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Monte Carlo Regression - Revision history
2026-04-20T21:12:08Z
Revision history for this page on the wiki
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Wikiroot at 14:57, 29 August 2025
2025-08-29T14:57:37Z
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Wikiroot
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Wikiroot: Replaced content with "{{#widget:Monte_Carlo_Regression}}"
2025-08-28T19:39:17Z
<p>Replaced content with "{{#widget:Monte_Carlo_Regression}}"</p>
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Wikiroot
https://euler.vaniercollege.qc.ca/gwikis/pwiki/index.php?title=Monte_Carlo_Regression&diff=1343&oldid=prev
Wikiroot: Created page with "<style> body { font-family: Arial, sans-serif; margin: 40px; text-align: center; } .input-grid { display: grid; grid-template-columns: repeat(3, 1fr); gap: 15px; max-width: 900px; margin: 0 auto 30px; } .input-grid strong { font-size: 16px; grid-column: span 3; text-align: left; padding-top: 10px; } input[type="text"] { padding: 8px; font-size: 14px; widt..."
2025-08-28T19:38:17Z
<p>Created page with "<style> body { font-family: Arial, sans-serif; margin: 40px; text-align: center; } .input-grid { display: grid; grid-template-columns: repeat(3, 1fr); gap: 15px; max-width: 900px; margin: 0 auto 30px; } .input-grid strong { font-size: 16px; grid-column: span 3; text-align: left; padding-top: 10px; } input[type="text"] { padding: 8px; font-size: 14px; widt..."</p>
<p><b>New page</b></p><div><style><br />
body {<br />
font-family: Arial, sans-serif;<br />
margin: 40px;<br />
text-align: center;<br />
}<br />
.input-grid {<br />
display: grid;<br />
grid-template-columns: repeat(3, 1fr);<br />
gap: 15px;<br />
max-width: 900px;<br />
margin: 0 auto 30px;<br />
}<br />
.input-grid strong {<br />
font-size: 16px;<br />
grid-column: span 3;<br />
text-align: left;<br />
padding-top: 10px;<br />
}<br />
input[type="text"] {<br />
padding: 8px;<br />
font-size: 14px;<br />
width: 100%;<br />
}<br />
button {<br />
padding: 10px 20px;<br />
margin: 10px;<br />
font-size: 16px;<br />
background-color: #4CAF50;<br />
color: white;<br />
border: none;<br />
border-radius: 4px;<br />
cursor: pointer;<br />
}<br />
button:hover {<br />
background-color: #45a049;<br />
}<br />
#plot {<br />
width: 100%;<br />
height: 75vh;<br />
}<br />
<br />
</style><br />
<br />
<div class="my-widget-container"><br />
<h1>Monte Carlo Linear Regression with Confidence Band</h1><br />
<p>Paste your data from Excel into the boxes below. Includes both x and y errors.</p><br />
<br />
<div class="input-grid"><br />
<div><strong>Axis Labels</strong></div><div></div><div></div><br />
<div style="grid-column: span 3;"><br />
<p>You can use HTML like <code>&lt;sub&gt;</code> and <code>&lt;sup&gt;</code> (e.g., H&lt;sub&gt;2&lt;/sub&gt;O → H<sub>2</sub>O).</p><br />
</div><br />
<input type="text" id="xLabel" placeholder="X Axis Label"><br />
<input type="text" id="yLabel" placeholder="Y Axis Label"><br />
<div></div><br />
<br />
<div><strong>X Values</strong></div><div></div><div></div><br />
<input type="text" id="xValues" placeholder="X Values (space-separated)"><br />
<input type="text" id="xErrors" placeholder="X Errors (optional)"><br />
<div></div><br />
<br />
<div><strong>Y Values</strong></div><div></div><div></div><br />
<input type="text" id="yValues" placeholder="Y Values"><br />
<input type="text" id="yErrors" placeholder="Y Errors (optional)"><br />
<div></div><br />
</div><br />
<br />
<button onclick="plotData()">Plot</button><br />
<button onclick="downloadPlot()">Download Chart</button><br />
<div id="plot"></div><br />
<br />
</div><br />
<br />
<script><br />
function parseValues(id) {<br />
const val = document.getElementById(id).value.trim();<br />
return val === "" ? [] : val.split(/\s+/).map(Number);<br />
}<br />
<br />
function plotData() {<br />
const x = parseValues('xValues');<br />
const y = parseValues('yValues');<br />
const xErr = parseValues('xErrors');<br />
const yErr = parseValues('yErrors');<br />
const xLabel = document.getElementById('xLabel').value || 'X Axis';<br />
const yLabel = document.getElementById('yLabel').value || 'Y Axis';<br />
