Multiple R is the correlation between your observed values and the values your regression model predicts. It measures how strongly your set of independent variables, working together, relates to your dependent variable. The value ranges from 0 to 1, where 0 means no linear relationship and 1 means a perfect fit. If you’ve run a regression in Excel or another tool and noticed “Multiple R” sitting at the top of the output, this is what it’s telling you: how well your model, as a whole, captures the pattern in your data.
How Multiple R Is Calculated
Multiple R is defined as the Pearson correlation coefficient between your actual Y values and the fitted (predicted) Y values from the regression model. In simpler terms, your regression equation produces a predicted value for every data point. Multiple R measures how closely those predictions track reality. A value of 0.90 means the predicted values move almost in lockstep with the real ones. A value of 0.30 means the predictions are only loosely related to what actually happened.
This is different from a simple correlation coefficient (lowercase r), which measures the relationship between just two variables. In simple linear regression with one predictor, Multiple R equals the absolute value of that basic correlation. But in multiple regression, where you have two or more predictors, Multiple R reflects their combined explanatory power. It can never be negative, because it represents the overall strength of the relationship regardless of direction.
Multiple R vs. R-Squared
The relationship between these two is straightforward: R-squared is just Multiple R multiplied by itself. If your Multiple R is 0.90, your R-squared is 0.81. If your Multiple R is 0.70, your R-squared is 0.49.
They answer slightly different questions. Multiple R tells you the strength of the correlation between predicted and observed values. R-squared tells you the proportion of variation in your dependent variable that the model explains. An R-squared of 0.49 means your predictors account for 49% of the variability in your outcome. The remaining 51% comes from factors not in your model, randomness, or measurement error. Many analysts prefer R-squared because percentages are easier to interpret, but both numbers come from the same underlying calculation.
Interpreting the Strength of Multiple R
The BMJ offers a commonly referenced scale for correlation strength. These thresholds apply to the absolute value of any correlation coefficient, including Multiple R:
- 0 to 0.19: Very weak
- 0.20 to 0.39: Weak
- 0.40 to 0.59: Moderate
- 0.60 to 0.79: Strong
- 0.80 to 1.00: Very strong
These cutoffs are useful as rough guidelines, but context matters more than any fixed label. A Multiple R of 0.50 in a social science study predicting human behavior might be impressive, because people are inherently unpredictable. That same value in an engineering model predicting material stress would signal a serious problem. Always compare your Multiple R against what’s typical in your field and for your type of data.
Where You’ll See It in Software Output
When you run a regression in Excel, Multiple R appears as the first line of the “Regression Statistics” section in the summary output. In Excel’s reporting, the relationship is made explicit: Multiple R is the square root of R-squared. So if your output shows an R-squared of 0.8025, your Multiple R will be approximately 0.896. The UC Davis economics department provides a useful example where a Multiple R of 0.8958, when squared, gives an R-squared of 0.8025, confirming the model explains about 80% of the variation in the outcome.
In SPSS, you’ll find it in the “Model Summary” table, also labeled simply as “R.” Other tools like R and Python statistical libraries report R-squared more prominently, but Multiple R is always just the square root of that value.
Why a High Multiple R Can Be Misleading
Multiple R has one important limitation: it can only stay the same or increase when you add more predictors to your model, even if those predictors are meaningless. Throwing in random, irrelevant variables will nudge Multiple R upward simply because the model has more flexibility to fit the specific dataset you’re working with. This is the core of the overfitting problem.
Research from UC Berkeley’s statistics curriculum illustrates this clearly. For a fixed dataset, a more complex model will always produce a higher R-squared (and therefore a higher Multiple R) than a simpler one. But the gains shrink with each addition, and the model increasingly tailors itself to quirks in your particular data rather than capturing genuine patterns. The result is a model that looks great on paper but performs poorly on new, unseen data.
This is why many analysts prefer adjusted R-squared, which penalizes the addition of predictors that don’t meaningfully improve the model. If your Multiple R jumps from 0.85 to 0.86 after adding three new variables, but your adjusted R-squared drops, those variables are likely adding noise rather than signal. When evaluating your regression, treat Multiple R as a starting point, not the final word on model quality.