Q-Q plot

Python Code

"""Statistics — Q-Q plot (Old Faithful waiting times)."""


import numpy as np
import plotly.graph_objects as go
from scipy import stats

URL = "https://vincentarelbundock.github.io/Rdatasets/csv/datasets/faithful.csv"


def generate():
    print("fetching Old Faithful data …")
    try:
        df = fetch_csv(URL)
        print(f"  cols: {list(df.columns)}")
        wait_col = next((c for c in df.columns if "wait" in c.lower()), df.columns[-1])
        waiting = df[wait_col].dropna().values
        used_synthetic = False
    except Exception as e:
        print(f"  fetch failed ({e}); generating synthetic bimodal waiting times")
        used_synthetic = True
        rng = np.random.default_rng(42)
        waiting = np.concatenate([
            rng.normal(54, 5, 97),
            rng.normal(80, 6, 175),
        ])

    n = len(waiting)
    sample_q = np.sort(waiting)
    # Theoretical normal quantiles
    prob = (np.arange(1, n + 1) - 0.5) / n
    theoretical_q = stats.norm.ppf(prob)

    # Reference line through Q1 and Q3 of each
    q1_th, q3_th = np.percentile(theoretical_q, [25, 75])
    q1_s,  q3_s  = np.percentile(sample_q,      [25, 75])
    slope = (q3_s - q1_s) / (q3_th - q1_th)
    intercept = q1_s - slope * q1_th

    # Extend reference line across full theoretical range
    x_ref = np.array([theoretical_q.min(), theoretical_q.max()])
    y_ref = slope * x_ref + intercept

    fig = go.Figure([
        go.Scatter(
            x=x_ref,
            y=y_ref,
            mode="lines",
            line=dict(color=TEAL, dash="dash", width=1.8),
            name="Reference line",
            hoverinfo="skip",
        ),
        go.Scatter(
            x=theoretical_q,
            y=sample_q,
            mode="markers",
            marker=dict(color=VIOLET, size=6, opacity=0.7),
            name="Waiting times",
            hovertemplate="theoretical=%{x:.2f}<br>sample=%{y:.1f} min<extra></extra>",
        ),
    ])
    fig.update_layout(
        xaxis=dict(title="Theoretical Quantiles"),
        yaxis=dict(title="Sample Quantiles (minutes)"),
        legend=dict(orientation="h", y=1.05, x=0),
        margin=dict(t=40, b=60, l=70, r=40),
        height=500,
    )
    return fig


if __name__ == "__main__":
    generate()

Made with Plotly