Update index.html

index.html

@@ -520,41 +520,52 @@
 
     // --- MATHEMATICAL REgRESSION ENGINE ---
     
-    // Linear regression
+    // Linear regression.
+    // "Force scale through origin" only pins the intercept when that line
+    // still fits. A negative straight line that does not pass through (0,0)
+    // must stay a negative linear fit, not get replaced by a curve.
     function calculateLinearFit(points) {
       if (points.length < 2) return null;
-      const n = points.length;
-      let sumX = 0, sumY = 0, sumXY = 0, sumXX = 0;
-      for (let p of points) {
-        sumX += p.x;
-        sumY += p.y;
-        sumXY += p.x * p.y;
-        sumXX += p.x * p.x;
-      }
-      let m, c;
-      if (forceOrigin) {
-        let sumXY_o = 0, sumXX_o = 0;
+
+      const fit = (throughOrigin) => {
+        const n = points.length;
+        let sumX = 0, sumY = 0, sumXY = 0, sumXX = 0;
         for (let p of points) {
-          sumXY_o += p.x * p.y;
-          sumXX_o += p.x * p.x;
+          sumX += p.x;
+          sumY += p.y;
+          sumXY += p.x * p.y;
+          sumXX += p.x * p.x;
         }
-        m = sumXX_o === 0 ? 0 : sumXY_o / sumXX_o;
-        c = 0;
-      } else {
-        const denominator = (n * sumXX) - (sumX * sumX);
-        if (denominator === 0) return null;
-        m = ((n * sumXY) - (sumX * sumY)) / denominator;
-        c = (sumY - (m * sumX)) / n;
-      }
-      const yMean = sumY / n;
-      let ssTot = 0, ssRes = 0;
-      for (let p of points) {
-        ssTot += Math.pow(p.y - yMean, 2);
-        const yPred = m * p.x + c;
-        ssRes += Math.pow(p.y - yPred, 2);
-      }
-      const r2 = ssTot === 0 ? 1 : 1 - (ssRes / ssTot);
-      return { m, c, r2, type: 'linear', label: 'Linear Fit', f: (x) => m * x + c };
+        let m, c;
+        if (throughOrigin) {
+          m = sumXX === 0 ? 0 : sumXY / sumXX;
+          c = 0;
+        } else {
+          const denominator = (n * sumXX) - (sumX * sumX);
+          if (denominator === 0) return null;
+          m = ((n * sumXY) - (sumX * sumY)) / denominator;
+          c = (sumY - (m * sumX)) / n;
+        }
+        const yMean = sumY / n;
+        let ssTot = 0, ssRes = 0;
+        for (let p of points) {
+          ssTot += Math.pow(p.y - yMean, 2);
+          const yPred = m * p.x + c;
+          ssRes += Math.pow(p.y - yPred, 2);
+        }
+        const r2 = ssTot === 0 ? 1 : 1 - (ssRes / ssTot);
+        return { m, c, r2, type: 'linear', label: 'Linear Fit', f: (x) => m * x + c };
+      };
+
+      const free = fit(false);
+      if (!free) return null;
+      if (!forceOrigin) return free;
+
+      const forced = fit(true);
+      // Origin constraint is only kept when it does not destroy a clearly linear trend
+      // (including a negative gradient whose intercept is not zero).
+      if (forced && forced.r2 >= 0.95 && forced.r2 >= free.r2 - 0.02) return forced;
+      return free;
     }
 
     // Quadratic regression