Bias-Variance Tradeoff (2D)

Model

Model complexity (degree) 1

Noise level (σ) 0.16

Training points per fit 14

Resampled fits shown 7

Show true function Show training points

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Bias²

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Variance

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Total error (≈bias²+var)

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Regime

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How it works

A polynomial of the chosen degree is least-squares fit (Gaussian elimination on the normal equations, with a small ridge term for numerical stability) to several independent noisy resamples of the same hidden function. Bias² measures how far the average fitted curve sits from the truth; variance measures how much the fits disagree with each other.

Low degree → curves agree with each other but miss the true shape (underfitting, high bias).
High degree → curves chase each sample's noise and scatter wildly (overfitting, high variance).
Total error ≈ bias² + variance is minimised at an intermediate complexity.

Fitted curves (per resample) True function Training points