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

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

C) Results from both analyses are equally reliable.

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

aianjie

 

The correct answer is C

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 percent 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.

aianjie

 

AIM 8: Explain the process of normality testing using histograms and normal probability plots.

An analyst is using a normal probability plot to determine if a data set is normally distributed. If the data is normally distributed, then the plot should resemble a:

A) bell shaped curve.

B) convex plot that asymptotically approaches one.

C) concave plot that asymptotically approaches one.

D) straight line.

aianjie

 

The correct answer is A

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.

aianjie

 

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

C) 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.

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

aianjie

 

The 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 percent of the variability in the dependent variable is explained by variability in the independent variable, while 70 percent 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.

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6、What does the R² of a simple regression of two variables measure and what calculation is used to equate the correlation coefficient to the coefficient of determination? fficeffice" />

        R² measures:                     Correlation coefficient

 

A)percent of variability of the independent variable that is explained by the variability of the dependent variable                                              R² = r × 2

B)percent of variability of the dependent variable that is explained by the variability of the independent variable                                                                          R² = r × 2

C)percent of variability of the independent variable that is explained by the variability of the dependent variable                                                                          R² = r²

D)percent of variability of the dependent variable that is explained by the variability of the independent variable                                                                          R² = r²

aianjie

 

The correct answer is D

R2, or the Coefficient of Determination, is the square of the coefficient of correlation (r). The coefficient of correlation describes the strength of the relationship between the X and Y variables. The standard error of the residuals is the standard deviation of the dispersion about the regression line. The t-statistic measures the statistical significance of the coefficients of the regression equation. In the response: "percent of variability of the independent variable that is explained by the variability of the dependent variable," the definitions of the variables are reversed.

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7、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)    0.599.

C)   2.950.

D)   0.130.

aianjie

 

The 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 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.