Correlation Playground

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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">
<meta name="color-scheme" content="light dark">
<title>Correlation Playground</title>
<link rel="icon" href="data:,">
<style>
/* sloprun design tokens — inline this block into every demo (self-contained rule).
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/* ---------- demo-local palette: the fitted line is never accent, never green ---- */
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</style>
</head>
<body>
<div class="wrap">

  <header class="head">
    <div>
      <h1>Correlation Playground</h1>
      <p class="lede">Click the grid to drop a point, drag it to move it. The correlation
        <em>r</em> and the best-fit line recompute on every pixel. Then load the four classic
        datasets below: identical averages, identical spread, identical <em>r</em>, identical
        line — and four pictures that look nothing alike.</p>
    </div>
    <div class="pill" id="pill">
      <span class="dot" aria-hidden="true"></span>
      <span id="pillText">set I &middot; n 11 &middot; r 0.816</span>
    </div>
  </header>

  <div class="top">

    <section class="panel" aria-labelledby="plotH">
      <div class="plot-head">
        <h2 id="plotH" class="ptitle">Scatter &middot; drag anything</h2>
        <p class="hint"><kbd>click</kbd> add &middot; <kbd>drag</kbd> move &middot;
           <kbd>alt</kbd>+click remove</p>
      </div>

      <canvas id="plot" class="plot" tabindex="0" role="application"
        aria-label="Editable scatter plot"
        aria-describedby="kbhelp"></canvas>

      <p id="kbhelp" class="sr">Keyboard: arrow keys move a crosshair, hold shift for bigger steps.
        Enter drops a point at the crosshair. Press N or P to step through the existing points; with a
        point selected the arrow keys move that point. Delete removes it. Escape deselects.</p>

      <div class="probe" id="probe"><span>hover a point to inspect it</span></div>

      <div class="bar" role="group" aria-label="Plot tools">
        <button type="button" id="bRandom">random cloud</button>
        <button type="button" id="bClear">clear</button>
        <button type="button" id="bUndo" disabled>undo</button>
        <span class="spacer"></span>
        <button type="button" id="bResid" class="tgl" aria-pressed="false"><span class="box" aria-hidden="true"></span>residuals</button>
        <button type="button" id="bMeans" class="tgl" aria-pressed="false"><span class="box" aria-hidden="true"></span>averages</button>
      </div>

      <p class="sr" id="live" role="status" aria-live="polite"></p>
    </section>

    <aside class="panel" aria-labelledby="statH">
      <h2 id="statH" class="sr">Statistics</h2>

      <div class="rbox">
        <p class="rlab">Pearson r</p>
        <p class="rval" id="rVal">0.816</p>
        <p class="rword" id="rWord">strong positive</p>
        <div class="meter" aria-hidden="true">
          <div class="mtrack">
            <div class="mfill" id="mFill" style="left:50%;width:0%"></div>
            <div class="mzero"></div>
          </div>
          <div class="mscale"><span>&minus;1</span><span>0</span><span>+1</span></div>
        </div>
      </div>

      <div class="rows">
        <div class="row"><span class="k">points</span><span class="v" id="sN">11</span></div>
        <div class="row"><span class="k">mean x</span><span class="v" id="sMx">9.00</span></div>
        <div class="row"><span class="k">mean y</span><span class="v" id="sMy">7.50</span></div>
        <div class="row"><span class="k">sd x</span><span class="v" id="sSx">3.32</span></div>
        <div class="row"><span class="k">sd y</span><span class="v" id="sSy">2.03</span></div>
        <div class="row"><span class="k">r&#178;</span><span class="v" id="sR2">0.67</span></div>
      </div>

      <div class="eqbox">
        <p class="rlab">least-squares fit</p>
        <p class="eq" id="sFit">y = 3.00 + 0.500x</p>
      </div>
    </aside>
  </div>

  <section class="panel" style="margin-top:12px" aria-labelledby="chipH">
    <h2 id="chipH" class="ptitle">Load a dataset &middot; the four look different, the numbers do not</h2>
    <div class="chips" id="chips" role="group" aria-label="Preset datasets"></div>
  </section>

  <div class="lesson">
    <strong>the lesson</strong>
    <p id="lessonText">A plain rising trend with ordinary scatter. This is what people picture
      when they hear &ldquo;r = 0.82&rdquo; — and it is only one of the four shapes that produce it.</p>
  </div>

  <section class="panel" style="margin-top:12px" aria-labelledby="tblH">
    <h2 id="tblH" class="ptitle">Same summary, four shapes &middot; every number computed in your browser</h2>
    <div class="tscroll">
      <table>
        <thead>
          <tr>
            <th scope="col">set</th><th scope="col">mean x</th><th scope="col">mean y</th>
            <th scope="col">sd x</th><th scope="col">sd y</th><th scope="col">r</th>
            <th scope="col">fit</th><th scope="col">what it looks like</th>
          </tr>
        </thead>
        <tbody id="tbody"></tbody>
      </table>
    </div>
    <p class="swipe" aria-hidden="true">&rarr; the table scrolls sideways</p>
    <p class="verified" id="verified" hidden><span class="tick" aria-hidden="true">&#10003;</span><span id="verifiedText"></span></p>
  </section>

