# Negative R² in Interviews: It’s Not a Bug—It’s Your Model Losing to the Mean # Negative R² in Interviews: It’s Not a Bug—It’s Your Model Losing to the Mean Negative R-squared illustration Many candidates assume R² must lie between 0 and 1. That’s a common misconception. R² is defined as: ```text 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.