Residual Plot — Plotly

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.

Python source (Plotly)

""" anyplot.ai
residual-plot: Residual Plot
Library: plotly 6.7.0 | Python 3.13.13
Quality: 96/100 | Updated: 2026-05-10
"""

import os
import sys

import numpy as np

# Avoid module shadowing by removing current directory from path during import
cwd = sys.path[0]
if cwd in sys.path:
    sys.path.remove(cwd)
import plotly.graph_objects as go

sys.path.insert(0, cwd)

# Theme tokens
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"
GRID = "rgba(26,26,23,0.10)" if THEME == "light" else "rgba(240,239,232,0.10)"

# Okabe-Ito palette
BRAND = "#009E73"
ACCENT = "#C475FD"
NEUTRAL = "#1A1A1A" if THEME == "light" else "#E8E8E0"

# Data - Generate realistic regression scenario with varying residual patterns
np.random.seed(42)
n_samples = 150

# Create features with some non-linearity to show interesting residual patterns
X = np.linspace(0, 10, n_samples)
# True relationship with slight curvature (linear model will miss this)
y_true = 2 * X + 0.3 * X**1.5 + np.random.randn(n_samples) * 2

# Simple linear regression (manual fit)
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
std_residuals = np.std(residuals)

# Identify outliers (beyond ±2 standard deviations)
outlier_mask = np.abs(residuals) > 2 * std_residuals
normal_mask = ~outlier_mask

# Create figure
fig = go.Figure()

# Add ±2 standard deviation bands (dashed lines)
fig.add_trace(
    go.Scatter(
        x=[y_pred.min(), y_pred.max()],
        y=[2 * std_residuals, 2 * std_residuals],
        mode="lines",
        line=dict(color=ACCENT, width=3, dash="dash"),
        name="+2 SD",
        showlegend=True,
    )
)

fig.add_trace(
    go.Scatter(
        x=[y_pred.min(), y_pred.max()],
        y=[-2 * std_residuals, -2 * std_residuals],
        mode="lines",
        line=dict(color=ACCENT, width=3, dash="dash"),
        name="-2 SD",
        showlegend=True,
    )
)

# Add horizontal reference line at y=0
fig.add_trace(
    go.Scatter(
        x=[y_pred.min(), y_pred.max()],
        y=[0, 0],
        mode="lines",
        line=dict(color=NEUTRAL, width=3),
        name="Zero Line",
        showlegend=False,
    )
)

# Add normal residuals (using brand green for first series)
fig.add_trace(
    go.Scatter(
        x=y_pred[normal_mask],
        y=residuals[normal_mask],
        mode="markers",
        marker=dict(size=14, color=BRAND, opacity=0.7, line=dict(width=1, color=BRAND)),
        name="Residuals",
        hovertemplate="Fitted: %{x:.2f}<br>Residual: %{y:.2f}<extra></extra>",
    )
)

# Add outlier residuals
if np.any(outlier_mask):
    fig.add_trace(
        go.Scatter(
            x=y_pred[outlier_mask],
            y=residuals[outlier_mask],
            mode="markers",
            marker=dict(size=16, color=ACCENT, opacity=0.9, line=dict(width=2, color=ACCENT), symbol="diamond"),
            name="Outliers (>2 SD)",
            hovertemplate="Fitted: %{x:.2f}<br>Residual: %{y:.2f}<extra></extra>",
        )
    )

# Add smoothing line to detect patterns
sorted_indices = np.argsort(y_pred)
window_size = 15
kernel = np.ones(window_size) / window_size
smoothed_residuals = np.convolve(residuals[sorted_indices], kernel, mode="same")

fig.add_trace(
    go.Scatter(
        x=y_pred[sorted_indices],
        y=smoothed_residuals,
        mode="lines",
        line=dict(color=INK_SOFT, width=4),
        name="Trend Line",
        hovertemplate="Fitted: %{x:.2f}<br>Smoothed Residual: %{y:.2f}<extra></extra>",
    )
)

# Update layout with theme-adaptive styling
fig.update_layout(
    title=dict(text="residual-plot · plotly · anyplot.ai", font=dict(size=28, color=INK), x=0.5, xanchor="center"),
    xaxis=dict(
        title=dict(text="Fitted Values", font=dict(size=22, color=INK)),
        tickfont=dict(size=18, color=INK_SOFT),
        showgrid=True,
        gridwidth=1,
        gridcolor=GRID,
        linecolor=INK_SOFT,
        zeroline=False,
    ),
    yaxis=dict(
        title=dict(text="Residuals (y_true - y_pred)", font=dict(size=22, color=INK)),
        tickfont=dict(size=18, color=INK_SOFT),
        showgrid=True,
        gridwidth=1,
        gridcolor=GRID,
        linecolor=INK_SOFT,
        zeroline=False,
    ),
    paper_bgcolor=PAGE_BG,
    plot_bgcolor=PAGE_BG,
    font=dict(color=INK),
    legend=dict(
        font=dict(size=18, color=INK_SOFT),
        x=0.02,
        y=0.98,
        xanchor="left",
        yanchor="top",
        bgcolor=ELEVATED_BG,
        bordercolor=INK_SOFT,
        borderwidth=1,
    ),
    margin=dict(l=100, r=50, t=100, b=80),
)

# Save as PNG and HTML with theme-suffixed filenames
fig.write_image(f"plot-{THEME}.png", width=1600, height=900, scale=3)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")

Part of Residual Plot on anyplot.ai.

Residual Plot — Plotly

Python source (Plotly)

Other implementations