Scatter Plot with Linear Regression — Plotly

A scatter plot that displays the relationship between two numeric variables with a fitted linear regression line and confidence interval band. This visualization extends the basic scatter plot by adding statistical modeling elements, making it ideal for understanding linear relationships, assessing model fit, and communicating the strength of correlations with visual uncertainty quantification.

Scatter Plot with Linear Regression rendered with Plotly

Python source (Plotly)

""" anyplot.ai
scatter-regression-linear: Scatter Plot with Linear Regression
Library: plotly 6.7.0 | Python 3.13.13
Quality: 94/100 | Updated: 2026-05-06
"""

import os

import numpy as np
import plotly.graph_objects as go


# 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)"

BRAND = "#009E73"
ACCENT = "#C475FD"

# Data - study hours vs exam scores
np.random.seed(42)
n_points = 100
study_hours = np.random.uniform(2, 10, n_points)
noise = np.random.normal(0, 8, n_points)
exam_scores = study_hours * 8.5 + 45 + noise

# Linear regression
n = len(study_hours)
x_mean = np.mean(study_hours)
y_mean = np.mean(exam_scores)
ss_xy = np.sum((study_hours - x_mean) * (exam_scores - y_mean))
ss_xx = np.sum((study_hours - x_mean) ** 2)
ss_yy = np.sum((exam_scores - y_mean) ** 2)

slope = ss_xy / ss_xx
intercept = y_mean - slope * x_mean
r_value = ss_xy / np.sqrt(ss_xx * ss_yy)
r_squared = r_value**2

# Regression line and confidence interval
x_line = np.linspace(study_hours.min() - 0.5, study_hours.max() + 0.5, 100)
y_line = slope * x_line + intercept

# Calculate 95% confidence interval
y_pred = slope * study_hours + intercept
residuals = exam_scores - y_pred
mse = np.sum(residuals**2) / (n - 2)
se_slope = np.sqrt(mse / ss_xx)

se_line = np.sqrt(mse * (1 / n + (x_line - x_mean) ** 2 / ss_xx))
t_val = 1.98
ci_upper = y_line + t_val * se_line
ci_lower = y_line - t_val * se_line

# Create figure
fig = go.Figure()

# Confidence interval band
fig.add_trace(
    go.Scatter(
        x=np.concatenate([x_line, x_line[::-1]]),
        y=np.concatenate([ci_upper, ci_lower[::-1]]),
        fill="toself",
        fillcolor="rgba(0, 158, 115, 0.15)",
        line=dict(color="rgba(0,0,0,0)"),
        hoverinfo="skip",
        name="95% CI",
        showlegend=True,
    )
)

# Scatter points
fig.add_trace(
    go.Scatter(
        x=study_hours,
        y=exam_scores,
        mode="markers",
        marker=dict(size=12, color=BRAND, opacity=0.65),
        name="Data points",
        hovertemplate="Study Hours: %{x:.1f}<br>Exam Score: %{y:.1f}<extra></extra>",
    )
)

# Regression line
fig.add_trace(
    go.Scatter(
        x=x_line,
        y=y_line,
        mode="lines",
        line=dict(color=ACCENT, width=4),
        name=f"Linear Regression (R² = {r_squared:.3f})",
        hoverinfo="skip",
    )
)

# Equation annotation
equation = f"y = {slope:.2f}x + {intercept:.1f}"
fig.add_annotation(
    x=0.98,
    y=0.05,
    xref="paper",
    yref="paper",
    text=f"{equation}<br>R² = {r_squared:.3f}",
    showarrow=False,
    font=dict(size=18, color=INK),
    align="right",
    bgcolor=ELEVATED_BG,
    bordercolor=INK_SOFT,
    borderwidth=1,
    borderpad=12,
)

# Layout
fig.update_layout(
    title=dict(
        text="scatter-regression-linear · plotly · anyplot.ai", font=dict(size=28, color=INK), x=0.5, xanchor="center"
    ),
    xaxis=dict(
        title=dict(text="Study Hours per Day", font=dict(size=22, color=INK)),
        tickfont=dict(size=18, color=INK_SOFT),
        gridcolor=GRID,
        showgrid=True,
        zeroline=False,
        linecolor=INK_SOFT,
        linewidth=1,
    ),
    yaxis=dict(
        title=dict(text="Exam Score (%)", font=dict(size=22, color=INK)),
        tickfont=dict(size=18, color=INK_SOFT),
        gridcolor=GRID,
        showgrid=True,
        zeroline=False,
        linecolor=INK_SOFT,
        linewidth=1,
    ),
    paper_bgcolor=PAGE_BG,
    plot_bgcolor=PAGE_BG,
    legend=dict(
        x=0.02,
        y=0.98,
        xanchor="left",
        yanchor="top",
        font=dict(size=16, color=INK_SOFT),
        bgcolor=ELEVATED_BG,
        bordercolor=INK_SOFT,
        borderwidth=1,
    ),
    margin=dict(l=80, r=60, t=100, b=80),
    hovermode="closest",
)

# Save as PNG and HTML
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 Scatter Plot with Linear Regression on anyplot.ai.

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