HuskyGrad2010

The standard error of estimate is closest to the:

A) standard deviation of the independent variable.

B) standard deviation of the residuals.

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).

HuskyGrad2010

A regression between the returns on a stock and its industry index returns gives the following results:

	Coefficient	Standard Error	t-value
Intercept	2.1	2.01	1.04
Industry Index	1.9	0.31	6.13

• The t-statistic critical value at the 0.01 level of significance is 2.58
• Standard error of estimate = 15.1
• Correlation coefficient = 0.849

The regression statistics presented indicate that the dispersion of stock returns about the regression line is:

A) 72.10.

B) 15.10.

C) 63.20.

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The standard deviation of the differences between the actual observations and the projection of those observations (the regression line) is called the standard error of the estimate. The standard error of the estimate is the unsystematic risk.

HuskyGrad2010

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

A) is the square of the coefficient of determination.

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

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.

HuskyGrad2010

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) standard error of the estimate (SEE).

B) sum of squared errors (SSE).

C) coefficient of determination (R2).

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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.

HuskyGrad2010

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) positively correlated.

B) very strong.

C) very weak.

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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.

HuskyGrad2010

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&P 500 Index, using the monthly return on Mid Cap stocks as the dependent variable and the monthly return on the S&P 500 as the independent variable. The results of the regression are shown below:

[/td][td=1,1,74] Coefficient	Standard Error of coefficient	t-Value
Intercept	1.71	2.950	0.58
S&P 500	1.52	0.130	11.69
R2= 0.599 [/td][td=1,1,74]

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

A) 0.130.

B) 0.599.

C) 0.774.

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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.

HuskyGrad2010

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&P 500 Index, using the monthly return on Mid Cap stocks as the dependent variable and the monthly return on the S&P 500 as the independent variable. The results of the regression are shown below:

[/td][td=1,1,74] Coefficient	Standard Error of coefficient	t-Value
Intercept	1.71	2.950	0.58
S&P 500	1.52	0.130	11.69
R2= 0.599 [/td][td=1,1,74]

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

A) 0.130.

B) 0.599.

C) 0.774.

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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.

HuskyGrad2010

Assume an analyst performs two simple regressions. The first regression analysis has an R-squared of 0.90 and a slope coefficient of 0.10. The second regression analysis has an R-squared of 0.70 and a slope coefficient of 0.25. Which one of the following statements is most accurate?

A) The first regression has more explanatory power than the second regression.

B) The influence on the dependent variable of a one unit increase in the independent variable is 0.9 in the first analysis and 0.7 in the second analysis.

C) Results of the second analysis are more reliable than the first analysis.

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The coefficient of determination (R-squared) is the percentage of variation in the dependent variable explained by the variation in the independent variable. The larger R-squared (0.90) of the first regression means that 90% of the variability in the dependent variable is explained by variability in the independent variable, while 70% of that is explained in the second regression. This means that the first regression has more explanatory power than the second regression. Note that the Beta is the slope of the regression line and doesn’t measure explanatory power

HuskyGrad2010

An analyst performs two simple regressions. The first regression analysis has an R-squared of 0.40 and a beta coefficient of 1.2. The second regression analysis has an R-squared of 0.77 and a beta coefficient of 1.75. Which one of the following statements is most accurate?

A) The second regression equation has more explaining power than the first regression equation.

B) The first regression equation has more explaining power than the second regression equation.

C) The R-squared of the first regression indicates that there is a 0.40 correlation between the independent and the dependent variables.

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The coefficient of determination (R-squared) is the percentage of variation in the dependent variable explained by the variation in the independent variable. The larger R-squared (0.77) of the second regression means that 77% of the variability in the dependent variable is explained by variability in the independent variable, while only 40% of that is explained in the first regression. This means that the second regression has more explaining power than the first regression. Note that the Beta is the slope of the regression line and doesn’t measure explaining power.

HuskyGrad2010

Consider the following estimated regression equation:

AUTOt = 0.89 + 1.32 PIt

The standard error of the coefficient is 0.42 and the number of observations is 22. The 95% confidence interval for the slope coefficient, b1, is:

A) {-0.766 < b1 < 3.406}.

B) {0.480 < b1 < 2.160}.

C) {0.444 < b1 < 2.196}.

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The degrees of freedom are found by n-k-1 with k being the number of independent variables or 1 in this case.  DF =  22-1-1 = 20.  Looking up 20 degrees of freedom on the student's t distribution for a 95% confidence level and a 2 tailed test gives us a critical value of 2.086.  The confidence interval is 1.32 ± 2.086 (0.42), or {0.444 < b1 < 2.196}.