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

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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.

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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).

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Unlike the coefficient of determination, the coefficient of correlation:

A) indicates the percentage of variation explained by a regression model.

B) indicates whether the slope of the regression line is positive or negative.

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.

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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.)

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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.

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Which model does not lend itself to correlation coefficient analysis?

A) Y = X3.

B) Y = X + 2.

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. Notice that Y – X = 2 is the same as Y = X + 2.

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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 covariance measures the strength of the linear relationship between two variables.

B) The actual value of the covariance is not very meaningful because the measurement is very sensitive to the scale of the 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.

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Consider the case when the Y variable is in U.S. dollars and the X variable is in U.S. dollars. The 'units' of the covariance between Y and X are:

A) a range of values from ?1 to +1.

B) squared U.S. dollars.

C) U.S. dollars.

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The covariance is in terms of the product of the units of Y and X. It is defined as the average value of the product of the deviations of observations of two variables from their means. The correlation coefficient is a standardized version of the covariance, ranges from ?1 to +1, and is much easier to interpret than the covariance.

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Which of the following statements about covariance and correlation is least accurate?

A) The covariance and correlation are always the same sign, positive or negative.

B) A zero covariance implies a zero correlation.

C) There is no relation between the sign of the covariance and the correlation.

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The correlation is the ratio of the covariance to the product of the standard deviations of the two variables. Therefore, the covariance and the correlation have the same sign.

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Which of the following statements regarding the coefficient of determination is least accurate? The coefficient of determination:

A) cannot decrease as independent variables are added to the model.

B) is the percentage of the total variation in the dependent variable that is explained by the independent variable.

C) may range from ?1 to +1.

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In a simple regression, the coefficient of determination is calculated as the correlation coefficient squared and ranges from 0 to +1.

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A simple linear regression equation had a coefficient of determination (R²) of 0.8. What is the correlation coefficient between the dependent and independent variables and what is the covariance between the two variables if the variance of the independent variable is 4 and the variance of the dependent variable is 9?

Correlation coefficient

Covariance

A) 0.91 4.80

B) 0.89 4.80

C) 0.89 5.34

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The correlation coefficient is the square root of the R², r = 0.89.

To calculate the covariance multiply the correlation coefficient by the product of the standard deviations of the two variables:

COV = 0.89 × √4 × √9 = 5.34