Modeling Relationships of Multiple Variables with Linear Regression

Interpreting the R-square Statistic

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Stat Cheat Sheet

Interpreting the R-square Statistic
The R-square statistic measures the regression model’s usefulness in predicting outcomes
– indicating how much of the dependent variable’s variation is due to its relationship with the independent variables. An R-square of 1 means that the independent variable explains 100% of the dependent variable’s variation—it entirely determines its values. Conversely, an R-square of
0 means that the independent variable explains none of the variation in the dependent variable—
it has no explanatory power whatsoever. The Model Summary table for our example shows the R-square is .713, meaning 71.3% of the variation from state to state in the percentages of births to teenage mothers can be explained by variation in their poverty rates. The remaining 28.7% can be explained by other factors that are not in the model. You may have also noticed that next to the R-square statistic is

Chapter 7 • Modeling Relationships of Multiple Variables with Linear Regression 167 the correlation between the two variables, R .844. In bivariate linear regressions, the R-square is actually calculated by squaring the correlation coefficient (.844*.844=.713).

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