Q1. 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.

Q2. 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.

Q3. 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.

Q4. 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).

答案和详解如下：

Q1. 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.

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

Q2. 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.

Correct answer is C)

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.

Q3. 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.

Correct answer is C)

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.

Q4. 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).

Correct answer is B)

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.