Reading 11: Correlation and Regression-LOS f 习题精选 2011, interpret, standard, center

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

LOS f: Calculate and interpret the standard error of estimate, the coefficient of determination, and a confidence interval for a regression coefficient.

 

 

Bea Carroll, CFA, has performed a regression analysis of the relationship between 6-month LIBOR and the U.S. Consumer Price Index (CPI). Her analysis indicates a standard error of estimate (SEE) that is high relative to total variability. Which of the following conclusions regarding the relationship between 6-month LIBOR and CPI can Carroll most accurately draw from her SEE analysis? The relationship between the two variables is:

A) very weak.

B) positively correlated.

C) very strong.

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The SEE is the standard deviation of the error terms in the regression, and is an indicator of the strength of the relationship between the dependent and independent variables. The SEE will be low if the relationship is strong and conversely will be high if the relationship is weak.

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The most appropriate measure of the degree of variability of the actual Y-values relative to the estimated Y-values from a regression equation is the:

A) sum of squared errors (SSE).

B) coefficient of determination (R2).

C) standard error of the estimate (SEE).

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The SEE is the standard deviation of the error terms in the regression, and is an indicator of the strength of the relationship between the dependent and independent variables. The SEE will be low if the relationship is strong, and conversely will be high if the relationship is weak.

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Which of the following statements about the standard error of estimate is least accurate? The standard error of estimate:

A) is the square root of the sum of the squared deviations from the regression line divided by (n ? 2).

B) is the square of the coefficient of determination.

C) measures the Y variable's variability that is not explained by the regression equation.

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Note: The coefficient of determination (R²) is the square of the correlation coefficient in simple linear regression.

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The standard error of estimate is closest to the:

A) standard deviation of the residuals.

B) standard deviation of the independent variable.

C) standard deviation of the dependent variable.

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The standard error of the estimate measures the uncertainty in the relationship between the actual and predicted values of the dependent variable. The differences between these values are called the residuals, and the standard error of the estimate helps gauge the fit of the regression line (the smaller the standard error of the estimate, the better the fit).

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The standard error of the estimate measures the variability of the:

A) predicted y-values around the mean of the observed y-values.

B) values of the sample regression coefficient.

C) actual dependent variable values about the estimated regression line.

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The standard error of the estimate (SEE) measures the uncertainty in the relationship between the independent and dependent variables and helps gauge the fit of the regression line (the smaller the standard error of the estimate, the better the fit).

Remember that the SEE is different from the sum of squared errors (SSE). SSE = the sum of (actual value - predicted value)². SEE is the the square root of the SSE "standardized" by the degrees of freedom, or SEE = [SSE / (n - 2)]^1/2

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Jason Brock, CFA, is performing a regression analysis to identify and evaluate any relationship between the common stock of ABT Corp and the S& 100 index. He utilizes monthly data from the past five years, and assumes that the sum of the squared errors is .0039. The calculated standard error of the estimate (SEE) is closest to:

A) 0.0082.

B) 0.0080.

C) 0.0360.

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The standard error of estimate of a regression equation measures the degree of variability between the actual and estimated Y-values. The SEE may also be referred to as the standard error of the residual or the standard error of the regression. The SEE is equal to the square root of the mean squared error. Expressed in a formula,

SEE = √(SSE / (n-2)) = √(.0039 / (60-2)) = .0082

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The standard error of the estimate in a regression is the standard deviation of the:<

A) differences between the actual values of the dependent variable and the mean of the dependent variable.

B) residuals of the regression.

C) dependent variable.

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The standard error is s_e = √[SSE/(n-2)]. It is the standard deviation of the residuals.

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Which of the following statements about the standard error of the estimate (SEE) is least accurate?

A) The larger the SEE the larger the R2.

B) The SEE will be high if the relationship between the independent and dependent variables is weak.

C) The SEE may be calculated from the sum of the squared errors and the number of observations.

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The R², or coefficient of determination, is the percentage of variation in the dependent variable explained by the variation in the independent variable. A higher R² means a better fit. The SEE is smaller when the fit is better.

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If X and Y are perfectly correlated, regressing Y onto X will result in which of the following:

A) the regression line will be sloped upward.

B) the standard error of estimate will be zero.

C) the alpha coefficient will be zero.

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If X and Y are perfectly correlated, all of the points will plot on the regression line, so the standard error of the estimate will be zero. Note that the sign of the correlation coefficient will indicate which way the regression line is pointing (there can be perfect negative correlation sloping downward as well as perfect positive correlation sloping upward). Alpha is the intercept and is not directly related to the correlation.

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A simple linear regression is run to quantify the relationship between the return on the common stocks of medium sized companies (Mid Caps) and the return on the S& 500 Index, using the monthly return on Mid Cap stocks as the dependent variable and the monthly return on the S& 500 as the independent variable. The results of the regression are shown below:

	Coefficient	Standard Error of coefficient	t-Value
Intercept	1.71	2.950	0.58
S& 500	1.52	0.130	11.69
R2= 0.599

The strength of the relationship, as measured by the correlation coefficient, between the return on Mid Cap stocks and the return on the S& 500 for the period under study was:

A) 0.130.

B) 0.774.

C) 0.599.

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You are given R² or the coefficient of determination of 0.599 and are asked to find R or the coefficient of correlation. The square root of 0.599 = 0.774.