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.
# ruff: noqa: F405
"""pyplots.ai
residual-plot: Residual Plot
Library: lets-plot | Python 3.13
Quality: pending | Created: 2025-12-26
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
LetsPlot.setup_html()
# Theme tokens (read from environment)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
RULE = "rgba(26,26,23,0.10)" if THEME == "light" else "rgba(240,239,232,0.10)"
# Okabe-Ito palette
BRAND = "#009E73" # Position 1: bluish green (normal points)
OUTLIER_COLOR = "#AE3030" # imprint red — outliers (>2σ)
# Data: Generate realistic regression scenario with deliberate pattern in residuals
np.random.seed(42)
n = 150
# Create feature with mild non-linearity to show residual patterns
X = np.linspace(10, 100, n)
noise = np.random.normal(0, 5, n)
# Add slight heteroscedasticity: variance increases with X
heteroscedastic_noise = noise * (0.5 + 0.01 * X)
y_true = 2.5 * X + 0.02 * X**2 + heteroscedastic_noise + 50
# Simple linear regression (manual implementation)
X_mean = np.mean(X)
y_mean = np.mean(y_true)
slope = np.sum((X - X_mean) * (y_true - y_mean)) / np.sum((X - X_mean) ** 2)
intercept = y_mean - slope * X_mean
y_pred = slope * X + intercept
# Calculate residuals
residuals = y_true - y_pred
# Calculate residual standard deviation for outlier bands
residual_std = np.std(residuals)
# Identify outliers (beyond ±2 standard deviations)
outlier_threshold = 2 * residual_std
is_outlier = np.abs(residuals) > outlier_threshold
# Create DataFrame for plotting
df = pd.DataFrame(
{"Fitted Values": y_pred, "Residuals": residuals, "Outlier": np.where(is_outlier, "Outlier (>2σ)", "Normal")}
)
# Create residual plot
plot = (
ggplot(df, aes(x="Fitted Values", y="Residuals"))
# Reference line at y=0
+ geom_hline(yintercept=0, color=INK_SOFT, size=1.5, linetype="solid")
# Outlier bands at ±2 standard deviations
+ geom_hline(yintercept=outlier_threshold, color=INK_MUTED, size=1, linetype="dashed", alpha=0.6)
+ geom_hline(yintercept=-outlier_threshold, color=INK_MUTED, size=1, linetype="dashed", alpha=0.6)
# Points colored by outlier status
+ geom_point(aes(color="Outlier"), size=5, alpha=0.75)
# LOWESS smoothing line to detect patterns
+ geom_smooth(method="loess", color=INK, size=2, se=False, span=0.6)
# Color scale for outliers (Normal: brand green, Outlier: vermillion)
+ scale_color_manual(values=[BRAND, OUTLIER_COLOR], name="Point Type")
# Labels
+ labs(title="residual-plot · letsplot · pyplots.ai", x="Fitted Values", y="Residuals (Observed - Predicted)")
# Theme
+ theme_minimal()
+ theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid_major=element_line(color=RULE, size=0.4),
panel_grid_minor=element_blank(),
plot_title=element_text(size=24, face="bold", color=INK),
axis_title=element_text(size=20, color=INK),
axis_text=element_text(size=16, color=INK_SOFT),
axis_line=element_line(color=INK_SOFT, size=0.5),
legend_title=element_text(size=18, color=INK),
legend_text=element_text(size=16, color=INK_SOFT),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_position="right",
)
# Size for export (1600 × 900 base, scaled 3x = 4800 × 2700)
+ ggsize(1600, 900)
)
# Save as PNG and HTML with theme-suffixed filenames
ggsave(plot, f"plot-{THEME}.png", path=".", scale=3)
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Residual Plot on anyplot.ai.