  <footer class="foot">
    <span>demo &middot; sloprun.dev</span>
    <span id="footRight">4 datasets &middot; 44 points &middot; 1 identical summary</span>
  </footer>
</div>

<script>
(function () {
  "use strict";

  /* ================================================================== *
   * Data — Anscombe's quartet (F.J. Anscombe, 1973).
   * ================================================================== */
  var XA = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5];
  var SETS = [
    { id: "I", name: "set I", shape: "a plain trend",
      sub: "ordinary scatter around a line",
      lesson: "A plain rising trend with ordinary scatter. This is what people picture when they hear “r = 0.82” — and it is only one of the four shapes that produce it.",
      x: XA, y: [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68] },
    { id: "II", name: "set II", shape: "a smooth curve",
      sub: "a perfect arch, not a line",
      lesson: "Not scatter at all — a smooth arch. Every point sits exactly on a curve, so the relationship is perfect, and a straight line is simply the wrong shape for it. Turn on residuals: they bend.",
      x: XA, y: [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74] },
    { id: "III", name: "set III", shape: "one point off",
      sub: "a tight line plus one stray",
      lesson: "Ten points sit on a near-perfect line, and one stray point up top tilts the fit away from all of them. Drag that stray back down and watch r jump to almost 1.",
      x: XA, y: [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73] },
    { id: "IV", name: "set IV", shape: "one point rules",
      sub: "a stack, and one far-off point",
      lesson: "Ten points share the exact same x, so on their own they say nothing about a trend. The single point far to the right invents the whole correlation — drag it downward and r collapses.",
      x: [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8],
      y: [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89] }
  ];

  var XD = [0, 20], YD = [0, 14];   /* fixed data window, so every dataset is comparable */
  var TXD = [3, 20], TYD = [2.4, 13.6];  /* tighter window for the 66px thumbnails */

  /* ================================================================== *
   * Stats
   * ================================================================== */
  function stats(pts) {
    var n = pts.length, i;
    var out = { n: n, ok: false, mx: NaN, my: NaN, sx: NaN, sy: NaN, r: NaN,
                slope: NaN, icept: NaN, why: "" };
    if (n === 0) { out.why = "no points yet"; return out; }
    var sx = 0, sy = 0;
    for (i = 0; i < n; i++) { sx += pts[i].x; sy += pts[i].y; }
    out.mx = sx / n; out.my = sy / n;
    if (n < 2) { out.why = "one point — r needs at least two"; return out; }
    var sxx = 0, syy = 0, sxy = 0, dx, dy;
    for (i = 0; i < n; i++) {
      dx = pts[i].x - out.mx; dy = pts[i].y - out.my;
      sxx += dx * dx; syy += dy * dy; sxy += dx * dy;
    }
    out.sx = Math.sqrt(sxx / (n - 1));
    out.sy = Math.sqrt(syy / (n - 1));
    if (sxx <= 1e-12 && syy <= 1e-12) { out.why = "every point is in the same spot"; return out; }
    if (sxx <= 1e-12) { out.why = "x never changes — r needs both to vary"; return out; }
    if (syy <= 1e-12) { out.why = "y never changes — r needs both to vary"; return out; }
    out.r = Math.max(-1, Math.min(1, sxy / Math.sqrt(sxx * syy)));
    out.slope = sxy / sxx;
    out.icept = out.my - out.slope * out.mx;
    out.ok = true;
    return out;
  }

  function fmt(v, d) { return (isFinite(v) ? v.toFixed(d) : "—"); }
  function eqText(s) {
    if (!s.ok) return "—";
    var b = s.slope, a = s.icept;
    return "y = " + a.toFixed(2) + (b < 0 ? " − " : " + ") + Math.abs(b).toFixed(3) + "x";
  }
  function word(r) {
    var a = Math.abs(r), dir = r < 0 ? "negative" : "positive";
    if (a >= 0.9995) return "perfectly " + dir;   /* rounds to 1.000 on screen */
    if (a >= 0.9) return "very strong " + dir;
    if (a >= 0.7) return "strong " + dir;
    if (a >= 0.4) return "moderate " + dir;
    if (a >= 0.2) return "weak " + dir;
    return "essentially none";
  }

