Reading 11: Correlation and Regression - LOS f, (Part 2):

white, black, simple, return, between

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:

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) 0.599.

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.