[scatter-regression-polynomial] regression-polynomial: Polynomial Regression

[MarkusNeusinger]

Plot Request

Scatter plot with polynomial regression curve fit.

Use Cases

• Non-linear relationships
• Trend analysis
• Scientific data fitting

Expected Features

• Scatter points
• Polynomial curve (degree 2-4)
• Confidence band optional

[claude]

✅ Spec ID: scatter-regression-polynomial

Rationale: Follows the established pattern from scatter-regression-linear, extending the naming convention for polynomial curve fitting which models non-linear relationships.

This is a valid new specification - polynomial regression is distinct from linear regression as it fits curved relationships using higher-degree polynomials (degree 2-4).

[github-actions]

✅ Specification Ready: scatter-regression-polynomial

PR: #2039

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specification.md

scatter-regression-polynomial: Scatter Plot with Polynomial Regression

Description

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.

Applications

• Analyzing diminishing returns in economics where initial gains decrease over time
• Studying growth curves in biology where populations follow sigmoid or exponential patterns
• Modeling physical phenomena like projectile motion or thermal expansion with quadratic relationships

Data

• x (numeric) - Independent variable values plotted on the horizontal axis
• y (numeric) - Dependent variable values plotted on the vertical axis following a non-linear relationship
• Size: 30-300 points recommended for clear polynomial curve visualization
• Example: Data with a clear curved pattern such as quadratic, cubic, or sigmoid trends

Notes

• Display R² value prominently on the plot to indicate goodness of fit
• Polynomial curve should be visually distinct from scatter points (solid line, contrasting color)
• Use polynomial degree 2 (quadratic) as default; higher degrees (3-4) for more complex curves
• Optional: Include confidence band with semi-transparent shading around the fitted curve
• Points should have moderate transparency (alpha ~0.6-0.7) to show density
• Include axis labels and descriptive title mentioning polynomial regression
• Consider annotating with the polynomial equation (y = ax² + bx + c)
• Avoid overfitting: higher-degree polynomials should only be used when justified by data pattern

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Next: Add approved label to merge this specification to main.

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