feat(plotly): implement scatter-lag (#5271)

## Implementation: `scatter-lag` - plotly

Implements the **plotly** version of `scatter-lag`.

**File:** `plots/scatter-lag/implementations/plotly.py`

**Parent Issue:** #5251

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/24313009870)*

---------

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

Author: github-actions[bot]

plots/scatter-lag/implementations/plotly.py

@@ -0,0 +1,162 @@
+""" pyplots.ai
+scatter-lag: Lag Plot for Time Series Autocorrelation Diagnosis
+Library: plotly 6.7.0 | Python 3.14.3
+Quality: 89/100 | Created: 2026-04-12
+"""
+
+import numpy as np
+import plotly.graph_objects as go
+
+
+# Data - synthetic AR(1) temperature process with strong autocorrelation
+np.random.seed(42)
+n_points = 500
+phi = 0.85
+noise = np.random.normal(0, 1, n_points)
+temperature = np.zeros(n_points)
+temperature[0] = 20.0
+for i in range(1, n_points):
+    temperature[i] = phi * temperature[i - 1] + (1 - phi) * 20.0 + noise[i]
+
+lag = 1
+y_t = temperature[:-lag]
+y_t_lag = temperature[lag:]
+time_index = np.arange(len(y_t))
+
+# Correlation coefficient
+correlation = np.corrcoef(y_t, y_t_lag)[0, 1]
+
+# Regression line through the data
+slope, intercept = np.polyfit(y_t, y_t_lag, 1)
+x_fit = np.array([y_t.min(), y_t.max()])
+y_fit = slope * x_fit + intercept
+
+# Plot
+fig = go.Figure()
+
+# Scatter points with Plasma for stronger visual contrast
+fig.add_trace(
+    go.Scatter(
+        x=y_t,
+        y=y_t_lag,
+        mode="markers",
+        marker={
+            "size": 7,
+            "color": time_index,
+            "colorscale": "Plasma",
+            "colorbar": {
+                "title": {"text": "Time Index", "font": {"size": 18, "color": "#444444"}},
+                "tickfont": {"size": 16, "color": "#666666"},
+                "thickness": 18,
+                "len": 0.65,
+                "outlinewidth": 0,
+                "y": 0.5,
+            },
+            "opacity": 0.55,
+            "line": {"width": 0.3, "color": "rgba(255,255,255,0.6)"},
+        },
+        hovertemplate=(
+            "<b>Time %{customdata}</b><br>Temp at t: %{x:.1f} °C<br>Temp at t+1: %{y:.1f} °C<extra></extra>"
+        ),
+        customdata=time_index,
+    )
+)
+
+# Diagonal reference line (y = x)
+data_min = min(y_t.min(), y_t_lag.min())
+data_max = max(y_t.max(), y_t_lag.max())
+padding = (data_max - data_min) * 0.05
+line_min = data_min - padding
+line_max = data_max + padding
+
+fig.add_trace(
+    go.Scatter(
+        x=[line_min, line_max],
+        y=[line_min, line_max],
+        mode="lines",
+        line={"color": "rgba(0,0,0,0.15)", "width": 1.5, "dash": "dot"},
+        showlegend=False,
+        hoverinfo="skip",
+        name="y = x",
+    )
+)
+
+# Regression trend line
+fig.add_trace(
+    go.Scatter(
+        x=x_fit,
+        y=y_fit,
+        mode="lines",
+        line={"color": "#306998", "width": 2.5},
+        showlegend=False,
+        hoverinfo="skip",
+        name="trend",
+    )
+)
+
+# Layout with custom background and removed axis borders
+fig.update_layout(
+    title={
+        "text": "scatter-lag · plotly · pyplots.ai",
+        "font": {"size": 28, "color": "#333333"},
+        "x": 0.5,
+        "xanchor": "center",
+        "y": 0.96,
+    },
+    xaxis={
+        "title": {"text": "Temperature (°C) at time t", "font": {"size": 22, "color": "#444444"}},
+        "tickfont": {"size": 18, "color": "#666666"},
+        "showgrid": True,
+        "gridcolor": "rgba(0,0,0,0.06)",
+        "gridwidth": 1,
+        "zeroline": False,
+        "showline": False,
+        "ticks": "",
+    },
+    yaxis={
+        "title": {"text": f"Temperature (°C) at time t+{lag}", "font": {"size": 22, "color": "#444444"}},
+        "tickfont": {"size": 18, "color": "#666666"},
+        "showgrid": True,
+        "gridcolor": "rgba(0,0,0,0.06)",
+        "gridwidth": 1,
+        "zeroline": False,
+        "showline": False,
+        "ticks": "",
+    },
+    template="plotly_white",
+    plot_bgcolor="#FFFFFF",
+    paper_bgcolor="#F8F9FA",
+    showlegend=False,
+    margin={"l": 90, "r": 130, "t": 100, "b": 90},
+)
+
+# Subtitle annotation for context
+fig.add_annotation(
+    text="AR(1) process  |  lag = 1  |  500 observations",
+    xref="paper",
+    yref="paper",
+    x=0.5,
+    y=1.06,
+    showarrow=False,
+    font={"size": 16, "color": "#999999"},
+    xanchor="center",
+)
+
+# Correlation annotation - prominent and well-styled
+fig.add_annotation(
+    text=f"<b>r = {correlation:.3f}</b>",
+    xref="paper",
+    yref="paper",
+    x=0.03,
+    y=0.97,
+    showarrow=False,
+    font={"size": 24, "color": "#306998"},
+    bgcolor="rgba(255,255,255,0.9)",
+    bordercolor="rgba(48,105,152,0.3)",
+    borderwidth=1.5,
+    borderpad=10,
+)
+
+# Save
+fig.write_image("plot.png", width=1600, height=900, scale=3)
+fig.write_html("plot.html", include_plotlyjs="cdn")