Adjusted R Squared Calculator
Adjusts R² for sample size and the number of fitted predictors. The form displays 1 − (1−R²)(n−1)/(n−p−1) beside adjusted r squared, using a worked condition that can be recalculated with the labeled inputs.
Set the model inputs
Adjusted R squared
What adjusted r squared answers
The adjusted r squared page adjusts R² for sample size and the number of fitted predictors.
Adjusted R squared is limited to the statistical quantity named by the result panel. The adjusted r squared calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Before entering the adjusted r squared data
- R squared: For adjusted r squared, the worked value for r squared is 0.7 ratio. Treat the r squared entry (0.7 ratio) explicitly as a count, proportion, rate, estimate, or model parameter before comparing adjusted r squared conditions. The form enforces minimum -10, maximum 1.
- Sample size: For adjusted r squared, the worked value for sample size is 40 observations. Treat the sample size entry (40 observations) explicitly as a count, proportion, rate, estimate, or model parameter before comparing adjusted r squared conditions. The form enforces minimum 3.
- Predictors: For adjusted r squared, the worked value for predictors is 3 variables. Treat the predictors entry (3 variables) explicitly as a count, proportion, rate, estimate, or model parameter before comparing adjusted r squared conditions. The form enforces minimum 0.
The entries used for adjusted r squared must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid adjusted r squared arithmetic for a nonexistent study.
Following the adjusted r squared relationship
For adjusted r squared, match every symbol in the relationship to a labeled field before substituting numbers. Adjusted R squared is reported in ratio.
While checking adjusted r squared, inspect every denominator in 1 − (1−R²)(n−1)/(n−p−1). For adjusted r squared, a zero or near-zero denominator can make adjusted r squared undefined or unstable.
Checking the displayed example
The default adjusted r squared condition is R squared = 0.7 ratio, Sample size = 40 observations, Predictors = 3 variables.
R²=0.70 with n=40 and three predictors gives adjusted R² about 0.675.
The live calculator reports Adjusted R squared 0.675 · Residual degrees of freedom 36. Repeating one intermediate step from 1 − (1−R²)(n−1)/(n−p−1) provides a fixed adjusted r squared reference check for later code changes.
Statistical context for adjusted r squared
The denominator requires more observations than predictors plus one, and the adjustment is not a guarantee of model selection quality.
For adjusted r squared, a fitted coefficient or association is conditional on the model and observed range; it does not by itself show that changing one variable will cause another to change.
How to interpret the adjusted r squared output
When interpreting adjusted r squared, inspect residual behavior, influential observations, nonlinearity, dependence, and extrapolation before carrying a regression result to a new setting.
As a second check for adjusted r squared, reversing the numerator and denominator answers a different question, so retain the direction printed in 1 − (1−R²)(n−1)/(n−p−1).
Varying a single adjusted r squared input at a time
Change r squared while holding the remaining entries fixed, then state why the direction and size of the adjusted r squared change are plausible from 1 − (1−R²)(n−1)/(n−p−1).
Repeat the adjusted r squared exercise with predictors. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that adjusted r squared scenario as exact.
When the analysis changes, compare coefficient of determination, regression standard error, and regression residual.
Reporting adjusted r squared reproducibly
Report adjusted r squared using 1 − (1−R²)(n−1)/(n−p−1), followed by the entered values, units, exclusions, and analysis date. Name the adjusted r squared population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Adjusted R squared 0.675 · Residual degrees of freedom 36. A later adjusted r squared review can then distinguish a changed input from a different convention or software implementation.
Questions about adjusted r squared
What should be saved with adjusted r squared?
Save the entered values and units for r squared, sample size, predictors, along with the analysis date, exclusions, software or formula version, and the relationship 1 − (1−R²)(n−1)/(n−p−1). That record is sufficient to rebuild this specific adjusted r squared calculation.
Does adjusted r squared establish a causal or population conclusion?
No. The displayed adjusted r squared value is conditional on the entered data and named method. The adjusted r squared design, measurement process, and assumptions determine what can be concluded beyond those values.
How should adjusted r squared be rounded?
Keep the unrounded adjusted r squared for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in adjusted r squared do not correct sampling or model error.
Which input deserves the closest boundary check?
For adjusted r squared, start with predictors and then r squared. Confirm the adjusted r squared units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different adjusted r squared?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change adjusted r squared. Compare the printed adjusted r squared formula and its input definitions before treating either output as wrong.