A 2x2 panel of diagnostic plots for evaluating linear regression model assumptions, replicating the classic output of R's `plot(lm)`. The four subplots are: (1) Residuals vs Fitted values to detect non-linearity and heteroscedasticity, (2) Normal Q-Q plot of standardized residuals to assess normality, (3) Scale-Location plot (square root of standardized residuals vs fitted values) to check homoscedasticity, and (4) Residuals vs Leverage with Cook's distance contours to identify influential observations. This composite display is the standard first step in regression model validation across statistics, academia, and regulated industries.
""" anyplot.ai
diagnostic-regression-panel: Regression Diagnostic Panel (Four-Plot Display)
Library: altair 6.1.0 | Python 3.13.13
Quality: 83/100 | Created: 2026-05-13
"""
import os
import sys
# Workaround for import conflict: remove script directory from path
_script_dir = os.path.dirname(os.path.abspath(__file__))
if _script_dir in sys.path:
sys.path.remove(_script_dir)
import altair as alt
import numpy as np
import pandas as pd
from scipy.stats import probplot
from statsmodels.nonparametric.smoothers_lowess import lowess
from statsmodels.regression.linear_model import OLS
from statsmodels.stats.outliers_influence import OLSInfluence
from statsmodels.tools import add_constant
# 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"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
BRAND = "#009E73"
ACCENT = "#C475FD"
# Data — housing price prediction scenario
np.random.seed(42)
n = 150
sqft = np.random.uniform(800, 3500, n)
bedrooms = np.random.randint(1, 6, n).astype(float)
age_yr = np.random.uniform(0, 50, n)
X = add_constant(np.column_stack([sqft, bedrooms, age_yr]))
price = X @ np.array([50000.0, 120.0, 8000.0, -800.0]) + np.random.normal(0, 25000, n)
# Introduce a few influential outliers
price[12] += 180000
price[47] -= 150000
price[88] += 120000
model = OLS(price, X).fit()
influence = OLSInfluence(model)
fitted = np.asarray(model.fittedvalues)
residuals = np.asarray(model.resid)
std_resid = np.asarray(influence.resid_studentized_internal)
leverage_vals = np.asarray(influence.hat_matrix_diag)
cooks_d_vals = np.asarray(influence.cooks_distance[0])
p_params = X.shape[1]
top3 = set(np.argsort(cooks_d_vals)[-3:])
# LOWESS smoothers for subplot 1 and 3
smooth1 = lowess(residuals, fitted, frac=0.4)
smooth3 = lowess(np.sqrt(np.abs(std_resid)), fitted, frac=0.4)
# Main DataFrame
df_main = pd.DataFrame(
{
"fitted": fitted,
"residuals": residuals,
"std_resid": std_resid,
"sqrt_abs_sr": np.sqrt(np.abs(std_resid)),
"leverage": leverage_vals,
"cooks_d": cooks_d_vals,
"obs": np.arange(n),
"label": [str(i) if i in top3 else "" for i in range(n)],
}
)
# Q-Q plot data
sort_order = np.argsort(std_resid)
(theoretical_q, sample_q), (slope, intercept, _) = probplot(std_resid, fit=True)
extreme_qq_pos = set(np.argsort(np.abs(sample_q))[-3:])
qq_df = pd.DataFrame(
{
"theoretical": theoretical_q,
"sample": sample_q,