  /* ================================================================== *
   * State
   * ================================================================== */
  var S = {
    pts: SETS[0].x.map(function (v, i) { return { x: v, y: SETS[0].y[i] }; }),
    preset: "I",
    sel: -1, hover: -1, drag: -1, moved: false,
    kb: false, cx: 10, cy: 7,
    fresh: false, editRun: -2,
    resid: false, means: false,
    undo: []
  };

  var $ = function (id) { return document.getElementById(id); };
  var cv = $("plot"), ctx = cv.getContext("2d");

  function snapshot() {
    S.undo.push({ pts: S.pts.map(function (p) { return { x: p.x, y: p.y }; }),
                  preset: S.preset, lesson: $("lessonText").textContent });
    if (S.undo.length > 40) S.undo.shift();
    $("bUndo").disabled = false;
  }
  function clampX(v) { return Math.max(XD[0], Math.min(XD[1], v)); }
  function clampY(v) { return Math.max(YD[0], Math.min(YD[1], v)); }

  /* ================================================================== *
   * Canvas geometry + drawing
   * ================================================================== */
  var G = { L: 44, R: 12, T: 12, B: 30, w: 0, h: 0, W: 0, H: 0 };

  function C(name) {
    return getComputedStyle(document.documentElement).getPropertyValue(name).trim();
  }

  function sizeCanvas() {
    var dpr = Math.min(window.devicePixelRatio || 1, 2.5);
    var rect = cv.getBoundingClientRect();
    G.W = Math.max(200, Math.round(rect.width));
    G.H = Math.max(160, Math.round(rect.height));
    var bw = Math.round(G.W * dpr), bh = Math.round(G.H * dpr);
    if (cv.width !== bw || cv.height !== bh) { cv.width = bw; cv.height = bh; }
    ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
    if (G.W < 420) { G.L = 32; G.B = 26; } else { G.L = 44; G.B = 30; }
    G.w = G.W - G.L - G.R;
    G.h = G.H - G.T - G.B;
  }
  function px(x) { return G.L + (x - XD[0]) / (XD[1] - XD[0]) * G.w; }
  function py(y) { return G.T + (1 - (y - YD[0]) / (YD[1] - YD[0])) * G.h; }
  function ux(p) { return XD[0] + (p - G.L) / G.w * (XD[1] - XD[0]); }
  function uy(p) { return YD[0] + (1 - (p - G.T) / G.h) * (YD[1] - YD[0]); }

  function draw() {
    sizeCanvas();
    var col = {
      surface: C("--surface"), bg: C("--bg"), ink: C("--ink"), muted: C("--muted"),
      line: C("--line"), accent: C("--accent"), fit: C("--fit"), danger: C("--danger")
    };
    var s = stats(S.pts);

    ctx.clearRect(0, 0, G.W, G.H);
    ctx.fillStyle = col.bg;
    roundRect(G.L, G.T, G.w, G.h, 6); ctx.fill();

    /* grid */
    ctx.strokeStyle = col.line; ctx.lineWidth = 1;
    ctx.font = "11px " + C("--font-mono");
    ctx.fillStyle = col.muted;
    var i, v;
    ctx.textAlign = "center"; ctx.textBaseline = "top";
    for (v = XD[0]; v <= XD[1] + 0.001; v += 4) {
      var gx = Math.round(px(v)) + 0.5;
      ctx.beginPath(); ctx.moveTo(gx, G.T); ctx.lineTo(gx, G.T + G.h); ctx.stroke();
      ctx.fillText(String(v), gx, G.T + G.h + 7);
    }
    ctx.textAlign = "right"; ctx.textBaseline = "middle";
    for (v = YD[0]; v <= YD[1] + 0.001; v += 2) {
      var gy = Math.round(py(v)) + 0.5;
      ctx.beginPath(); ctx.moveTo(G.L, gy); ctx.lineTo(G.L + G.w, gy); ctx.stroke();
      ctx.fillText(String(v), G.L - 7, gy);
    }
    ctx.save();
    ctx.globalAlpha = 0.85;
    ctx.textAlign = "left"; ctx.textBaseline = "top";
    ctx.fillText("y", G.L + 7, G.T + 6);
    ctx.textAlign = "right"; ctx.textBaseline = "bottom";
    ctx.fillText("x", G.L + G.w - 7, G.T + G.h - 5);
    ctx.restore();

    /* average lines */
    if (S.means && s.n >= 1) {
      ctx.save();
      ctx.strokeStyle = col.muted; ctx.lineWidth = 1; ctx.setLineDash([4, 4]);
      ctx.globalAlpha = 0.75;
      var mxp = px(clampX(s.mx)), myp = py(clampY(s.my));
      ctx.beginPath(); ctx.moveTo(mxp, G.T); ctx.lineTo(mxp, G.T + G.h); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(G.L, myp); ctx.lineTo(G.L + G.w, myp); ctx.stroke();
      ctx.setLineDash([]); ctx.globalAlpha = 1;
      ctx.font = "10px " + C("--font-mono");
      ctx.fillStyle = col.muted; ctx.textAlign = "left"; ctx.textBaseline = "bottom";
      ctx.fillText("mean y " + s.my.toFixed(2), G.L + 4, myp - 3);
      ctx.textAlign = "center"; ctx.textBaseline = "top";
      ctx.fillText("mean x " + s.mx.toFixed(2),
                   Math.min(Math.max(mxp, G.L + 34), G.L + G.w - 34), G.T + 4);
      ctx.restore();
    }

