invic

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

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

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

C) R2 = RSS / SST.

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

invic

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.

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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.

invic

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 CORRECT.

invic

A 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.

invic

A 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.

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.

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

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 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

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