Start with what your R² is comparing
In a standard least-squares regression with an intercept, R² compares the fitted model’s squared errors with the squared errors from predicting the outcome mean. An R² of 0.50 says the fitted model accounts for half of the variation used by that comparison. It does not say that half of every outcome is caused by the predictors, that predictions are 50% accurate, or that the model is correctly specified.
| Observed value | Defensible interpretation | What it does not establish |
|---|---|---|
| R² = 0 | No improvement over the reference on this in-sample variation measure | That every predictor is unrelated in every context |
| R² = 0.50 | Half of the reference variation is accounted for in this setting | That the model is “50% correct” |
| R² = 1 | Perfect fit to the evaluated observations | That the model will predict new data perfectly |
| R² < 0 | Worse than the reference under an evaluation that permits negative values | That the software is necessarily broken |
The first three lines describe familiar reference points, not quality bands. The final line commonly appears in out-of-sample evaluation: a negative R² means the predictions lost to the reference prediction on the evaluated data.2
Why a single threshold is not defensible
The expected R² changes with the structure of the problem. Outcomes dominated by individual behavior, measurement noise, or omitted influences can yield modest R² values even when an estimated relationship is useful. Highly controlled calibration problems may require much tighter fit. Cross-sectional and time-series settings can produce very different magnitudes for reasons unrelated to research quality.1
That makes the responsible threshold table short:
| Value | Label | Source | Discipline/context | Category |
|---|---|---|---|---|
| No single cutoff | Compare with relevant models, prior work, and decision needs | Rubinfeld, Reference Guide on Multiple Regression1 | Cross-disciplinary regression evaluation | NO UNIVERSAL THRESHOLD |
Numeric bands such as “above .7 is good” become meaningful only when a named source, discipline, and use case support them. Without those details, the label is a floating rule of thumb.
Why a sourced number may still be the wrong threshold
The same statistic can serve very different jobs:
| Published value or rule | What the source uses it for | What it does not establish | Category |
|---|---|---|---|
| R² ≥ .99 | EPA acceptance criterion for specified chromatographic calibration models4 | A general cutoff for explanatory, behavioral, economic, or biological regression | DISCIPLINE CONVENTION |
| About .02, .13, and .26 | Cohen’s f²-linked effect-size conventions for behavioral-science power analysis3 | Universal model-quality bands | ORIGINAL CONVENTION |
| Several selectable bands | Named rules implemented by one R package5 | Independent validation of every underlying field claim | SOFTWARE DEFAULT |
The EPA criterion is useful precisely because its scope is narrow: controlled instrument calibration is not interchangeable with explaining variation among people or natural systems. Cohen likewise warned that the same R² convention could look small in some fields and large in others. If a source does not verify a benchmark for the context in front of you, the correct conclusion is that there is no verified universal benchmark for that context—not that a generic table should fill the gap.
Use four checks instead of one cutoff
1. Is the comparison appropriate?
Confirm whether the output is ordinary in-sample R², adjusted R², a pseudo-R², or out-of-sample R². These are not interchangeable. R, R², and adjusted R² explains how to identify the reported statistic.
2. Do the residuals reveal a misspecified model?
A high R² can coexist with curvature, nonconstant variance, dependence, influential observations, or leakage. Inspect residual plots and influential observations before treating fit as trustworthiness.
3. Does the model beat a meaningful baseline?
For prediction, compare errors on held-out data with a simple baseline and with plausible alternatives. RMSE, MAE, and MAPE answer a different question from R² because they express prediction error on a scale tied to the outcome.
4. Is the model useful for its purpose?
Explanation, prediction, calibration, and causal estimation demand different evidence. A modest R² may be compatible with a precisely estimated coefficient; a high R² may add little if the model answers the wrong question. Statistical significance and overall fit are not substitutes for one another.
Low R-squared but a significant coefficient
This combination is possible because the statistics answer different questions. A coefficient test asks whether the data are inconsistent with a specified null value under the model. R² summarizes overall variation accounted for. With enough information, a small but consistent relationship can be estimated precisely while leaving most outcome variation unexplained.
Do not “fix” the result by calling the model good or bad from either number alone. Report the coefficient and interval, describe the R², inspect assumptions, and explain whether the effect is meaningful in the domain.
Adjusted and negative R-squared
Adjusted R² penalizes additional predictors. It can decrease when a new variable adds too little fit to offset that penalty, and it can be negative when the adjusted model performs poorly relative to its reference. The detailed comparison belongs in the R versus R-squared guide.
Out-of-sample R² can also be negative when predictions perform worse than a baseline.2 Identify the definition and evaluation data before interpreting the sign.
R-squared is one model-quality coordinate
No information criterion, residual check, or error metric is universally decisive either. AIC and BIC compare candidate models under their own assumptions; they do not repair a weak design. The ResultAtlas approach to threshold claims is described in where statistical thresholds come from. For R², that approach leads to a direct conclusion: context is not an exception to the cutoff—it is what makes any evaluation defensible.