From 54d0647a6d2df27a335cec550cda377f82031255 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marc-Andr=C3=A9=20Bombeck?= <mbombeck@gmail.com>
Date: Tue, 3 Nov 2026 20:58:37 +0100
Subject: [PATCH] =?UTF-8?q?fix(stats):=20keep=20r=C2=B2=20within=20[0,=201?=
 =?UTF-8?q?]=20when=20y=20sits=20far=20from=20zero?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

The centred sums lose their last digits when every y is close to one
large value, and a two-point fit came out at r² 1.00000004. Clamp the
ratio to 1 and the y sum of squares at 0, and pin the two shrunk
counterexamples the nightly property run found.
---
 .../stats/__tests__/stats.property.test.ts    | 21 ++++++++++++++++++-
 src/lib/stats/linear-fit.ts                   |  9 ++++++--
 2 files changed, 27 insertions(+), 3 deletions(-)

diff --git a/src/lib/stats/__tests__/stats.property.test.ts b/src/lib/stats/__tests__/stats.property.test.ts
index 15991c4a1..6471ed73b 100644
--- a/src/lib/stats/__tests__/stats.property.test.ts
+++ b/src/lib/stats/__tests__/stats.property.test.ts
@@ -244,11 +244,30 @@ describe("least-squares line", () => {
           return;
         }
         expect(fit.r2).toBeGreaterThanOrEqual(0);
-        expect(fit.r2).toBeLessThanOrEqual(1 + 1e-9);
+        expect(fit.r2).toBeLessThanOrEqual(1);
       }),
     );
   });
 
+  // Shrunk counterexamples of the property above from two nightly seeds
+  // (802398975 and 1070990592): two points on a line far from zero, where
+  // the centred sums rounded r² above 1.
+  it.each([
+    [
+      [0, 1],
+      [-999.87, -999.97],
+    ],
+    [
+      [0, -1],
+      [9996.28, 9993.55],
+    ],
+  ])("keeps r² at most 1 for x %j, y %j", (xs, ys) => {
+    const fit = linearFit(xs, ys)!;
+    expect(fit.r2).not.toBeNull();
+    expect(fit.r2!).toBeLessThanOrEqual(1);
+    expect(fit.r2!).toBeGreaterThan(0.999);
+  });
+
   it("refuses a vertical line instead of inventing a slope", () => {
     assertProperty(
       fc.property(
diff --git a/src/lib/stats/linear-fit.ts b/src/lib/stats/linear-fit.ts
index 2b05f8592..870d280c2 100644
--- a/src/lib/stats/linear-fit.ts
+++ b/src/lib/stats/linear-fit.ts
@@ -48,7 +48,9 @@ export function fitFromSums(sums: FitSums): LinearFit | null {
   if (n < 2) return null;
   const sxx = sumXx - (sumX * sumX) / n;
   const sxy = sumXy - (sumX * sumY) / n;
-  const syy = sumYy - (sumY * sumY) / n;
+  // A sum of squares is never negative; the subtraction can still land a
+  // hair below zero when every y sits close to one large value.
+  const syy = Math.max(0, sumYy - (sumY * sumY) / n);
   if (sxx === 0) return null;
   const slope = sxy / sxx;
   const meanX = sumX / n;
@@ -56,7 +58,10 @@ export function fitFromSums(sums: FitSums): LinearFit | null {
   return {
     slope,
     intercept: meanY - slope * meanX,
-    r2: syy === 0 ? null : (sxy * sxy) / (sxx * syy),
+    // r² is at most 1 by Cauchy–Schwarz. With y far from zero and little
+    // spread (two weighings of about 1000, a tenth apart) the centred sums
+    // lose their last digits and the ratio came out at 1.00000004.
+    r2: syy === 0 ? null : Math.min(1, (sxy * sxy) / (sxx * syy)),
     n,
     meanX,
     meanY,