Negative R² in Interviews: It’s Not a Bug—It’s Your Model Losing to the Mean

Many candidates assume R² must lie between 0 and 1. That’s a common misconception. R² is defined as:

R² = 1 − SSE / SST

where SSE is the model's sum of squared errors and SST is the total sum of squares (the variance around the mean). If SSE > SST, the fraction SSE/SST exceeds 1 and R² becomes negative. In plain language: your model predicts worse than a trivial predictor that always outputs the mean ȳ.

Why R² goes negative

• Baseline reminder: the mean predictor ȳ has SSE = SST, so it has R² = 0 by definition. Negative R² simply means your model's SSE is larger than that baseline.
• Common causes:
  • Model misspecification: e.g., fitting a straight line to strongly nonlinear data.
  • Evaluating on a test set after overfitting the train set: the model generalizes poorly so SSE_test outgrows SST_test.
  • Forcing a model without an intercept: removing the intercept often increases SSE relative to SST.
  • Bad preprocessing or target leakage issues that break generalization.

Quick numeric example

Suppose SST = 100 and SSE = 150. Then

R² = 1 − 150 / 100 = 1 − 1.5 = −0.5.

Interpretation: your model is making predictions so bad that the mean of y would have been a better forecast.

What to say (and why) in an interview

Be concise and precise. For example:

"Negative R² means the model's SSE exceeds the total variance SST, so it performs worse than the baseline predictor ȳ. Typical causes are misspecification (e.g., linear model for nonlinear data), evaluating on a test set after severe overfitting, or removing the intercept. Remedies include adding an intercept, transforming features, regularization, or choosing a more appropriate model."

That answer shows you know the formula, the intuition (comparison to the mean), and practical causes and fixes.

How to fix or avoid it

• Restore/allow an intercept unless there's a good reason not to.
• Try feature transformations (polynomials, logs) or non-linear models.
• Use regularization (Ridge, Lasso) to prevent overfitting.
• Validate on a properly held-out test set or with cross-validation.
• Check data preprocessing and leakage issues.

Bottom line

Negative R² isn't a bug in the metric — it's a signal. It tells you the model is doing worse than the dumb baseline that always predicts the mean. Say that clearly in interviews and follow up with likely causes and fixes.