土豆妮

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

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.

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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.

土豆妮

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.

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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.

土豆妮

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.

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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.

土豆妮

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.

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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.

土豆妮

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.

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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.

土豆妮

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.

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

土豆妮

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 4.80

C) 0.89 5.34

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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

土豆妮

Which model does not lend itself to correlation coefficient analysis?

A) Y = X3.

B) Y = X + 2.

C) X = Y × 2.

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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.

土豆妮

Unlike the coefficient of determination, the coefficient of correlation:

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.

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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.

土豆妮

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.

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