invic

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.

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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.

invic

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.

invic

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.

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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.

invic

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.

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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.

invic

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

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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

invic

The table below shows a sample of returns on two securities:

Period	1	2	3	4	Mean
Security P	0.2%	0.5%	1.1%	−0.6%	0.3%
Security Q	−0.3%	0.9%	1.5%	−0.5%	0.4%

The sample covariance between the two securities’ returns is closest to:

A) 0.47.

B) 0.62.

C) 0.78.

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Period	1	2	3	4	Sum
	−0.1	0.2	0.8	−0.9
	−0.7	0.5	1.1	−0.9
	0.07	0.10	0.88	0.81	1.86

invic

A sample of paired points A and B is shown below. What is the covariance between the values of A and B?

Sample	A	B
1	1	2
2	4	5
3	9	7
4	11	10
5	14	12

A) 20.55.

B) 29.76.

C) 7.80.

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Sample	A	A-mean (A)	B	B-mean (B)	Product
1	1	−6.8	2	−5.2	35.36
2	4	−3.8	5	−2.2	8.36
3	9	1.2	7	−0.2	−0.24
4	11	3.2	10	2.8	8.96
5	14	6.2	12	4.8	29.76
mean	7.8		7.2	Sum	82.2

Cov = 82.20 / (5 – 1) = 20.55

invic

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

A) Coefficient of variation.

B) Goodness of fit.

C) Coefficient of determination.

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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.

invic

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

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

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

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

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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.

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invic

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

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

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

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

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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.