.

C) X = Y × 2.

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

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

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

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

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

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

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) U.S. dollars.

C) squared U.S. dollars.

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) U.S. dollars.

C) squared U.S. dollars.

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.

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.

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

A) may range from ?1 to +1.

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

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

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

A) may range from ?1 to +1.

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

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

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) 0.89   5.34

B) 0.91   4.80

C) 0.89   4.80

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) 0.89   5.34

B) 0.91   4.80

C) 0.89   4.80

Which term is least likely to apply to a regression model?

A) Goodness of fit.

B) Coefficient of determination.

C) Coefficient of variation.

Which term is least likely to apply to a regression model?

A) Goodness of fit.

B) Coefficient of determination.

C) Coefficient of variation.

A sample covariance for the common stock of the Earth Company and the S& 500 is ?9.50. Which of the following statements regarding the estimated covariance of the two variables is most accurate?

A) The two variables will have a slight tendency to move together.

B) The two variables will have a strong tendency to move in opposite directions.

C) The relationship between the two variables is not easily predicted by the calculated covariance.

A sample covariance for the common stock of the Earth Company and the S& 500 is ?9.50. Which of the following statements regarding the estimated covariance of the two variables is most accurate?

A) The two variables will have a slight tendency to move together.

B) The two variables will have a strong tendency to move in opposite directions.

C) The relationship between the two variables is not easily predicted by the calculated covariance.

A sample covariance of two random variables is most commonly utilized to:

A) calculate the correlation coefficient, which is a measure of the strength of their linear relationship.

B) identify and measure strong nonlinear relationships between the two variables.

C) estimate the “pure” measure of the tendency of two variables to move together over a period of time.

A sample covariance of two random variables is most commonly utilized to:

A) calculate the correlation coefficient, which is a measure of the strength of their linear relationship.

B) identify and measure strong nonlinear relationships between the two variables.

C) estimate the “pure” measure of the tendency of two variables to move together over a period of time.

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

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

C) The correlation coefficient can vary between ?1 and +1.

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

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

C) The correlation coefficient can vary between ?1 and +1.

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 correlation between X and Y is close to zero.

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

C) X is perfectly positively correlated to Y.

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 correlation between X and Y is close to zero.

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

C) X is perfectly positively correlated to Y.

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

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

B) R2 = RSS / SST.

C) The correlation coefficient, ρ, of two assets x and y = (covariancex,y) × standard deviationx × standard deviationy.

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

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

B) R2 = RSS / SST.

C) The correlation coefficient, ρ, of two assets x and y = (covariancex,y) × standard deviationx × standard deviationy.

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) 0.400.

B) 0.160.

C) 0.013.

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) 0.400.

B) 0.160.

C) 0.013.