    /* residuals */
    if (S.resid && s.ok) {
      ctx.save();
      ctx.strokeStyle = col.muted; ctx.lineWidth = 1.5; ctx.globalAlpha = 0.7;
      ctx.setLineDash([3, 3]);
      for (i = 0; i < S.pts.length; i++) {
        var p = S.pts[i], yh = s.icept + s.slope * p.x;
        ctx.beginPath();
        ctx.moveTo(px(p.x), py(clampY(p.y)));
        ctx.lineTo(px(p.x), py(clampY(yh)));
        ctx.stroke();
      }
      ctx.restore();
    }

    /* fitted line */
    if (s.ok) {
      ctx.save();
      roundRect(G.L, G.T, G.w, G.h, 6); ctx.clip();   /* clip FIRST — roundRect resets the path */
      var yl = s.icept + s.slope * XD[0], yr = s.icept + s.slope * XD[1];
      ctx.strokeStyle = col.fit; ctx.lineWidth = 2.25; ctx.lineCap = "round";
      ctx.beginPath();
      ctx.moveTo(px(XD[0]), py(yl));
      ctx.lineTo(px(XD[1]), py(yr));
      ctx.stroke();
      ctx.restore();
    }

    /* keyboard crosshair */
    if (S.kb && S.sel < 0) {
      ctx.save();
      ctx.strokeStyle = col.accent; ctx.lineWidth = 1; ctx.setLineDash([2, 3]);
      var kx = px(S.cx), ky = py(S.cy);
      ctx.beginPath(); ctx.moveTo(kx, G.T); ctx.lineTo(kx, G.T + G.h); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(G.L, ky); ctx.lineTo(G.L + G.w, ky); ctx.stroke();
      ctx.setLineDash([]);
      ctx.beginPath(); ctx.arc(kx, ky, 6, 0, 6.2832); ctx.stroke();
      ctx.restore();
    }

    /* empty grid — say so on the canvas, not just in the panel */
    if (S.pts.length === 0) {
      ctx.save();
      ctx.fillStyle = col.muted; ctx.globalAlpha = 0.9;
      ctx.textAlign = "center"; ctx.textBaseline = "middle";
      ctx.font = "13px " + C("--font-sans");
      ctx.fillText("click anywhere to place a point",
                   G.L + G.w / 2, G.T + G.h * 0.31);
      ctx.font = "11px " + C("--font-mono");
      ctx.globalAlpha = 0.75;
      ctx.fillText("or load one of the four sets below",
                   G.L + G.w / 2, G.T + G.h * 0.31 + 21);
      ctx.restore();
    }

    /* points */
    for (i = 0; i < S.pts.length; i++) {
      var q = S.pts[i], X = px(q.x), Y = py(q.y);
      var on = (i === S.sel), hv = (i === S.hover || i === S.drag);
      if (on || hv) {
        ctx.beginPath(); ctx.arc(X, Y, on ? 11 : 9, 0, 6.2832);
        ctx.strokeStyle = col.accent; ctx.lineWidth = on ? 2 : 1;
        ctx.globalAlpha = on ? 1 : 0.6; ctx.stroke(); ctx.globalAlpha = 1;
      }
      ctx.beginPath(); ctx.arc(X, Y, on ? 6.5 : 5.5, 0, 6.2832);
      ctx.fillStyle = col.accent; ctx.fill();
      ctx.lineWidth = 1.5; ctx.strokeStyle = col.surface; ctx.stroke();
    }
  }

  function roundRect(x, y, w, h, r) {
    ctx.beginPath();
    ctx.moveTo(x + r, y);
    ctx.arcTo(x + w, y, x + w, y + h, r);
    ctx.arcTo(x + w, y + h, x, y + h, r);
    ctx.arcTo(x, y + h, x, y, r);
    ctx.arcTo(x, y, x + w, y, r);
    ctx.closePath();
  }

  /* ================================================================== *
   * Panel rendering
   * ================================================================== */
  var SEP = '<span class="sep" aria-hidden="true">&middot;</span>';
  function setProbe(html) { $("probe").innerHTML = html; }

  function describePoint(i) {
    var s = stats(S.pts), p = S.pts[i];
    var bits = "<span>point <b>" + (i + 1) + "</b></span>" + SEP +
               "<span>x <b>" + p.x.toFixed(2) + "</b></span>" + SEP +
               "<span>y <b>" + p.y.toFixed(2) + "</b></span>";
    if (s.ok) {
      var res = p.y - (s.icept + s.slope * p.x);
      bits += SEP + "<span>off the line by <b>" + (res >= 0 ? "+" : "−") +
              Math.abs(res).toFixed(2) + "</b></span>";
    }
    return bits;
  }

  function render() {
    var s = stats(S.pts);

