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: seaborn 0.13.2 | Python 3.13.13
Quality: 87/100 | Created: 2026-05-13
"""
import os
import sys
sys.path.pop(0)
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
import statsmodels.api as sm
from scipy import stats
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"
INFLUENCE = "#BD8233"
sns.set_theme(
style="ticks",
rc={
"figure.facecolor": PAGE_BG,
"axes.facecolor": PAGE_BG,
"axes.edgecolor": INK_SOFT,
"axes.labelcolor": INK,
"text.color": INK,
"xtick.color": INK_SOFT,
"ytick.color": INK_SOFT,
"grid.color": INK,
"grid.alpha": 0.10,
"legend.facecolor": ELEVATED_BG,
"legend.edgecolor": INK_SOFT,
},
)
np.random.seed(42)
n = 150
X = np.column_stack([np.random.normal(0, 1, n), np.random.normal(0, 1, n), np.random.uniform(-2, 2, n)])
y = X @ np.array([2.5, -1.8, 0.9]) + 5 + np.random.normal(0, 1.5, n)
y[42] += 12
y[99] -= 10
X[130, 0] = 3.5
X_sm = sm.add_constant(X)
model = sm.OLS(y, X_sm).fit()
infl = model.get_influence()
fitted = np.asarray(model.fittedvalues)
residuals = np.asarray(model.resid)
std_res = infl.resid_studentized_internal
leverage = infl.hat_matrix_diag
cooks_d = infl.cooks_distance[0]
p = X_sm.shape[1]
top3 = list(np.argsort(cooks_d)[-3:])
sorted_idx = np.argsort(std_res)
(theoretical_q, sample_q), (qq_slope, qq_intercept, _) = stats.probplot(std_res)
fig, axes = plt.subplots(2, 2, figsize=(16, 9), facecolor=PAGE_BG)
fig.patch.set_facecolor(PAGE_BG)
regplot_sc_kws = {"color": BRAND, "alpha": 0.65, "s": 70, "edgecolors": PAGE_BG, "linewidths": 0.4, "zorder": 2}
line_kws = {"color": ACCENT, "linewidth": 2.5, "zorder": 3}
annot_kw = {"fontsize": 14, "color": INK_MUTED, "xytext": (14, 10), "textcoords": "offset points"}
# Subplot 1: Residuals vs Fitted — sns.regplot with LOWESS smoother
ax1 = axes[0, 0]
sns.regplot(x=fitted, y=residuals, ax=ax1, lowess=True, ci=None, scatter_kws=regplot_sc_kws, line_kws=line_kws)
ax1.axhline(0, color=INK_SOFT, linewidth=1.2, linestyle="--", alpha=0.7)
for i in top3:
ax1.annotate(str(i), (fitted[i], residuals[i]), **annot_kw)
ax1.set_xlabel("Fitted Values", fontsize=20, color=INK)
ax1.set_ylabel("Residuals", fontsize=20, color=INK)
ax1.set_title("Residuals vs Fitted", fontsize=20, color=INK, fontweight="medium")
ax1.tick_params(labelsize=16, colors=INK_SOFT)
sns.despine(ax=ax1)
ax1.spines["left"].set_color(INK_SOFT)
ax1.spines["bottom"].set_color(INK_SOFT)
ax1.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)
# Subplot 2: Normal Q-Q — sns.scatterplot with Q-Q reference line
ax2 = axes[0, 1]
sns.scatterplot(
x=theoretical_q, y=sample_q, ax=ax2, color=BRAND, alpha=0.65, s=70, edgecolor=PAGE_BG, linewidth=0.4, zorder=2
)
xr = np.array([theoretical_q[0], theoretical_q[-1]])
ax2.plot(xr, qq_slope * xr + qq_intercept, color=ACCENT, linewidth=2.5, zorder=3)
for k, orig in enumerate(sorted_idx):
if orig in top3:
