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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 negatively associated.

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

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

The correlation coefficient is the covariance divided by the product of the two standard deviations, i.e. ?0.003 / (0.08 × 0.05).

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

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

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

In a simple linear regression the coefficient of determination (R²) is the squared correlation coefficient, so it is positive even when the correlation is negative.

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

A)	The covariance must be negative.

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

C)	The covariance can never be negative.

In order for the correlation between two variables to be negative, the covariance must be negative. (Standard deviations are always positive.)

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

A)	is significantly different from zero.

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

C)	indicates a positive covariance between the two variables.

A test of significance requires the sample size, so we cannot conclude anything about significance. There is some positive relation between the two variables, but one may or may not cause the other.

The correlation coefficient is a measure of linear association. All of the functions except for Y = X³ are linear functions. Notice that Y – X = 2 is the same as Y = X + 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 covariance measures the strength of the linear relationship between two variables.

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

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

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.

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:

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.

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)	A zero covariance implies a zero correlation.

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

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.

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.

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

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?

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

A)	Coefficient of variation.

B)	Goodness of fit.

C)	Coefficient of determination.

Goodness of fit and coefficient of determination are different names for the same concept. The coefficient of variation is not directly part of a regression model.

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.

The actual value of the covariance for two variables is not very meaningful because its measurement is extremely sensitive to the scale of the two variables, ranging from negative to positive infinity. Covariance can, however be converted into the correlation coefficient, which is more straightforward to interpret.

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

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

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

Since the actual value of a sample covariance can range from negative to positive infinity depending on the scale of the two variables, it is most commonly used to calculate a more useful measure, the correlation coefficient.

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.

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.

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

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

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

C)	X is perfectly positively correlated to Y.

Perfect correlation means that all the observations fall on the regression line. An R² of 100% means perfect correlation. When there is no correlation, the regression line is horizontal.

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.

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!

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?

The correlation coefficient is:

Thomas Manx is attempting to determine the correlation between the number of times a stock quote is requested on his firm’s website and the number of trades his firm actually processes. He has examined samples from several days trading and quotes and has determined that the covariance between these two variables is 88.6, the standard deviation of the number of quotes is 18, and the standard deviation of the number of trades processed is 14. Based on Manx’s sample, what is the correlation between the number of quotes requested and the number of trades processed?

Correlation = Cov (X,Y) / (Std. Dev. X)(Std. Dev. Y)
Correlation = 88.6 / (18)(14) = 0.35

In the scatter plot below, the correlation between the return on stock A and the market index is:

In the scatter plot, higher values of the return on stock A are associated with higher values of the return on the market, i.e. a positive correlation between the two variables.

If the correlation between two variables is ?1.0, the scatter plot would appear along a:

A)	straight line running from southwest to northeast.

B)	straight line running from northwest to southeast.

C)	a curved line running from southwest to northeast.

If the correlation is ?1.0, then higher values of the y-variable will be associated with lower values of the x-variable. The points would lie on a straight line running from northwest to southeast.

Which of the following statements regarding scatter plots is most accurate? Scatter plots:

A)	illustrate the scatterings of a single variable.

B)	illustrate the relationship between two variables.

C)	are used to examine the third moment of a distribution (skewness).

A scatter plot is a collection of points on a graph where each point represents the values of two variables. They are used to examine the relationship between two variables.