<br />
if (x.length !== y.length) {<br />
alert('X and Y values must be the same length.');<br />
return;<br />
}<br />
<br />
const N = 10000;<br />
const slopes = [], intercepts = [];<br />
<br />
function randn_bm() {<br />
let u = 0, v = 0;<br />
while (u === 0) u = Math.random();<br />
while (v === 0) v = Math.random();<br />
return Math.sqrt(-2.0 * Math.log(u)) * Math.cos(2.0 * Math.PI * v);<br />
}<br />
<br />
function linregress(xs, ys) {<br />
const n = xs.length;<br />
const xMean = xs.reduce((a, b) => a + b, 0) / n;<br />
const yMean = ys.reduce((a, b) => a + b, 0) / n;<br />
let num = 0, den = 0;<br />
for (let i = 0; i < n; i++) {<br />
num += (xs[i] - xMean) * (ys[i] - yMean);<br />
den += (xs[i] - xMean) ** 2;<br />
}<br />
const slope = num / den;<br />
const intercept = yMean - slope * xMean;<br />
return { slope, intercept };<br />
}<br />
<br />
for (let i = 0; i < N; i++) {<br />
const xSim = x.map((xi, j) => xi + randn_bm() * (xErr[j] || 0));<br />
const ySim = y.map((yi, j) => yi + randn_bm() * (yErr[j] || 0));<br />
const { slope, intercept } = linregress(xSim, ySim);<br />
if (isFinite(slope) && isFinite(intercept)) {<br />
slopes.push(slope);<br />
intercepts.push(intercept);<br />
}<br />
}<br />
<br />
const xRange = [];<br />
const xmin = Math.min(...x), xmax = Math.max(...x);<br />
const steps = 100;<br />
const step = (xmax - xmin) / steps;<br />
for (let i = 0; i <= steps; i++) {<br />
xRange.push(xmin + i * step);<br />
}<br />
<br />
const lower = [], upper = [], meanLine = [];<br />
for (let xi of xRange) {<br />
const ySamples = slopes.map((m, i) => m * xi + intercepts[i]);<br />
ySamples.sort((a, b) => a - b);<br />
const lo = ySamples[Math.floor(0.025 * ySamples.length)];<br />
const hi = ySamples[Math.floor(0.975 * ySamples.length)];<br />
const avg = ySamples.reduce((a, b) => a + b, 0) / ySamples.length;<br />
lower.push(lo);<br />
upper.push(hi);<br />
meanLine.push(avg);<br />
}<br />
<br />
const mean = arr => arr.reduce((a, b) => a + b, 0) / arr.length;<br />
const std = arr => {<br />
const m = mean(arr);<br />
return Math.sqrt(arr.reduce((s, v) => s + (v - m) ** 2, 0) / (arr.length - 1));<br />
};<br />
const slopeStat = { mean: mean(slopes), std: std(slopes) };<br />
const interceptStat = { mean: mean(intercepts), std: std(intercepts) };<br />
<br />
const annotationText = `y = (${slopeStat.mean.toExponential(3)} ± ${slopeStat.std.toExponential(3)})x + (${interceptStat.mean.toExponential(3)} ± ${interceptStat.std.toExponential(3)})`;<br />
<br />
const data = [];<br />
<br />
// Original data points with error bars<br />
data.push({<br />
x: x,<br />
y: y,<br />
mode: 'markers',<br />
type: 'scatter',<br />
name: 'Data',<br />
marker: { color: 'black', size: 7, symbol: 'x-thin-open' },<br />
error_x: xErr.length === x.length ? {<br />
type: 'data',<br />
array: xErr,<br />
visible: true<br />
} : undefined,<br />
error_y: yErr.length === y.length ? {<br />
type: 'data',<br />
array: yErr,<br />
visible: true<br />
} : undefined<br />
});<br />
<br />
// Confidence band<br />
data.push({<br />
x: [...xRange, ...xRange.slice().reverse()],<br />
y: [...upper, ...lower.slice().reverse()],<br />
fill: 'toself',<br />
fillcolor: 'rgba(255, 0, 0, 0.2)',<br />
line: { color: 'transparent' },<br />
name: '95% Confidence Band',<br />
type: 'scatter',<br />
showlegend: false<br />
});<br />
<br />
// Mean regression line<br />
data.push({<br />
x: xRange,<br />
y: meanLine,<br />
mode: 'lines',<br />
type: 'scatter',<br />
name: 'Mean Fit',<br />
line: { color: 'red', width: 2 }<br />
});<br />
<br />
const layout = {<br />
title: '',<br />
xaxis: { title: xLabel },<br />
yaxis: { title: yLabel },<br />
showlegend: false,<br />
annotations: [{<br />
x: 0.05,<br />
y: 0.95,<br />
xref: 'paper',<br />
yref: 'paper',<br />
text: annotationText,<br />
showarrow: false,<br />
font: { color: 'black', size: 14 }<br />
}]<br />
};<br />
<br />
Plotly.newPlot('plot', data, layout);<br />
}<br />
<br />
function downloadPlot() {<br />
Plotly.downloadImage('plot', { format: 'png', filename: 'monte_carlo_regression' });<br />
}<br />
<br />
</script></div>
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