Logistic Regression Curve Plot — lets-plot

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.

Logistic Regression Curve Plot rendered with lets-plot

Python source (lets-plot)

""" anyplot.ai
logistic-regression: Logistic Regression Curve Plot
Library: letsplot 4.9.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-18
"""

import os
import shutil

import numpy as np
import pandas as pd
from lets_plot import *
from lets_plot.export import ggsave
from sklearn.linear_model import LogisticRegression


LetsPlot.setup_html()

# Theme tokens (see prompts/default-style-guide.md "Background" + "Theme-adaptive Chrome")
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"

# Okabe-Ito palette (first two colors for binary classification)
IMPRINT = ["#009E73", "#C475FD"]

# Data - Generate binary classification data with clear sigmoidal relationship
np.random.seed(42)
n_samples = 200

# Feature: Study hours (0 to 10 hours)
x = np.random.uniform(0, 10, n_samples)

# True probability follows a logistic function
true_prob = 1 / (1 + np.exp(-1.5 * (x - 5)))

# Binary outcome (pass/fail exam based on study hours)
y = (np.random.random(n_samples) < true_prob).astype(int)

# Fit logistic regression model using sklearn
X_reshaped = x.reshape(-1, 1)
model = LogisticRegression()
model.fit(X_reshaped, y)

# Get model parameters for annotation
coef = model.coef_[0][0]
intercept = model.intercept_[0]
accuracy = model.score(X_reshaped, y)

# Generate smooth curve for prediction
x_line = np.linspace(0, 10, 200)
X_line = x_line.reshape(-1, 1)
y_prob = model.predict_proba(X_line)[:, 1]

# Calculate confidence intervals using approximate standard error
se = np.sqrt(y_prob * (1 - y_prob) / n_samples) * 2
ci_lower = np.clip(y_prob - 1.96 * se, 0, 1)
ci_upper = np.clip(y_prob + 1.96 * se, 0, 1)

# Add jitter to y values for visibility
y_jittered = y + np.random.normal(0, 0.03, n_samples)
y_jittered = np.clip(y_jittered, -0.1, 1.1)

# Create DataFrames
df_points = pd.DataFrame(
    {"Study Hours": x, "Probability": y_jittered, "Class": ["Pass" if yi == 1 else "Fail" for yi in y]}
)

df_curve = pd.DataFrame({"Study Hours": x_line, "Probability": y_prob})

df_ci = pd.DataFrame({"Study Hours": x_line, "ci_lower": ci_lower, "ci_upper": ci_upper})

# Create plot with theme-adaptive styling
anyplot_theme = theme(
    plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
    panel_background=element_rect(fill=PAGE_BG),
    panel_grid_major=element_line(color=INK, size=0.3),
    panel_grid_minor=element_blank(),
    axis_title=element_text(color=INK, size=20),
    axis_text=element_text(color=INK_SOFT, size=16),
    axis_line=element_line(color=INK_SOFT, size=0.5),
    plot_title=element_text(color=INK, size=24),
    legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
    legend_text=element_text(color=INK_SOFT, size=16),
    legend_title=element_text(color=INK, size=18),
)

plot = (
    ggplot()
    # Confidence interval ribbon
    + geom_ribbon(aes(x="Study Hours", ymin="ci_lower", ymax="ci_upper"), data=df_ci, fill=IMPRINT[0], alpha=0.15)
    # Logistic curve
    + geom_line(aes(x="Study Hours", y="Probability"), data=df_curve, color=IMPRINT[0], size=2.5)
    # Decision threshold line
    + geom_hline(yintercept=0.5, linetype="dashed", color=INK_SOFT, size=1, alpha=0.6)
    # Data points with jitter
    + geom_point(aes(x="Study Hours", y="Probability", color="Class"), data=df_points, size=5, alpha=0.65)
    # Colors for classes using Okabe-Ito
    + scale_color_manual(values=IMPRINT)
    # Labels with model annotation
    + labs(
        x="Study Hours",
        y="Probability",
        title="logistic-regression · python · letsplot · anyplot.ai",
        color="Class",
        subtitle=f"Coefficient: {coef:.2f} | Accuracy: {accuracy:.1%}",
    )
    # Y-axis from 0 to 1
    + scale_y_continuous(limits=[-0.1, 1.1])
    # Theme and size
    + anyplot_theme
    + ggsize(1600, 900)
)

# Save as PNG and HTML with theme suffix
ggsave(plot, f"plot-{THEME}.png", scale=3)
ggsave(plot, f"plot-{THEME}.html")

# Move files from lets-plot-images subfolder to current directory
if os.path.exists("lets-plot-images"):
    for filename in [f"plot-{THEME}.png", f"plot-{THEME}.html"]:
        src = os.path.join("lets-plot-images", filename)
        if os.path.exists(src):
            shutil.move(src, filename)

Part of Logistic Regression Curve Plot on anyplot.ai.

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