feat(matplotlib): implement residual-plot (#2349)

## Implementation: `residual-plot` - matplotlib

Implements the **matplotlib** version of `residual-plot`.

**File:** `plots/residual-plot/implementations/matplotlib.py`

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/20528203798)*

---------

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Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]

plots/residual-plot/implementations/matplotlib.py

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+""" pyplots.ai
+residual-plot: Residual Plot
+Library: matplotlib 3.10.8 | Python 3.13.11
+Quality: 93/100 | Created: 2025-12-26
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+# Data - Generate realistic regression scenario
+np.random.seed(42)
+
+# Independent variable with some structure
+X = np.linspace(0, 10, 150)
+
+# True relationship with some non-linearity to make residuals interesting
+# (quadratic component makes linear model show patterns in residuals)
+y_true = 2.5 * X + 0.3 * X**2 + np.random.randn(150) * 3
+
+# Fit linear regression manually: y = a + b*x
+# Using least squares formulas
+x_mean = np.mean(X)
+y_mean = np.mean(y_true)
+b = np.sum((X - x_mean) * (y_true - y_mean)) / np.sum((X - x_mean) ** 2)
+a = y_mean - b * x_mean
+y_pred = a + b * X
+
+# Calculate residuals
+residuals = y_true - y_pred
+
+# Identify outliers (beyond 2 standard deviations)
+std_residuals = np.std(residuals)
+outlier_mask = np.abs(residuals) > 2 * std_residuals
+
+# Create plot
+fig, ax = plt.subplots(figsize=(16, 9))
+
+# Plot normal points
+ax.scatter(
+    y_pred[~outlier_mask],
+    residuals[~outlier_mask],
+    s=150,
+    alpha=0.7,
+    color="#306998",
+    edgecolors="white",
+    linewidth=0.5,
+    label="Residuals",
+)
+
+# Plot outliers with different color
+ax.scatter(
+    y_pred[outlier_mask],
+    residuals[outlier_mask],
+    s=180,
+    alpha=0.9,
+    color="#FFD43B",
+    edgecolors="#306998",
+    linewidth=1.5,
+    label="Outliers (>2σ)",
+)
+
+# Reference line at y=0
+ax.axhline(y=0, color="#333333", linewidth=2, linestyle="-", label="Perfect fit (y=0)")
+
+# Add ±2 standard deviation bands
+ax.axhline(y=2 * std_residuals, color="#888888", linewidth=1.5, linestyle="--", alpha=0.7)
+ax.axhline(y=-2 * std_residuals, color="#888888", linewidth=1.5, linestyle="--", alpha=0.7)
+
+# Get x limits for the band
+xlim = (y_pred.min() - 2, y_pred.max() + 2)
+ax.fill_between(xlim, -2 * std_residuals, 2 * std_residuals, alpha=0.1, color="#306998", label="±2σ band")
+
+# Add trend line using polynomial fit to detect patterns
+z = np.polyfit(y_pred, residuals, 3)
+p = np.poly1d(z)
+x_smooth = np.linspace(y_pred.min(), y_pred.max(), 100)
+ax.plot(x_smooth, p(x_smooth), color="#D62728", linewidth=2.5, linestyle="-", alpha=0.8, label="Trend line")
+
+# Labels and styling
+ax.set_xlabel("Fitted Values", fontsize=20)
+ax.set_ylabel("Residuals (Observed - Predicted)", fontsize=20)
+ax.set_title("residual-plot · matplotlib · pyplots.ai", fontsize=24)
+ax.tick_params(axis="both", labelsize=16)
+ax.legend(fontsize=14, loc="upper left", framealpha=0.9)
+ax.grid(True, alpha=0.3, linestyle="--")
+ax.set_xlim(xlim)
+
+plt.tight_layout()
+plt.savefig("plot.png", dpi=300, bbox_inches="tight")

plots/residual-plot/metadata/matplotlib.yaml

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+library: matplotlib
+specification_id: residual-plot
+created: '2025-12-26T19:36:37Z'
+updated: '2025-12-26T19:42:38Z'
+generated_by: claude-opus-4-5-20251101
+workflow_run: 20528203798
+issue: 0
+python_version: 3.13.11
+library_version: 3.10.8
+preview_url: https://storage.googleapis.com/pyplots-images/plots/residual-plot/matplotlib/plot.png
+preview_thumb: https://storage.googleapis.com/pyplots-images/plots/residual-plot/matplotlib/plot_thumb.png
+preview_html: null
+quality_score: 93
+review:
+  strengths:
+  - Excellent implementation of all spec requirements including reference line, ±2σ
+    bands, outlier highlighting, and trend line
+  - Deliberately generated data with quadratic component to demonstrate non-linear
+    residual pattern detection
+  - Clean, well-structured code following KISS principles with clear data generation
+    logic
+  - Good visual design with colorblind-safe colors (blue/yellow) and appropriate transparency
+    levels
+  - Comprehensive legend explaining all visual elements
+  weaknesses:
+  - Axis labels could include units or more context (e.g., "Fitted Values (ŷ)" or
+    similar notation)
+  - Could demonstrate heteroscedasticity more clearly with variance that changes across
+    fitted values