"label": [str(sort_order[i]) if i in extreme_qq_pos else "" for i in range(n)],
}
)
qq_ref_df = pd.DataFrame(
{
"theoretical": [theoretical_q[0], theoretical_q[-1]],
"sample": [intercept + slope * theoretical_q[0], intercept + slope * theoretical_q[-1]],
}
)
# LOWESS DataFrames
loess1_df = pd.DataFrame({"fitted": smooth1[:, 0], "smoothed": smooth1[:, 1]})
loess3_df = pd.DataFrame({"fitted": smooth3[:, 0], "smoothed": smooth3[:, 1]})
# Cook's distance contour data for subplot 4
h_vals = np.linspace(0.002, max(leverage_vals) * 1.5, 500)
sr_max = max(np.abs(std_resid)) * 1.15
contour_rows = []
for D in [0.5, 1.0]:
sr_curve = np.sqrt(D * p_params * (1 - h_vals) / h_vals)
for branch, sr_vals in [("pos", sr_curve), ("neg", -sr_curve)]:
for h, sr in zip(h_vals, sr_vals, strict=True):
if abs(sr) <= sr_max:
contour_rows.append({"leverage": h, "std_resid": sr, "level": f"D={D}", "branch": f"{D}_{branch}"})
contour_df = (
pd.DataFrame(contour_rows) if contour_rows else pd.DataFrame(columns=["leverage", "std_resid", "level", "branch"])
)
zero_df = pd.DataFrame({"y": [0.0]})
W, H = 740, 395
# ── Chart 1: Residuals vs Fitted ──
c1_pts = (
alt.Chart(df_main)
.mark_circle(color=BRAND, opacity=0.6, size=70)
.encode(
x=alt.X("fitted:Q", title="Fitted Values"),
y=alt.Y("residuals:Q", title="Residuals"),
tooltip=["obs:Q", alt.Tooltip("residuals:Q", format=".0f")],
)
)
c1_ref = alt.Chart(zero_df).mark_rule(color=INK_SOFT, strokeDash=[6, 3], strokeWidth=1.5).encode(y="y:Q")
c1_loess = alt.Chart(loess1_df).mark_line(color=ACCENT, strokeWidth=2.5).encode(x="fitted:Q", y="smoothed:Q")
c1_lbl = (
alt.Chart(df_main[df_main["label"] != ""])
.mark_text(color=INK_MUTED, fontSize=14, dx=8, dy=-8)
.encode(x="fitted:Q", y="residuals:Q", text="label:N")
)
chart1 = (c1_pts + c1_ref + c1_loess + c1_lbl).properties(
width=W, height=H, title=alt.TitleParams(text="Residuals vs Fitted", fontSize=20, color=INK, anchor="start")
)
# ── Chart 2: Normal Q-Q ──
c2_pts = (
alt.Chart(qq_df)
.mark_circle(color=BRAND, opacity=0.6, size=70)
.encode(
x=alt.X("theoretical:Q", title="Theoretical Quantiles"), y=alt.Y("sample:Q", title="Standardized Residuals")
)
)
c2_ref = (
alt.Chart(qq_ref_df)
.mark_line(color=INK_SOFT, strokeDash=[6, 3], strokeWidth=1.5)
.encode(x="theoretical:Q", y="sample:Q")
)
c2_lbl = (
alt.Chart(qq_df[qq_df["label"] != ""])
.mark_text(color=INK_MUTED, fontSize=14, dx=8, dy=-8)
.encode(x="theoretical:Q", y="sample:Q", text="label:N")
)
chart2 = (c2_pts + c2_ref + c2_lbl).properties(
width=W, height=H, title=alt.TitleParams(text="Normal Q–Q", fontSize=20, color=INK, anchor="start")
)
# ── Chart 3: Scale-Location ──
c3_pts = (
alt.Chart(df_main)
.mark_circle(color=BRAND, opacity=0.6, size=70)
.encode(
x=alt.X("fitted:Q", title="Fitted Values"),
y=alt.Y("sqrt_abs_sr:Q", title="√|Standardized Residuals|"),
tooltip=["obs:Q", alt.Tooltip("sqrt_abs_sr:Q", format=".3f")],
)
)
c3_loess = alt.Chart(loess3_df).mark_line(color=ACCENT, strokeWidth=2.5).encode(x="fitted:Q", y="smoothed:Q")
c3_lbl = (
alt.Chart(df_main[df_main["label"] != ""])
