Regression Metrics Explorer 2D — MAE, RMSE, R² & MAPE

Dataset

Points 18

Noise spread 0.60

Outlier strength 0.0

Metric Focus

Bar color intensity in the lower panel shows each point's contribution to the MAE total — watch how the outlier point lights up differently per metric.

Live Metrics

MAE

0.00

RMSE

0.00

R²

0.00

MAPE

0.0%

RMSE / MAE ratio

1.00×

How it works

Each column is one (actual, predicted) pair. The top panel plots the actual value as a teal dot and the predicted value as an amber dot connected by a red residual line; the bottom panel turns those same residuals into a per-point bar chart so you can compare their raw contribution to each metric side by side. The four evaluation metrics all reduce these n residuals to a single number, but they weigh errors very differently:

MAE  = (1/n) Σ |eᵢ|
RMSE = sqrt( (1/n) Σ eᵢ² )
R²   = 1 − ( Σ eᵢ² / Σ (actualᵢ − mean)² )
MAPE = (1/n) Σ ( |eᵢ| / |actualᵢ| ) × 100%

Noise spread — random scatter applied to every prediction. Raises MAE and RMSE roughly together and barely moves their ratio.
Outlier strength — pushes ONE point's prediction far from its actual value. Because RMSE squares the residual before averaging, a single large miss inflates RMSE much faster than MAE — that gap is exactly why RMSE is called "outlier-sensitive" and MAE "outlier-robust".
RMSE / MAE ratio — always ≥ 1 (a consequence of the power-mean inequality); it equals 1 only when every residual has identical magnitude, and grows the more concentrated the error is in a few points.
R² — the fraction of the actual values' variance the model explains; 1.0 is a perfect fit, 0.0 is no better than predicting the mean every time, and it can go negative for a model worse than that baseline.
MAPE — expresses error as a percentage of the true value, which makes it comparable across datasets with different scales but unstable when actual values sit near zero.
Metric Focus buttons — recolor each bar by that metric's per-point contribution, so you can see visually which points a given metric actually "cares about".
Drag the top panel — pans the visible window when there are more points than fit on screen; scroll/pinch zooms it.

Real-world relevance: choosing MAE vs RMSE vs MAPE as the model-selection metric is one of the most consequential decisions in a regression project — a hyperparameter search that optimizes RMSE will happily sacrifice typical-case accuracy to avoid rare large misses, while one that optimizes MAE will tolerate one bad outlier if it keeps everything else tight.

Actual value Predicted value Residual (error)

Drag to pan · scroll/pinch to zoom