Question threw me for a loop since I didn’t know how slope was even relevant. Can someone smarter than me advise? 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. Your answer: A was correct! 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.
A is correct. B would be correct if modified as "The influence on the dependent variable of a one unit increase in the independent variable is 0.10 in the first analysis and 0.25 in the second analysis. "
The influence of a 1 unit change in the 1st regression is 0.25 and not 0.9 (which is the R^2). Similarly on the 2nd regression change of 1 unit of the independent variable makes a 0.1 change on the dependent variable and not the R^2 of 0.7. So Statement 2 is thus wrong. Between A) and C) because Regression 1 has 0.9 for R^2 --> which is more than that for Regression 2 - and R^2 = Variance of dependent variable explained by regression / Total Variance of the Dependent variable - A) is the right choice for this question.
slope is definitely relevant in regression analysis, just not in this question. in this question, it’s just a distractor. If you substitute the slope for the R2 in B, you’ll have a true statement.