    $("sN").textContent = String(s.n);
    $("sMx").textContent = fmt(s.mx, 2);
    $("sMy").textContent = fmt(s.my, 2);
    $("sSx").textContent = fmt(s.sx, 2);
    $("sSy").textContent = fmt(s.sy, 2);
    $("sR2").textContent = s.ok ? (s.r * s.r).toFixed(2) : "—";
    $("sFit").textContent = eqText(s);

    if (s.ok) {
      $("rVal").textContent = (s.r >= 0 ? "" : "−") + Math.abs(s.r).toFixed(3);
      $("rWord").textContent = word(s.r);
      var pct = Math.abs(s.r) * 50;
      $("mFill").style.left = (s.r >= 0 ? 50 : 50 - pct) + "%";
      $("mFill").style.width = pct + "%";
    } else {
      $("rVal").textContent = "—";
      $("rWord").textContent = s.why;
      $("mFill").style.left = "50%";
      $("mFill").style.width = "0%";
    }

    var label = S.preset ? ("set " + S.preset) : "your points";
    $("pillText").textContent = label + " · n " + s.n + " · r " +
      (s.ok ? (s.r >= 0 ? "" : "−") + Math.abs(s.r).toFixed(3) : "—");

    if (S.sel >= 0) setProbe(describePoint(S.sel) + SEP + "<span>selected</span>");
    else if (S.hover >= 0) setProbe(describePoint(S.hover));
    else if (!s.ok && s.n > 0) setProbe("<span>" + s.why + "</span>");
    else if (s.n === 0) setProbe("<span>empty grid — click anywhere to start placing points</span>");
    else setProbe("<span>hover a point to inspect it</span>");

    /* chips + table active row */
    var chips = document.querySelectorAll(".chip"), t;
    for (t = 0; t < chips.length; t++) {
      chips[t].setAttribute("aria-pressed", chips[t].getAttribute("data-set") === S.preset ? "true" : "false");
    }
    var rows = document.querySelectorAll("#tbody tr");
    for (t = 0; t < rows.length; t++) {
      rows[t].setAttribute("data-on", rows[t].getAttribute("data-set") === S.preset ? "1" : "0");
    }
    $("bUndo").disabled = S.undo.length === 0;
    $("footRight").textContent = S.preset
      ? ("4 datasets · 44 points · 1 identical summary")
      : ("your own points · n " + s.n);

    draw();
  }

  function say(msg) { $("live").textContent = msg; }

  /* ================================================================== *
   * Mutations
   * ================================================================== */
  function loadSet(id) {
    var set = null, i;
    for (i = 0; i < SETS.length; i++) if (SETS[i].id === id) set = SETS[i];
    if (!set) return;
    snapshot();
    S.pts = set.x.map(function (v, k) { return { x: v, y: set.y[k] }; });
    S.preset = id; S.sel = -1; S.hover = -1; S.editRun = -2;
    $("lessonText").textContent = set.lesson;
    render();
    var s = stats(S.pts);
    say("Loaded set " + id + ", " + set.shape + ". r is " + s.r.toFixed(3) +
        ", fit " + eqText(s) + ".");
  }

  function markCustom() {
    if (S.preset === null) return;
    var from = S.preset;
    S.preset = null;
    $("lessonText").textContent = "You are editing set " + from + " now — so it is your data, not " +
      "Anscombe's. Keep an eye on the right-hand column while you move things: the summary " +
      "always follows the picture, and never the other way round.";
  }

  function addPoint(x, y) {
    snapshot(); markCustom();
    S.pts.push({ x: clampX(x), y: clampY(y) });
    S.editRun = -2;
    return S.pts.length - 1;
  }

  function removePoint(i) {
    if (i < 0 || i >= S.pts.length) return;
    snapshot(); markCustom();
    S.pts.splice(i, 1);
    S.editRun = -2;
    if (S.sel === i) S.sel = -1; else if (S.sel > i) S.sel--;
    if (S.hover === i) S.hover = -1; else if (S.hover > i) S.hover--;
  }

  function gauss() {
    var u = 0, v = 0;
    while (u === 0) u = Math.random();
    while (v === 0) v = Math.random();
    return Math.sqrt(-2 * Math.log(u)) * Math.cos(2 * Math.PI * v);
  }

  function randomCloud() {
    snapshot(); markCustom();
    var rho = (Math.random() * 1.8 - 0.9);
    var n = 18 + Math.floor(Math.random() * 12);
    var pts = [], i, z1, z2;
    for (i = 0; i < n; i++) {
      z1 = gauss(); z2 = gauss();
      pts.push({
        x: clampX(10 + 3.5 * z1),
        y: clampY(7 + 2.4 * (rho * z1 + Math.sqrt(1 - rho * rho) * z2))
      });
    }
    S.pts = pts; S.sel = -1; S.hover = -1; S.editRun = -2;
    $("lessonText").textContent = "A fresh random cloud, aimed at r ≈ " + rho.toFixed(2) +
      ". Do this a few times and you build an eye for what a given r actually looks like — " +
      "the number alone is a poor picture.";
    render();
    var rs = stats(S.pts);
    say("Random cloud of " + n + " points, r " + (rs.ok ? rs.r.toFixed(3) : "undefined") + ".");
  }

