Weights explain the estimate
At each query, Gaussian distance weights are normalized to sum to one. The estimate is their weighted average.
Let nearby points speak louder.
Fit without choosing a fixed equation. Then make the flexibility answer to leave-one-out error, point weights, and visible residuals.
Observed data and tuning grid
wᵢ(x)=exp[-0.5((x-xᵢ)/h)²]
ŷ(x)=Σwᵢyᵢ / Σwᵢ
CV(h)=mean[(yᵢ-ŷ₋ᵢ(xᵢ))²]
AWAITING FITGAUSSIAN NADARAYA-WATSON
BEST BANDWIDTH—
LOOCV MSE—
ŷ AT QUERY—
Run the fit to inspect dominant normalized weights.
Bandwidth is the argument.
Small h listens locally and can chase noise. Large h pools broadly and can erase structure. Cross-validation makes that tradeoff measurable.
Leave one point out
Each observed y is predicted without using itself. Mean squared error compares candidate bandwidths on equal terms.
Flexible is not causal
The red curve estimates association in this sample. It does not provide confidence intervals, extrapolation guarantees, or causal effects.
Trace the saved watermark counting rules and fixture limits
Read the explanation
The saved kernel lab uses exponential of minus one half squared normalized distance. A point one bandwidth away has unnormalized weight about point six zero six five; two bandwidths away has weight about point one three five three. Both bars show weight at eight hundred pixels per unit. All weights are divided by their sum before averaging observed responses. Nearer observations matter more, without providing a causal interpretation. Bandwidth changes the normalized distance. For an illustrative point two units from the query, bandwidth one gives weight exponential minus two, about point one three five three. Bandwidth two gives exponential minus one half, about point six zero six five. Both bars use eight hundred pixels per unnormalized weight unit. Larger bandwidth admits more distant points; it does not guarantee lower prediction error. The lab chooses candidate bandwidth by leave-one-out mean squared error. It predicts each observed point after omitting that point, squares its residual and averages. Illustrative residuals one and two contribute squared errors one and four. Both bars measure squared response units at one hundred thirty pixels per unit. The fitted CSV exports a one hundred one point grid. Source limitations explicitly omit confidence intervals and boundary correction, and the selected fit establishes association rather than causation.