In regression analysis, the coefficient of determination (r^2) represents?

• A. The proportion of variance in the dependent variable explained by the independent variable
• B. The square root of the correlation coefficient
• C. The slope of the regression line
• D. The standard error of estimate

Answer: (A)

The main idea is that r^2 measures how much of the variability in the dependent variable is explained by the regression model. In simple regression, it represents the proportion of the total variance in the dependent variable that the independent variable helps to explain. It’s calculated as the regression sum of squares divided by the total sum of squares, and it also equals the square of the Pearson correlation between the variables. So if r^2 is, say, 0.75, then 75% of the observed variation in the dependent variable is accounted for by the model, while the remaining 25% comes from other factors or random error. It’s a gauge of fit, not a measure of the slope or the standard error, and it doesn’t by itself imply causation. In multiple regression, it extends to the portion of variance in the dependent variable explained by all predictors together.