Reading 11: Correlation and Regression-LOS a 习题精选 2011, interpret, center, style

土豆妮

Session 3: Quantitative Methods for Valuation
Reading 11: Correlation and Regression

LOS a: Calculate and interpret a sample covariance and a sample correlation coefficient, and interpret a scatter plot.

 

 

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.

---

 

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

土豆妮

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).

---

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.

土豆妮

Suppose the covariance between Y and X is 12, the variance of Y is 25, and the variance of X is 36. What is the correlation coefficient (r), between Y and X?

A) 0.160.

B) 0.400.

C) 0.013.

---

The correlation coefficient is:

土豆妮

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.

---

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

土豆妮

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.

---

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.

土豆妮

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) straight line running from northwest to southeast.

C) a curved line running from southwest to northeast.

---

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.

土豆妮

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.

---

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.

土豆妮

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

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

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

C) R2 = RSS / SST.

---

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

土豆妮

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

A) Coefficient of variation.

B) Goodness of fit.

C) Coefficient of determination.

---

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.

土豆妮

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

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

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

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

---

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.