A scatter plot displaying the relationship between two numeric variables with a fitted polynomial regression curve (degree 2-4). This visualization extends beyond linear regression to capture non-linear relationships in data, making it ideal for modeling curved trends, parabolic patterns, and complex data relationships where a straight line would not adequately represent the underlying pattern.
""" anyplot.ai
scatter-regression-polynomial: Scatter Plot with Polynomial Regression
Library: plotly 6.9.0 | Python 3.13.14
Quality: 91/100 | Updated: 2026-08-11
"""
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)"
# Imprint palette - first series is always #009E73
BRAND = "#009E73"
ACCENT = "#C475FD"
# Data - Temperature vs Energy Consumption (environmental/building efficiency)
np.random.seed(42)
# Simulate heating/cooling season data where energy consumption follows a U-shaped curve
# (more energy needed for both heating in winter and cooling in summer)
outdoor_temp = np.linspace(-10, 40, 100)
base_consumption = 30
energy_consumption = 0.12 * (outdoor_temp - 15) ** 2 + base_consumption + np.random.normal(0, 5, len(outdoor_temp))
# Polynomial regression (degree 2 - quadratic, capturing the U-shaped curve)
coeffs = np.polyfit(outdoor_temp, energy_consumption, 2)
poly = np.poly1d(coeffs)
x_fit = np.linspace(outdoor_temp.min(), outdoor_temp.max(), 200)
y_fit = poly(x_fit)
# Calculate R²
y_pred = poly(outdoor_temp)
residuals = energy_consumption - y_pred
ss_res = np.sum(residuals**2)
ss_tot = np.sum((energy_consumption - np.mean(energy_consumption)) ** 2)
r_squared = 1 - (ss_res / ss_tot)
# 95% confidence band around the fit, from the residual spread
residual_std = np.std(residuals)
y_upper = y_fit + 1.96 * residual_std
y_lower = y_fit - 1.96 * residual_std
# Format polynomial equation with explicit sign handling (avoids "+ -3.63x")
a, b, c = coeffs
sign_b = "-" if b < 0 else "+"
sign_c = "-" if c < 0 else "+"
equation = f"y = {a:.4f}x² {sign_b} {abs(b):.2f}x {sign_c} {abs(c):.1f}"
# Curve vertex - the "balance point" temperature where energy use is minimized
vertex_x = -b / (2 * a)
vertex_y = poly(vertex_x)
# Create figure
fig = go.Figure()
# Confidence band (drawn first so it sits behind the scatter and fit line)
fig.add_trace(
go.Scatter(
x=np.concatenate([x_fit, x_fit[::-1]]),
y=np.concatenate([y_upper, y_lower[::-1]]),
fill="toself",
fillcolor="rgba(196, 117, 253, 0.15)",
line={"width": 0},
hoverinfo="skip",
showlegend=False,
name="95% Confidence Band",
)
)
# Scatter points with brand color
fig.add_trace(
go.Scatter(
x=outdoor_temp,
y=energy_consumption,
mode="markers",
name="Measured Data",
marker={"size": 10, "color": BRAND, "opacity": 0.6, "line": {"width": 1, "color": PAGE_BG}},
hovertemplate="%{x:.1f}°C, %{y:.1f} kWh/day<extra></extra>",
)
)
# Polynomial regression curve
fig.add_trace(
go.Scatter(
x=x_fit,
y=y_fit,
mode="lines",
name="Polynomial Fit (degree 2)",
line={"color": ACCENT, "width": 3.5},
hovertemplate="Fit: %{x:.1f}°C, %{y:.1f} kWh/day<extra></extra>",
)
)
# Highlight the curve's minimum - the real-world "balance point" insight
fig.add_trace(
go.Scatter(
x=[vertex_x],
y=[vertex_y],
mode="markers",
name="Balance Point",
showlegend=False,
marker={"size": 13, "symbol": "diamond", "color": INK, "line": {"width": 2, "color": ACCENT}},
hovertemplate=f"Balance point: {vertex_x:.1f}°C, {vertex_y:.1f} kWh/day<extra></extra>",
)
)
# Title fontsize scaled from the 16px/67-char baseline
title_text = "Energy vs. Temperature: Quadratic Regression · scatter-regression-polynomial · plotly · anyplot.ai"
title_fontsize = max(round(16 * 67 / len(title_text)), 11)
# Layout with theme-adaptive chrome
fig.update_layout(
autosize=False,
title={"text": title_text, "font": {"size": title_fontsize, "color": INK}, "x": 0.5, "xanchor": "center"},
xaxis={
"title": {"text": "Outdoor Temperature (°C)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridwidth": 1,
"gridcolor": GRID,
"linecolor": INK_SOFT,
"zeroline": False,
},
yaxis={
"title": {"text": "Energy Consumption (kWh/day)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridwidth": 1,
"gridcolor": GRID,
"linecolor": INK_SOFT,
"zeroline": False,
},
legend={"font": {"size": 10, "color": INK_SOFT}, "x": 0.02, "y": 0.98, "bgcolor": ELEVATED_BG, "borderwidth": 0},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
margin={"l": 80, "r": 40, "t": 80, "b": 60},
annotations=[
{
"x": vertex_x,
"y": vertex_y,
"xref": "x",
"yref": "y",
"text": "Balance point",
"showarrow": True,
"arrowhead": 2,
"arrowcolor": INK_SOFT,
"ax": 0,
"ay": -36,
"font": {"size": 10, "color": INK},
"bgcolor": ELEVATED_BG,
"borderwidth": 0,
"borderpad": 4,
},
{
"x": 0.98,
"y": 0.05,
"xref": "paper",
"yref": "paper",
"text": f"R² = {r_squared:.4f}<br>{equation}",
"showarrow": False,
"font": {"size": 11, "color": INK},
"bgcolor": ELEVATED_BG,
"borderwidth": 0,
"borderpad": 10,
"xanchor": "right",
"yanchor": "bottom",
},
],
)
# Save as PNG and HTML with theme-suffixed filenames — canonical 3200×1800 canvas
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/scatter-regression-polynomial/plotly/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": "scatter-regression-polynomial",
"language": "python",
"library": "plotly",
"page": "https://anyplot.ai/scatter-regression-polynomial/python/plotly",
"hub": "https://anyplot.ai/scatter-regression-polynomial",
"code_json": "https://api.anyplot.ai/specs/scatter-regression-polynomial/plotly/code",
"spec_json": "https://api.anyplot.ai/specs/scatter-regression-polynomial",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-regression-polynomial/python/plotly/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-regression-polynomial/python/plotly/plot-dark.png",
"interactive_light_html": "https://storage.googleapis.com/anyplot-images/plots/scatter-regression-polynomial/python/plotly/plot-light.html",
"interactive_dark_html": "https://storage.googleapis.com/anyplot-images/plots/scatter-regression-polynomial/python/plotly/plot-dark.html",
"quality_score": 91.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Scatter Plot with Polynomial Regression on anyplot.ai.