Q1. 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:

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)   0.599.

C)   0.774.

Q2. 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.

Q3. 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 both analyses are equally reliable.

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

Q4. 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.

答案和详解如下：

Q1. 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:

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)   0.599.

C)   0.774.

Correct answer is C)

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.

Q2. 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.

Correct answer is A)

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.

Q3. 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 both analyses are equally reliable.

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

Correct answer is B)

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.

Q4. 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.

Correct answer is A)

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.

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