A residual plot displays the difference between observed and predicted values (residuals) against fitted values or an independent variable in regression analysis. This diagnostic visualization helps identify violations of regression assumptions including non-linearity, heteroscedasticity (non-constant variance), and outliers. A well-fitting model shows residuals randomly scattered around zero with no discernible pattern.
# anyplot.ai
# residual-plot: Residual Plot
# Library: makie 0.21.9 | Julia 1.11.9
# Quality: 94/100 | Created: 2026-09-05
using CairoMakie
using Colors
using Random
using Statistics
Random.seed!(42)
# --- Theme tokens -----------------------------------------------------------
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const MUTED = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"
const IMPRINT_PALETTE = [
colorant"#009E73", colorant"#C475FD", colorant"#4467A3", colorant"#BD8233",
colorant"#AE3030", colorant"#2ABCCD", colorant"#954477", colorant"#99B314",
]
# --- Data ---------------------------------------------------------------
# Advertising spend ($1000s) predicting weekly revenue ($1000s). The true
# relationship is linear but noise variance grows with spend, so a simple
# OLS fit leaves heteroscedastic residuals — exactly what this plot is
# meant to expose.
n = 300
ad_spend = sort(rand(n) .* 190 .+ 10)
noise_scale = 1.0 .+ 0.06 .* ad_spend
revenue = 50 .+ 4.5 .* ad_spend .+ randn(n) .* noise_scale .* 3.5
spend_mean = mean(ad_spend)
revenue_mean = mean(revenue)
slope = sum((ad_spend .- spend_mean) .* (revenue .- revenue_mean)) / sum((ad_spend .- spend_mean) .^ 2)
intercept = revenue_mean - slope * spend_mean
fitted_revenue = intercept .+ slope .* ad_spend
residuals = revenue .- fitted_revenue
resid_std = std(residuals)
is_outlier = abs.(residuals) .> 2 * resid_std
# Quantify the heteroscedasticity story: local spread in the narrow (low
# fitted-revenue) and wide (high fitted-revenue) quartiles, called out
# directly on the plot instead of leaving the funnel shape to speak for itself.
lo_cut = quantile(fitted_revenue, 0.25)
hi_cut = quantile(fitted_revenue, 0.75)
lo_mask = fitted_revenue .< lo_cut
hi_mask = fitted_revenue .> hi_cut
lo_sigma = std(residuals[lo_mask])
hi_sigma = std(residuals[hi_mask])
lo_anchor_x = quantile(fitted_revenue[lo_mask], 0.5)
hi_anchor_x = quantile(fitted_revenue[hi_mask], 0.5)
lo_anchor_y = maximum(residuals[lo_mask])
hi_anchor_y = maximum(residuals[hi_mask])
idx_max = argmax(residuals)
idx_min = argmin(residuals)
# --- Plot -----------------------------------------------------------------
fig = Figure(
resolution = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "residual-plot · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
subtitle = "Residual spread widens with fitted revenue — a classic heteroscedasticity signature",
subtitlesize = 13,
subtitlecolor = INK_SOFT,
xlabel = "Fitted Revenue (\$1000s)",
ylabel = "Residual (\$1000s)",
xlabelsize = 14,
ylabelsize = 14,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 12,
yticklabelsize = 12,
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),
xminorgridvisible = false,
yminorgridvisible = false,
)
hspan!(ax, -2 * resid_std, 2 * resid_std; color = RGBAf(MUTED.r, MUTED.g, MUTED.b, 0.10))
hlines!(ax, [-2resid_std, 2resid_std]; color = MUTED, linewidth = 1.5, linestyle = :dot)
hlines!(ax, [0]; color = INK_SOFT, linewidth = 2.5, linestyle = :dash)
scatter!(
ax, fitted_revenue[.!is_outlier], residuals[.!is_outlier];
color = IMPRINT_PALETTE[1], markersize = 11, alpha = 0.65, strokewidth = 0,
label = "Residual",
)
scatter!(
ax, fitted_revenue[is_outlier], residuals[is_outlier];
color = IMPRINT_PALETTE[5], markersize = 14, strokewidth = 1, strokecolor = PAGE_BG,
label = "Outlier (|residual| > 2σ)",
)
# Quantified spread callouts anchored directly in data coordinates — makes the
# heteroscedasticity insight explicit rather than leaving the funnel to speak
# for itself.
text!(
ax, lo_anchor_x, lo_anchor_y;
text = "SD ≈ $(round(lo_sigma, digits = 1))", color = INK, fontsize = 13,
font = :bold, align = (:center, :bottom), offset = (0, 10),
)
text!(
ax, hi_anchor_x, hi_anchor_y;
text = "SD ≈ $(round(hi_sigma, digits = 1))", color = INK, fontsize = 13,
font = :bold, align = (:center, :bottom), offset = (0, 10),
)
# Label the two most extreme outliers to give the outlier cluster a
# deliberate focal point instead of leaving it as undifferentiated dots.
text!(
ax, fitted_revenue[idx_max], residuals[idx_max];
text = "largest overshoot: +$(round(Int, residuals[idx_max]))",
color = IMPRINT_PALETTE[5], fontsize = 12, font = :bold,
align = (:left, :bottom), offset = (12, 8),
)
text!(
ax, fitted_revenue[idx_min], residuals[idx_min];
text = "largest undershoot: $(round(Int, residuals[idx_min]))",
color = IMPRINT_PALETTE[5], fontsize = 12, font = :bold,
align = (:left, :top), offset = (12, -8),
)
axislegend(
ax;
position = :lb,
labelcolor = INK_SOFT,
labelsize = 12,
framevisible = false,
backgroundcolor = :transparent,
)
# --- Save -------------------------------------------------------------------
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/residual-plot/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": "residual-plot",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/residual-plot/julia/makie",
"hub": "https://anyplot.ai/residual-plot",
"code_json": "https://api.anyplot.ai/specs/residual-plot/makie/code",
"spec_json": "https://api.anyplot.ai/specs/residual-plot",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/residual-plot/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/residual-plot/julia/makie/plot-dark.png",
"quality_score": 94.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Residual Plot on anyplot.ai.