.mark_text(color=INK_MUTED, fontSize=14, dx=8, dy=-8)
.encode(x="fitted:Q", y="sqrt_abs_sr:Q", text="label:N")
)
chart3 = (c3_pts + c3_loess + c3_lbl).properties(
width=W, height=H, title=alt.TitleParams(text="Scale–Location", fontSize=20, color=INK, anchor="start")
)
# ── Chart 4: Residuals vs Leverage ──
c4_pts = (
alt.Chart(df_main)
.mark_circle(color=BRAND, opacity=0.6, size=70)
.encode(
x=alt.X("leverage:Q", title="Leverage"),
y=alt.Y("std_resid:Q", title="Standardized Residuals"),
tooltip=[
"obs:Q",
alt.Tooltip("leverage:Q", format=".3f"),
alt.Tooltip("cooks_d:Q", format=".3f", title="Cook's D"),
],
)
)
c4_ref = alt.Chart(zero_df).mark_rule(color=INK_SOFT, strokeDash=[6, 3], strokeWidth=1.5).encode(y="y:Q")
c4_lbl = (
alt.Chart(df_main[df_main["label"] != ""])
.mark_text(color=INK_MUTED, fontSize=14, dx=8, dy=-8)
.encode(x="leverage:Q", y="std_resid:Q", text="label:N")
)
if len(contour_df) > 0:
contour_05_df = contour_df[contour_df["level"] == "D=0.5"]
contour_10_df = contour_df[contour_df["level"] == "D=1.0"]
c4_c05 = (
alt.Chart(contour_05_df)
.mark_line(color=INK_SOFT, strokeWidth=1.5, strokeDash=[6, 3], opacity=0.8)
.encode(x="leverage:Q", y="std_resid:Q", detail="branch:N")
)
c4_c10 = (
alt.Chart(contour_10_df)
.mark_line(color=INK_MUTED, strokeWidth=1.5, strokeDash=[3, 2], opacity=0.8)
.encode(x="leverage:Q", y="std_resid:Q", detail="branch:N")
)
# Text labels at the end of positive contour branches
contour_label_rows = []
for D, df_c in [(0.5, contour_05_df), (1.0, contour_10_df)]:
pos = df_c[df_c["branch"] == f"{D}_pos"]
if len(pos) > 0:
row = pos.iloc[-1]
contour_label_rows.append({"leverage": row["leverage"], "std_resid": row["std_resid"], "label": f"D={D}"})
if contour_label_rows:
c4_clabels = (
alt.Chart(pd.DataFrame(contour_label_rows))
.mark_text(color=INK_SOFT, fontSize=13, dx=4, dy=-6)
.encode(x="leverage:Q", y="std_resid:Q", text="label:N")
)
chart4_layers = c4_pts + c4_ref + c4_c05 + c4_c10 + c4_clabels + c4_lbl
else:
chart4_layers = c4_pts + c4_ref + c4_c05 + c4_c10 + c4_lbl
else:
chart4_layers = c4_pts + c4_ref + c4_lbl
chart4 = chart4_layers.properties(
width=W, height=H, title=alt.TitleParams(text="Residuals vs Leverage", fontSize=20, color=INK, anchor="start")
)
# ── Compose 2×2 panel ──
panel = (
alt.concat(chart1, chart2, chart3, chart4, columns=2)
.properties(
title=alt.TitleParams(
text="diagnostic-regression-panel · altair · anyplot.ai", fontSize=26, color=INK, anchor="middle", offset=14
),
background=PAGE_BG,
)
.configure_view(fill=PAGE_BG, stroke=INK_SOFT, strokeWidth=0.5)
.configure_concat(spacing=50)
.configure_axis(
domainColor=INK_SOFT,
tickColor=INK_SOFT,
gridColor=INK,
gridOpacity=0.10,
labelColor=INK_SOFT,
titleColor=INK,
labelFontSize=16,
titleFontSize=18,
)
.configure_legend(
fillColor=ELEVATED_BG,
strokeColor=INK_SOFT,
labelColor=INK_SOFT,
titleColor=INK,
labelFontSize=14,
titleFontSize=15,
)
)
panel.save(f"plot-{THEME}.png", scale_factor=3.0)
panel.save(f"plot-{THEME}.html")
Part of Regression Diagnostic Panel (Four-Plot Display) on anyplot.ai.