The same plot in 14 other libraries — Python: Altair, Bokeh, lets-plot, Plotly, plotnine, Pygal, Seaborn; R: ggplot2; Julia: Makie.jl; JavaScript: Chart.js, D3.js, Apache ECharts, Highcharts, MUI X Charts. Compare all 15 side by side: Residual Plot in Python, R, Julia and JavaScript.
A residual plot displays the difference between observed and predicted values (residuals) against fitted values 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: matplotlib 3.10.9 | Python 3.13.13
Quality: 84/100 | Updated: 2026-05-10
"""
import matplotlib.pyplot as plt
import numpy as np
# Data - Generate realistic regression scenario
np.random.seed(42)
# Independent variable with some structure
X = np.linspace(0, 10, 150)
# True relationship with some non-linearity to make residuals interesting
# (quadratic component makes linear model show patterns in residuals)
y_true = 2.5 * X + 0.3 * X**2 + np.random.randn(150) * 3
# Fit linear regression manually: y = a + b*x
# Using least squares formulas
x_mean = np.mean(X)
y_mean = np.mean(y_true)
b = np.sum((X - x_mean) * (y_true - y_mean)) / np.sum((X - x_mean) ** 2)
a = y_mean - b * x_mean
y_pred = a + b * X
# Calculate residuals
residuals = y_true - y_pred
# Identify outliers (beyond 2 standard deviations)
std_residuals = np.std(residuals)
outlier_mask = np.abs(residuals) > 2 * std_residuals
# Create plot
fig, ax = plt.subplots(figsize=(16, 9))
# Plot normal points
ax.scatter(
y_pred[~outlier_mask],
residuals[~outlier_mask],
s=150,
alpha=0.7,
color="#306998",
edgecolors="white",
linewidth=0.5,
label="Residuals",
)
# Plot outliers with different color
ax.scatter(
y_pred[outlier_mask],
residuals[outlier_mask],
s=180,
alpha=0.9,
color="#FFD43B",
edgecolors="#306998",
linewidth=1.5,
label="Outliers (>2σ)",
)
# Reference line at y=0
ax.axhline(y=0, color="#333333", linewidth=2, linestyle="-", label="Perfect fit (y=0)")
# Add ±2 standard deviation bands
ax.axhline(y=2 * std_residuals, color="#888888", linewidth=1.5, linestyle="--", alpha=0.7)
ax.axhline(y=-2 * std_residuals, color="#888888", linewidth=1.5, linestyle="--", alpha=0.7)
# Get x limits for the band
xlim = (y_pred.min() - 2, y_pred.max() + 2)
ax.fill_between(xlim, -2 * std_residuals, 2 * std_residuals, alpha=0.1, color="#306998", label="±2σ band")
# Add trend line using polynomial fit to detect patterns
z = np.polyfit(y_pred, residuals, 3)
p = np.poly1d(z)
x_smooth = np.linspace(y_pred.min(), y_pred.max(), 100)
ax.plot(x_smooth, p(x_smooth), color="#D62728", linewidth=2.5, linestyle="-", alpha=0.8, label="Trend line")
# Labels and styling
ax.set_xlabel("Fitted Values", fontsize=20)
ax.set_ylabel("Residuals (Observed - Predicted)", fontsize=20)
ax.set_title("residual-plot · matplotlib · pyplots.ai", fontsize=24)
ax.tick_params(axis="both", labelsize=16)
ax.legend(fontsize=14, loc="upper left", framealpha=0.9)
ax.grid(True, alpha=0.3, linestyle="--")
ax.set_xlim(xlim)
plt.tight_layout()
plt.savefig("plot.png", dpi=300, bbox_inches="tight")
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/residual-plot/matplotlib/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": "python",
"library": "matplotlib",
"page": "https://anyplot.ai/residual-plot/python/matplotlib",
"hub": "https://anyplot.ai/residual-plot",
"code_json": "https://api.anyplot.ai/specs/residual-plot/matplotlib/code",
"spec_json": "https://api.anyplot.ai/specs/residual-plot",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/residual-plot/python/matplotlib/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/residual-plot/python/matplotlib/plot-dark.png",
"quality_score": 84.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Residual Plot on anyplot.ai.