Reading 11: Correlation and Regression-LOS f, (Part 2)习题精选 interpret, center, simple, div, class

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

LOS f, (Part 2): Calculate and interpret a confidence interval for a regression coefficient.

 

 

 

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) 0.774.

B) 0.130.

C) 0.599.

土豆妮

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) 0.774.

B) 0.130.

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.

土豆妮

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 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.

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

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

土豆妮

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 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.

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

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

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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.

土豆妮

Assume you perform two simple regressions. The first regression analysis has an R-squared of 0.80 and a beta coefficient of 0.10. The second regression analysis has an R-squared of 0.80 and a beta coefficient of 0.25. Which one of the following statements is most accurate?

A) The influence on the dependent variable of a one-unit increase in the independent variable is the same in both analyses.

B) Results from the first analysis are more reliable than the second analysis.

C) Results from both analyses are equally reliable.

土豆妮

Assume you perform two simple regressions. The first regression analysis has an R-squared of 0.80 and a beta coefficient of 0.10. The second regression analysis has an R-squared of 0.80 and a beta coefficient of 0.25. Which one of the following statements is most accurate?

A) The influence on the dependent variable of a one-unit increase in the independent variable is the same in both analyses.

B) Results from the first analysis are more reliable than the second analysis.

C) Results from both analyses are equally reliable.

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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 R-squared (0.80) being identical between the first and second regressions means that 80% of the variability in the dependent variable is explained by variability in the independent variable for both regressions. This means that the first regression has the same explaining power as the second regression.

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土豆妮

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 first regression equation has more explaining power than the second regression equation.

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

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

土豆妮

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 first regression equation has more explaining power than the second regression equation.

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

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

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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.

土豆妮

Consider the following estimated regression equation:

ROE_t = 0.23 - 1.50 CE_t

The standard error of the coefficient is 0.40 and the number of observations is 32. The 95% confidence interval for the slope coefficient, b₁, is:

A) {-2.317 < b1 < -0.683}.

B) {0.683 < b1 < 2.317}.

C) {-2.300 < b1 < -0.700}.

土豆妮

Consider the following estimated regression equation:

ROE_t = 0.23 - 1.50 CE_t

The standard error of the coefficient is 0.40 and the number of observations is 32. The 95% confidence interval for the slope coefficient, b₁, is:

A) {-2.317 < b1 < -0.683}.

B) {0.683 < b1 < 2.317}.

C) {-2.300 < b1 < -0.700}.

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The confidence interval is -1.50 ± 2.042 (0.40), or {-2.317 < b₁ < -0.683}.