A scatter plot with a LOWESS (Locally Weighted Scatterplot Smoothing) regression curve overlaid. LOWESS is a non-parametric method that fits smooth curves by performing local weighted regressions at each point, adapting to local data patterns without assuming a specific functional form. This makes it ideal for exploring complex relationships where the underlying pattern is unknown or varies across the data range.
# anyplot.ai
# scatter-regression-lowess: Scatter Plot with LOWESS Regression
# Library: makie 0.21.9 | Julia 1.11.9
# Quality: 86/100 | Created: 2026-09-09
using CairoMakie
using Colors
using Random
# --- Theme tokens -------------------------------------------------------------
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const BRAND = colorant"#009E73" # Imprint palette position 1 — scatter points
const CURVE_COLOR = colorant"#4467A3" # Imprint palette position 3 — LOWESS fit
# --- Data: light-response curve of net photosynthesis -------------------------
Random.seed!(42)
n = 200
light_intensity = sort(rand(n) .* 2000) # PAR, μmol photons m⁻² s⁻¹
true_response = 13.5 .* (1 .- exp.(-light_intensity ./ 280)) .- 0.0016 .* light_intensity
net_photosynthesis = true_response .+ randn(n) .* 0.9 # μmol CO2 m⁻² s⁻¹
# --- LOWESS smoothing: local weighted linear regression, tricube weights ------
# A pointwise 95% confidence band is derived from the weighted-regression standard
# error at each evaluation point (weighted residual variance scaled by the local
# effective sample size sw^2 / sum(w^2)).
frac = 0.35
k = ceil(Int, frac * n)
eval_x = collect(range(minimum(light_intensity), maximum(light_intensity); length = 200))
fitted_y = similar(eval_x)
band_lo = similar(eval_x)
band_hi = similar(eval_x)
for (i, x0) in enumerate(eval_x)
dist = abs.(light_intensity .- x0)
d_max = sort(dist)[k]
w = ifelse.(dist .<= d_max, (1 .- clamp.(dist ./ d_max, 0, 1) .^ 3) .^ 3, 0.0)
sw = sum(w)
sx = sum(w .* light_intensity)
sy = sum(w .* net_photosynthesis)
sxx = sum(w .* light_intensity .^ 2)
sxy = sum(w .* light_intensity .* net_photosynthesis)
slope = (sw * sxy - sx * sy) / (sw * sxx - sx^2)
intercept = (sy - slope * sx) / sw
fitted_y[i] = intercept + slope * x0
resid = net_photosynthesis .- (intercept .+ slope .* light_intensity)
weighted_var = sum(w .* resid .^ 2) / sw
effective_n = sw^2 / sum(w .^ 2)
se = sqrt(weighted_var / effective_n)
band_lo[i] = fitted_y[i] - 1.96 * se
band_hi[i] = fitted_y[i] + 1.96 * se
end
# --- Plot -----------------------------------------------------------------
fig = Figure(
resolution = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "scatter-regression-lowess · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Light Intensity (μmol photons m⁻² s⁻¹)",
ylabel = "Net Photosynthesis (μmol CO₂ m⁻² s⁻¹)",
xlabelsize = 14,
ylabelsize = 14,
xticklabelsize = 12,
yticklabelsize = 12,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
)
band!(ax, eval_x, band_lo, band_hi; color = (CURVE_COLOR, 0.35))
scatter!(
ax, light_intensity, net_photosynthesis;
color = (BRAND, 0.55), markersize = 9,
strokecolor = PAGE_BG, strokewidth = 1,
)
lines!(ax, eval_x, fitted_y; color = CURVE_COLOR, linewidth = 3)
# `band!` has no automatic legend entry in Makie, so the legend is built explicitly
# from proxy elements that mirror the actual plot styling.
legend_elements = [
MarkerElement(color = (BRAND, 0.55), marker = :circle, markersize = 9, strokecolor = PAGE_BG, strokewidth = 1),
LineElement(color = CURVE_COLOR, linewidth = 3),
PolyElement(color = (CURVE_COLOR, 0.35)),
]
legend_labels = ["Observations", "LOWESS fit", "95% CI"]
axislegend(ax, legend_elements, legend_labels; position = :lt, backgroundcolor = ELEVATED_BG, labelcolor = INK, framevisible = false)
# --- Save -------------------------------------------------------------------
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/scatter-regression-lowess/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "scatter-regression-lowess",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/scatter-regression-lowess/julia/makie",
"hub": "https://anyplot.ai/scatter-regression-lowess",
"code_json": "https://api.anyplot.ai/specs/scatter-regression-lowess/makie/code",
"spec_json": "https://api.anyplot.ai/specs/scatter-regression-lowess",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-regression-lowess/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-regression-lowess/julia/makie/plot-dark.png",
"quality_score": 86.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Scatter Plot with LOWESS Regression on anyplot.ai.