A logistic regression visualization showing the characteristic S-shaped (sigmoid) probability curve for binary classification. The plot displays data points colored by their binary class, the fitted logistic curve representing predicted probabilities, confidence intervals around the curve, and an optional decision threshold line. This visualization is essential for understanding how a logistic model maps continuous input features to class probabilities.
# anyplot.ai
# logistic-regression: Logistic Regression Curve Plot
# Library: makie 0.21.9 | Julia 1.11.9
# Quality: 92/100 | Created: 2026-09-02
using CairoMakie
using Colors
using LinearAlgebra
using Random
using Statistics
Random.seed!(42)
# --- Theme tokens ------------------------------------------------------------
THEME = get(ENV, "ANYPLOT_THEME", "light")
PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
# Imprint palette — semantic exception: outcome maps to health status (good/bad)
HEALTHY_COLOR = colorant"#009E73" # class 0, no diabetes — brand green, always-first series
DIABETIC_COLOR = colorant"#AE3030" # class 1, diabetes — semantic anchor for the adverse outcome
CURVE_COLOR = INK # fitted probability curve — neutral reference line
THRESHOLD_COLOR = colorant"#DDCC77" # decision threshold — amber warning anchor
# --- Data: fasting glucose vs. diabetes diagnosis -----------------------------
n = 220
glucose = clamp.(120.0 .+ 28.0 .* randn(n), 65.0, 210.0) # fasting glucose, mg/dL
glucose_mean = mean(glucose)
glucose_std = std(glucose)
glucose_z = (glucose .- glucose_mean) ./ glucose_std
true_intercept = -0.3
true_slope = 1.6
true_prob = 1.0 ./ (1.0 .+ exp.(-(true_intercept .+ true_slope .* glucose_z)))
diagnosis = Float64.(rand(n) .< true_prob) # 0 = no diabetes, 1 = diabetes
# --- Fit logistic regression via Newton-Raphson (IRLS) ------------------------
design = hcat(ones(n), glucose_z)
beta = zeros(2)
weights = ones(n)
for _ in 1:25
eta = design * beta
mu = 1.0 ./ (1.0 .+ exp.(-eta))
global weights = max.(mu .* (1.0 .- mu), 1e-8)
hessian = design' * (design .* weights)
gradient = design' * (diagnosis .- mu)
global beta = beta + hessian \ gradient
end
covariance = inv(design' * (design .* weights))
# --- Fitted curve + 95% confidence band on a smooth glucose grid --------------
grid_n = 200
glucose_grid = collect(range(minimum(glucose), maximum(glucose), length=grid_n))
grid_z = (glucose_grid .- glucose_mean) ./ glucose_std
design_grid = hcat(ones(grid_n), grid_z)
eta_grid = design_grid * beta
prob_grid = 1.0 ./ (1.0 .+ exp.(-eta_grid))
se_eta = [sqrt(design_grid[i, :]' * covariance * design_grid[i, :]) for i in 1:grid_n]
prob_lower = 1.0 ./ (1.0 .+ exp.(-(eta_grid .- 1.96 .* se_eta)))
prob_upper = 1.0 ./ (1.0 .+ exp.(-(eta_grid .+ 1.96 .* se_eta)))
# Jitter the binary outcomes slightly so overlapping points stay visible
y_jitter = diagnosis .+ (rand(n) .- 0.5) .* 0.08
healthy_mask = diagnosis .== 0.0
# --- Plot ----------------------------------------------------------------------
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "logistic-regression · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Fasting Glucose (mg/dL)",
ylabel = "Probability of Diabetes",
xlabelsize = 16,
ylabelsize = 16,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 13,
yticklabelsize = 13,
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, 0.12),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.12),
xminorgridvisible = false,
yminorgridvisible = false,
)
ylims!(ax, -0.08, 1.08)
band!(ax, glucose_grid, prob_lower, prob_upper; color = (CURVE_COLOR, 0.15), label = "95% confidence band")
hlines!(ax, [0.5]; color = THRESHOLD_COLOR, linewidth = 2.5, linestyle = :dash, label = "Decision threshold (p = 0.5)")
lines!(ax, glucose_grid, prob_grid; color = CURVE_COLOR, linewidth = 3, label = "Fitted probability")
scatter!(ax, glucose[healthy_mask], y_jitter[healthy_mask];
color = HEALTHY_COLOR, markersize = 11, alpha = 0.6, strokewidth = 0, label = "No diabetes")
scatter!(ax, glucose[.!healthy_mask], y_jitter[.!healthy_mask];
color = DIABETIC_COLOR, markersize = 11, alpha = 0.6, strokewidth = 0, label = "Diabetes")
axislegend(ax; position = :rb, backgroundcolor = ELEVATED_BG, framevisible = false, labelcolor = INK_SOFT, labelsize = 13)
# --- Save ----------------------------------------------------------------------
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/logistic-regression/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": "logistic-regression",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/logistic-regression/julia/makie",
"hub": "https://anyplot.ai/logistic-regression",
"code_json": "https://api.anyplot.ai/specs/logistic-regression/makie/code",
"spec_json": "https://api.anyplot.ai/specs/logistic-regression",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/logistic-regression/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/logistic-regression/julia/makie/plot-dark.png",
"quality_score": 92.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Logistic Regression Curve Plot on anyplot.ai.