  /* ================================================================== *
   * Pointer interaction
   * ================================================================== */
  function localPos(e) {
    var r = cv.getBoundingClientRect();
    return { px: e.clientX - r.left, py: e.clientY - r.top };
  }
  function hitTest(mx, my) {
    var best = -1, bd = 15 * 15, i, dx, dy, d;
    for (i = S.pts.length - 1; i >= 0; i--) {
      dx = px(S.pts[i].x) - mx; dy = py(S.pts[i].y) - my; d = dx * dx + dy * dy;
      if (d < bd) { bd = d; best = i; }
    }
    return best;
  }

  cv.addEventListener("pointerdown", function (e) {
    if (e.button !== 0 && e.pointerType === "mouse") return;
    var m = localPos(e), hit = hitTest(m.px, m.py);
    S.kb = false;

    if ((e.altKey || e.metaKey) && hit >= 0) {
      removePoint(hit); render(); say("Point removed. " + S.pts.length + " left."); return;
    }
    if (hit < 0 && (m.px < G.L - 6 || m.px > G.L + G.w + 6 || m.py < G.T - 6 || m.py > G.T + G.h + 6)) return;

    if (hit >= 0) { S.drag = hit; S.sel = hit; S.fresh = false; }
    else { S.drag = addPoint(ux(m.px), uy(m.py)); S.sel = S.drag; S.fresh = true; }
    S.moved = false; S.editRun = -2;
    try { cv.setPointerCapture(e.pointerId); } catch (err) {}
    e.preventDefault();
    render();
  });

  cv.addEventListener("pointermove", function (e) {
    var m = localPos(e);
    if (S.drag >= 0) {
      /* one undo step per drag: a freshly added point already snapshotted on add */
      if (!S.moved && !S.fresh) snapshot();
      markCustom();
      S.pts[S.drag].x = clampX(ux(m.px));
      S.pts[S.drag].y = clampY(uy(m.py));
      S.moved = true;
      render();
    } else {
      var h = hitTest(m.px, m.py);
      cv.style.cursor = h >= 0 ? "grab" : "crosshair";
      if (h !== S.hover) { S.hover = h; render(); }
    }
  });

  function endDrag(e) {
    if (S.drag < 0) return;
    var i = S.drag;
    S.drag = -1;
    try { cv.releasePointerCapture(e.pointerId); } catch (err) {}
    var s = stats(S.pts);
    say((S.moved ? "Point moved to x " : "Point placed at x ") + S.pts[i].x.toFixed(2) +
        ", y " + S.pts[i].y.toFixed(2) + ". r is now " + (s.ok ? s.r.toFixed(3) : "undefined") + ".");
    render();
  }
  cv.addEventListener("pointerup", endDrag);
  cv.addEventListener("pointercancel", endDrag);
  cv.addEventListener("pointerleave", function () {
    if (S.drag < 0 && S.hover !== -1) { S.hover = -1; render(); }
  });

  cv.addEventListener("contextmenu", function (e) {
    var m = localPos(e), hit = hitTest(m.px, m.py);
    if (hit >= 0) {
      e.preventDefault();
      removePoint(hit); render(); say("Point removed. " + S.pts.length + " left.");
    }
  });

  /* ================================================================== *
   * Keyboard interaction
   * ================================================================== */
  cv.addEventListener("focus", function () {
    var vis = true;
    try { vis = cv.matches(":focus-visible"); } catch (err) { vis = true; }
    if (S.kb !== vis) { S.kb = vis; render(); }
  });
  cv.addEventListener("blur", function () { S.kb = false; render(); });

  var HANDLED = ["ArrowLeft", "ArrowRight", "ArrowUp", "ArrowDown", "Enter", " ", "Spacebar",
                 "n", "N", "p", "P", "Delete", "Backspace", "Escape"];

