yardstick rsq_trad() in R: Traditional R-Squared Score

The yardstick rsq_trad() function in R computes the traditional 1 - SS_res / SS_tot R-squared on regression predictions, returning a tidy one-row score that, unlike rsq(), can fall below zero whenever a model performs worse than just predicting the mean of the outcome.

rsq_trad(df, truth, estimate)                     # basic call
rsq_trad(df, truth = obs, estimate = pred)        # named arguments
df |> group_by(fold) |> rsq_trad(obs, pred)       # by resample
rsq_trad(df, obs, pred, na_rm = TRUE)             # drop missing rows
rsq_trad_vec(truth_vec, pred_vec)                 # vector interface
rsq_trad(df, obs, pred, case_weights = w)         # weighted score
metric_set(rsq_trad, rmse)(df, obs, pred)         # multi-metric bundle

What rsq_trad() measures

rsq_trad() reports the traditional R-squared, defined as 1 minus the residual sum of squares over the total sum of squares. You pass a data frame with the observed numeric outcome and the predicted values, and the function returns a one-row tibble with three columns: .metric, .estimator, and .estimate. The estimate hits 1.0 when predictions are perfect, sits near 0 when predictions are no better than the outcome mean, and goes negative whenever predictions are actively worse than that mean baseline.

That negative-score behaviour is the whole reason rsq_trad() exists as a separate metric. Plain rsq() reports the squared Pearson correlation, so it stays inside [0, 1] no matter how badly biased a model is. rsq_trad() instead uses the textbook ordinary-least-squares formula, so a constant offset, a wrong scale, or a model that always predicts the worst-case value will all drag the score down past zero. Use it whenever bias and calibration matter, not just shape.

rsq_trad() syntax and arguments

The signature mirrors every other numeric yardstick metric. Once the call shape is familiar, the same pattern works for rmse(), mae(), mape(), and the rest of the regression family.

A vector flavour, rsq_trad_vec(), takes truth and estimate as numeric vectors and returns a bare double, handy inside summarise() or custom loops.

Compute traditional R-squared: four examples

The examples below fit a small regression on mtcars, score it on held-out rows, then probe edge cases. First, load the packages and split the data.

Example 1 calls rsq_trad() on the held-out predictions. With positional arguments the function picks up obs as truth and pred as estimate.

About 80 percent of the variance in held-out mpg is explained by the linear fit. Because predictions are roughly unbiased, this estimate sits close to what rsq() would report on the same pair.

Example 2 shows how a constant bias pulls rsq_trad() apart from rsq(). Add 10 mpg to every prediction and rescore.

The squared correlation does not move because the shape of the prediction curve is identical. rsq_trad() collapses to roughly -1.9 because the residuals are now much larger than the variance of the truth. That gap is the entire point of keeping both metrics in the yardstick toolbox.

Example 3 reaches for the vector interface. rsq_trad_vec() skips the tibble wrapper and returns a plain double, handy inside summarise().

The vector form ignores group context, so wrap it in summarise() if you want grouped output without leaving the data-frame interface.

Example 4 bundles rsq_trad() into a multi-metric report. metric_set() glues several metrics into one scoring function.

Reading rsq and rsq_trad side by side flags calibration drift instantly. The same bundle plugs into fit_resamples() or last_fit() for tuning workflows.

rsq_trad() vs rsq(): when the two disagree

Two R-squared formulas, two answers. The choice matters whenever predictions live on a different scale or with a different mean than the truth.

For a calibrated OLS model on training data the two metrics are mathematically identical, which is why textbooks rarely distinguish them. They diverge on held-out predictions, on regularised models with shrunk coefficients, and on any case where the prediction mean drifts from the truth mean. In those situations rsq_trad() is the honest answer; rsq() is the optimistic one.

For the squared-correlation companion metric and the standard way to call it inside tidymodels, see yardstick rsq() in R. For the residual-scale companions, see yardstick rmse() in R and yardstick mae() in R.

Common pitfalls

Three rsq_trad() failure modes trip up most newcomers. Knowing them up front saves time debugging a model that is fine and a metric that is fine but mismatched.

1. A negative score is informative, not broken. Below-zero values mean the predictions lose to a constant-mean baseline. The fix is the model, not the metric.
2. Truth and estimate must be numeric. Passing a factor or character column raises Error: ... must be numeric, not a <factor>. Coerce with as.numeric() only when the levels already encode numbers.
3. Single-row groups return NA. rsq_trad() needs at least two rows per group to compute SS_tot. Filter degenerate groups before averaging.

Try it yourself

Related yardstick functions

• rsq() for the squared Pearson correlation variant that ignores bias.
• rmse() for root mean squared error in outcome units; pairs naturally with rsq_trad().
• mae() for mean absolute error when outliers should count less.
• ccc() for Lin's concordance correlation, which punishes both bias and shape.
• metric_set() to bundle rsq_trad with companions in one reusable scoring function.

For the full yardstick reference and the canonical tidymodels scoring API, see the yardstick documentation for rsq_trad.

FAQ

Why does rsq_trad() return a negative number?

A negative rsq_trad() means the residual sum of squares is larger than the total sum of squares, so the predictions are worse than always guessing the mean of the truth. The number quantifies how badly the model loses to that baseline, where -1 means residuals carry twice the variance of the outcome itself. Treat it as a calibration alarm, not a software error.

When should I use rsq_trad() instead of rsq()?

Use rsq_trad() whenever bias or scale should count against the score. The traditional formula 1 - SSE / SST punishes predictions that are systematically high, low, or on a different scale, so it is the right default on held-out predictions, regularised models, and external forecasts. Reach for rsq() only when shape alone matters and a constant offset is acceptable.

Does rsq_trad() match summary(lm())$r.squared on training data?

Yes, exactly, provided the model has an intercept and you score on the training rows the model was fitted to. On any other data the equality breaks because the OLS identity that makes rsq() and rsq_trad() coincide no longer holds. That is why yardstick separates the two: held-out scoring needs the honest formula.

Can rsq_trad() handle missing values in truth or estimate?

Yes. By default na_rm = TRUE, so any row with NA in either column is dropped before scoring. Set na_rm = FALSE if you want the function to error rather than silently shrink the sample. The same toggle applies to rsq_trad_vec().