Quantitative Analysis 【Reading 11】Sample market, return, between, 2012

invic

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

A) negative.

B) not discernable using the scatter plot.

C) positive.

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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

invic

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?

A) 0.78.

B) 0.18.

C) 0.35.





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

invic

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

A) illustrate the relationship between two variables.

B) illustrate the scatterings of a single variable.

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

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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.

invic

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) a curved line running from southwest to northeast.

C) straight line running from northwest to southeast.

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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.

invic

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.

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

invic

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.

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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.

invic

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.)

invic

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.

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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.

invic

Which model does not lend itself to correlation coefficient analysis?

A) Y = X + 2.

B) Y = X3.

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.

invic

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.

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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.