ax2.annotate(str(orig), (theoretical_q[k], sample_q[k]), **annot_kw)
ax2.set_xlabel("Theoretical Quantiles", fontsize=20, color=INK)
ax2.set_ylabel("Standardized Residuals", fontsize=20, color=INK)
ax2.set_title("Normal Q-Q", fontsize=20, color=INK, fontweight="medium")
ax2.tick_params(labelsize=16, colors=INK_SOFT)
sns.despine(ax=ax2)
ax2.spines["left"].set_color(INK_SOFT)
ax2.spines["bottom"].set_color(INK_SOFT)
ax2.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)
# Subplot 3: Scale-Location — sns.regplot with LOWESS smoother
ax3 = axes[1, 0]
sqrt_abs_res = np.sqrt(np.abs(std_res))
sns.regplot(x=fitted, y=sqrt_abs_res, ax=ax3, lowess=True, ci=None, scatter_kws=regplot_sc_kws, line_kws=line_kws)
for i in top3:
ax3.annotate(str(i), (fitted[i], sqrt_abs_res[i]), **annot_kw)
ax3.set_xlabel("Fitted Values", fontsize=20, color=INK)
ax3.set_ylabel("√|Standardized Residuals|", fontsize=20, color=INK)
ax3.set_title("Scale-Location", fontsize=20, color=INK, fontweight="medium")
ax3.tick_params(labelsize=16, colors=INK_SOFT)
sns.despine(ax=ax3)
ax3.spines["left"].set_color(INK_SOFT)
ax3.spines["bottom"].set_color(INK_SOFT)
ax3.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)
# Subplot 4: Residuals vs Leverage — sns.scatterplot with Cook's D contours
ax4 = axes[1, 1]
sns.scatterplot(
x=leverage, y=std_res, ax=ax4, color=BRAND, alpha=0.65, s=70, edgecolor=PAGE_BG, linewidth=0.4, zorder=2
)
ax4.axhline(0, color=INK_SOFT, linewidth=1.2, linestyle="--", alpha=0.7)
y_bound = max(np.abs(std_res).max() * 1.1, 4.0)
lev_rng = np.linspace(max(leverage.min() * 0.5, 1e-4), min(leverage.max() * 1.3, 0.99), 400)
for cd_level, ls in [(0.5, "--"), (1.0, "-")]:
cd_vals = np.sqrt(cd_level * p * (1 - lev_rng) / lev_rng)
valid = cd_vals <= y_bound
if valid.any():
ax4.plot(
lev_rng[valid],
cd_vals[valid],
color=INFLUENCE,
linewidth=1.8,
linestyle=ls,
alpha=0.8,
label=f"Cook's D={cd_level}",
)
ax4.plot(lev_rng[valid], -cd_vals[valid], color=INFLUENCE, linewidth=1.8, linestyle=ls, alpha=0.8)
for i in top3:
ax4.annotate(str(i), (leverage[i], std_res[i]), **annot_kw)
ax4.set_ylim(-y_bound, y_bound)
ax4.set_xlabel("Leverage", fontsize=20, color=INK)
ax4.set_ylabel("Standardized Residuals", fontsize=20, color=INK)
ax4.set_title("Residuals vs Leverage", fontsize=20, color=INK, fontweight="medium")
ax4.tick_params(labelsize=16, colors=INK_SOFT)
sns.despine(ax=ax4)
ax4.spines["left"].set_color(INK_SOFT)
ax4.spines["bottom"].set_color(INK_SOFT)
ax4.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)
ax4.legend(fontsize=14, loc="upper right", framealpha=0.9)
fig.suptitle("diagnostic-regression-panel · seaborn · anyplot.ai", fontsize=24, fontweight="medium", color=INK)
plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=300, bbox_inches="tight", facecolor=PAGE_BG)
Part of Regression Diagnostic Panel (Four-Plot Display) on anyplot.ai.