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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.

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.
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.

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.
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.

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.
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.
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.

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!
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) 0.400.
 B) 0.160.
 C) 0.013.

The correlation coefficient is: Ron James, CFA, computed the correlation coefficient for historical oil prices and the occurrence of a leap year and has identified a statistically significant relationship. Specifically, the price of oil declined every fourth calendar year, all other factors held constant. James has most likely identified which of the following conditions in correlation analysis?
 A) Positive correlation.
 B) Spurious correlation.
 C) Outliers.

Spurious correlation occurs when the analysis erroneously indicates a linear relationship between two variables when none exists. There is no economic explanation for this relationship; therefore this would be classified as spurious correlation.
One major limitation of the correlation analysis of two random variables is when two variables are highly correlated, but no economic relationship exists. This condition most likely indicates the presence of:
 A) outliers.
 B) nonlinear relationships.
 C) spurious correlation.

Spurious correlation occurs when the analysis erroneously indicates a relationship between two variables when none exists.
One of the limitations of correlation analysis of two random variables is the presence of outliers, which can lead to which of the following erroneous assumptions?
 A) The presence of a nonlinear relationship between the two variables, when in fact, there is a linear relationship.
 B) The absence of a relationship between the two variables, when in fact, there is a linear relationship.
 C) The presence of a nonlinear relationship between the two variables, when in fact, there is no relationship whatsoever between the two variables.

Outliers represent a few extreme values for sample observations in a correlation analysis. They can either provide statistical evidence that a significant relationship exists, when there is none, or provide evidence that no relationship exists when one does.
We are examining the relationship between the number of cold calls a broker makes and the number of accounts the firm as a whole opens. We have determined that the correlation coefficient is equal to 0.70, based on a sample of 16 observations. Is the relationship statistically significant at a 10% level of significance, why or why not? The relationship is:
 A) significant; the t-statistic exceeds the critical value by 3.67.
 B) not significant; the critical value exceeds the t-statistic by 1.91.
 C) significant; the t-statistic exceeds the critical value by 1.91.

The calculated test statistic is t-distributed with n – 2 degrees of freedom:
t = r√(n – 2) / √(1 – r2) = 2.6192 / 0.7141 = 3.6678
From a table, the critical value = 1.76
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