  cv.addEventListener("keydown", function (e) {
    /* never swallow a browser shortcut (ctrl/cmd/alt + key) */
    if (e.ctrlKey || e.metaKey || e.altKey) return;
    var step = e.shiftKey ? 1 : 0.25, k = e.key, dx = 0, dy = 0, used = true;
    if (HANDLED.indexOf(k) < 0) return;   /* leave Tab, typing, F-keys alone */
    S.kb = true;
    if (k === "ArrowLeft") dx = -step;
    else if (k === "ArrowRight") dx = step;
    else if (k === "ArrowUp") dy = step;
    else if (k === "ArrowDown") dy = -step;
    else if (k === "Enter" || k === " " || k === "Spacebar") {
      if (S.sel >= 0) {
        S.cx = S.pts[S.sel].x; S.cy = S.pts[S.sel].y; S.sel = -1; S.editRun = -2;
        say("Deselected. Crosshair at x " + S.cx.toFixed(2) + ", y " + S.cy.toFixed(2) + ".");
      } else {
        S.sel = addPoint(S.cx, S.cy);
        var sa = stats(S.pts);
        say("Point placed at x " + S.cx.toFixed(2) + ", y " + S.cy.toFixed(2) + ". " +
            S.pts.length + (S.pts.length === 1 ? " point" : " points") + ", r " +
            (sa.ok ? sa.r.toFixed(3) : "undefined") +
            ". It is selected: arrow keys move it, Enter drops it and frees the crosshair.");
      }
      e.preventDefault(); render(); return;
    }
    else if (k === "n" || k === "N" || k === "p" || k === "P") {
      if (!S.pts.length) { say("No points to step through."); e.preventDefault(); return; }
      var d = (k === "n" || k === "N") ? 1 : -1;
      S.sel = (S.sel < 0 ? (d > 0 ? 0 : S.pts.length - 1)
                         : (S.sel + d + S.pts.length) % S.pts.length);
      S.editRun = -2;
      var ps = S.pts[S.sel];
      say("Point " + (S.sel + 1) + " of " + S.pts.length + " selected, x " +
          ps.x.toFixed(2) + ", y " + ps.y.toFixed(2) + ". Arrow keys move it.");
      e.preventDefault(); render(); return;
    }
    else if (k === "Delete" || k === "Backspace") {
      if (S.sel >= 0) {
        removePoint(S.sel);
        say("Point removed. " + S.pts.length + " left.");
      } else say("Nothing selected. Press N to select a point.");
      e.preventDefault(); render(); return;
    }
    else if (k === "Escape") {
      if (S.sel >= 0) { S.cx = S.pts[S.sel].x; S.cy = S.pts[S.sel].y; S.sel = -1; S.editRun = -2; say("Deselected."); }
      e.preventDefault(); render(); return;
    }
    else used = false;

    if (!used) return;
    e.preventDefault();
    if (S.sel >= 0) {
      if (S.editRun !== S.sel) { snapshot(); S.editRun = S.sel; }
      markCustom();
      S.pts[S.sel].x = clampX(S.pts[S.sel].x + dx);
      S.pts[S.sel].y = clampY(S.pts[S.sel].y + dy);
      var s2 = stats(S.pts);
      say("x " + S.pts[S.sel].x.toFixed(2) + ", y " + S.pts[S.sel].y.toFixed(2) +
          ". r " + (s2.ok ? s2.r.toFixed(3) : "undefined") + ".");
    } else {
      S.cx = clampX(S.cx + dx); S.cy = clampY(S.cy + dy);
      say("Crosshair x " + S.cx.toFixed(2) + ", y " + S.cy.toFixed(2) + ". Enter to place.");
    }
    render();
  });

  /* ================================================================== *
   * Buttons
   * ================================================================== */
  $("bClear").addEventListener("click", function () {
    snapshot(); markCustom();
    S.pts = []; S.sel = -1; S.hover = -1; S.editRun = -2;
    $("lessonText").textContent = "Empty grid. Click to place points one at a time and watch r " +
      "wander — two points always give exactly ±1, and the number only starts meaning " +
      "something once there is a real cloud.";
    render(); say("Grid cleared.");
  });

  $("bRandom").addEventListener("click", randomCloud);

  $("bUndo").addEventListener("click", function () {
    var prev = S.undo.pop();
    if (!prev) return;
    S.pts = prev.pts; S.preset = prev.preset; S.sel = -1; S.hover = -1; S.editRun = -2;
    $("lessonText").textContent = prev.lesson;
    render(); say("Undone. " + S.pts.length + " points.");
  });

  function toggle(btn, key, onMsg, offMsg) {
    btn.addEventListener("click", function () {
      S[key] = !S[key];
      btn.setAttribute("aria-pressed", S[key] ? "true" : "false");
      render(); say(S[key] ? onMsg : offMsg);
    });
  }
  toggle($("bResid"), "resid",
    "Residuals shown — each dashed stub is the gap the fit is minimising.",
    "Residuals hidden.");
  toggle($("bMeans"), "means",
    "Average lines shown.", "Average lines hidden.");

