What does the r value (R^2) tell us?

What does the r value (R^2) tell us?

• A. How much of the variance of the dependent variable can be explained by the exploratory variable
• B. The mean of the dependent variable
• C. The p-value of the regression
• D. The standard error of the estimate

Answer: (A)

R-squared shows how much of the variability in the outcome the model can explain with the predictor(s). It’s computed as the proportion of explained variance relative to the total variance in the dependent variable. In simple regression, it’s the square of the correlation between the predictor and the outcome, so a higher value means the line captures more of the data’s pattern. An R-squared near 0 means the predictor explains little of the variance; near 1 means it explains most of it. It doesn’t tell you about the mean of the outcome, nor the p-value for the predictor, nor the standard error of the estimate. It’s a measure of fit, and with many predictors it can inflate, so adjusted R-squared is often used for model comparison.

R-squared shows how much of the variability in the outcome the model can explain with the predictor(s). It’s computed as the proportion of explained variance relative to the total variance in the dependent variable. In simple regression, it’s the square of the correlation between the predictor and the outcome, so a higher value means the line captures more of the data’s pattern. An R-squared near 0 means the predictor explains little of the variance; near 1 means it explains most of it. It doesn’t tell you about the mean of the outcome, nor the p-value for the predictor, nor the standard error of the estimate. It’s a measure of fit, and with many predictors it can inflate, so adjusted R-squared is often used for model comparison.