Reading 11- LOS F (Part 2): Q19 class, 2008, statements, following, simple

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19.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 beta coefficient of the 2nd regression indicates that this regression has more explaining power than the first.

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

D)   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 correct answer was 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 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.