  /* ================================================================== *
   * Preset chips + comparison table (built from the data, not hardcoded)
   * ================================================================== */
  var thumbs = [];

  function buildChips() {
    var host = $("chips"), html = "", i;
    for (i = 0; i < SETS.length; i++) {
      html += '<button type="button" class="chip" data-set="' + SETS[i].id +
              '" aria-pressed="false">' +
              '<canvas aria-hidden="true"></canvas>' +
              '<span class="nm">' + SETS[i].name + '</span>' +
              '<span class="sb">' + SETS[i].sub + '</span></button>';
    }
    host.innerHTML = html;
    var btns = host.querySelectorAll(".chip");
    for (i = 0; i < btns.length; i++) {
      thumbs.push(btns[i].querySelector("canvas"));
      btns[i].addEventListener("click", function () { loadSet(this.getAttribute("data-set")); });
    }
  }

  function drawThumbs() {
    var dpr = Math.min(window.devicePixelRatio || 1, 2.5);
    for (var i = 0; i < thumbs.length; i++) {
      var c = thumbs[i], k = c.getContext("2d"), set = SETS[i];
      var r = c.getBoundingClientRect();
      var W = Math.max(40, Math.round(r.width)), H = Math.max(30, Math.round(r.height));
      c.width = Math.round(W * dpr); c.height = Math.round(H * dpr);
      k.setTransform(dpr, 0, 0, dpr, 0, 0);
      var pad = 7;
      var fx = function (x) { return pad + (x - TXD[0]) / (TXD[1] - TXD[0]) * (W - 2 * pad); };
      var fy = function (y) { return pad + (1 - (y - TYD[0]) / (TYD[1] - TYD[0])) * (H - 2 * pad); };
      k.clearRect(0, 0, W, H);
      k.fillStyle = C("--surface");
      k.fillRect(0, 0, W, H);
      k.strokeStyle = C("--line"); k.lineWidth = 1;
      k.strokeRect(0.5, 0.5, W - 1, H - 1);
      var st = stats(set.x.map(function (v, j) { return { x: v, y: set.y[j] }; }));
      k.strokeStyle = C("--fit"); k.lineWidth = 1.5;
      k.beginPath();
      k.moveTo(fx(TXD[0]), fy(st.icept + st.slope * TXD[0]));
      k.lineTo(fx(TXD[1]), fy(st.icept + st.slope * TXD[1]));
      k.stroke();
      k.fillStyle = C("--accent");
      for (var j = 0; j < set.x.length; j++) {
        k.beginPath(); k.arc(fx(set.x[j]), fy(set.y[j]), 2.5, 0, 6.2832); k.fill();
      }
    }
  }

  function buildTable() {
    var body = $("tbody"), html = "", i, keys = [], allSame = true;
    for (i = 0; i < SETS.length; i++) {
      var st = stats(SETS[i].x.map(function (v, j) { return { x: v, y: SETS[i].y[j] }; }));
      var cells = [st.mx.toFixed(2), st.my.toFixed(2), st.sx.toFixed(2), st.sy.toFixed(2),
                   st.r.toFixed(2), eqText(st)];
      keys.push(cells.join("|"));
      html += '<tr data-set="' + SETS[i].id + '" data-on="0"><th scope="row">' + SETS[i].name + '</th>' +
              '<td>' + cells[0] + '</td><td>' + cells[1] + '</td><td>' + cells[2] + '</td>' +
              '<td>' + cells[3] + '</td><td>' + cells[4] + '</td><td>' + cells[5] + '</td>' +
              '<td class="shape">' + SETS[i].shape + '</td></tr>';
    }
    body.innerHTML = html;
    for (i = 1; i < keys.length; i++) if (keys[i] !== keys[0]) allSame = false;
    if (allSame) {
      $("verified").hidden = false;
      $("verifiedText").textContent = "checked in your browser · all 4 sets agree on every " +
        "column to 2 decimal places";
    }
  }

  /* ================================================================== *
   * Theme + resize
   * ================================================================== */
  window.addEventListener("message", function (e) {
    var d = e.data;
    if (d && d.type === "sloprun:theme" && (d.theme === "light" || d.theme === "dark")) {
      document.documentElement.setAttribute("data-theme", d.theme);
      draw(); drawThumbs();
    }
  });
  /* canvases hold baked-in colours, so any theme flip must repaint them — including a
     data-theme attribute set directly on <html> with no message behind it */
  if (window.MutationObserver) {
    try {
      new MutationObserver(function () { draw(); drawThumbs(); })
        .observe(document.documentElement, { attributes: true, attributeFilter: ["data-theme"] });
    } catch (err) {}
  }

  var mq = window.matchMedia("(prefers-color-scheme: dark)");
  var onScheme = function () { draw(); drawThumbs(); };
  if (mq.addEventListener) mq.addEventListener("change", onScheme);
  else if (mq.addListener) mq.addListener(onScheme);

  var raf = 0;
  function onResize() {
    if (raf) return;
    raf = requestAnimationFrame(function () { raf = 0; draw(); drawThumbs(); });
  }
  window.addEventListener("resize", onResize);
  if (window.ResizeObserver) {
    try { new ResizeObserver(onResize).observe(document.body); } catch (err) {}
  }

  /* ================================================================== *
   * Go
   * ================================================================== */
  buildChips();
  buildTable();
  render();
  drawThumbs();
  /* fonts can land after first paint and shift metrics slightly */
  if (document.fonts && document.fonts.ready && document.fonts.ready.then) {
    document.fonts.ready.then(function () { draw(); drawThumbs(); });
  }
})();
</script>
</body>
</html>