2d:null 2e:["$","title",null,{"children":"Sigmoidal Regression | Harry Stevens | Observable"}] 33:[] 31:{"id":"1f1e488c4a1c6e84","slug":"sigmoidal-regression","title":"Sigmoidal Regression","thumbnail":"7f16d239a88597be61a41d9c7cce801765df1d301be22a1b86ea5a124d6e973e","access_level":"public","create_time":"$D2026-07-06T14:18:56.424Z","update_time":"$D2026-07-06T23:55:08.807Z","view_time":null,"first_public_time":"$D2026-07-06T14:20:50.773Z","has_unpublished_edits":null,"fork":{"id":"029483e7d788c317","slug":"logistic-regression","title":"Logistic Regression","owner":{"id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens"}},"stars":0,"starred":false,"owner":{"type":"team","id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":"starter_2024"},"version":343,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":null}],"members":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":null,"role":"editor"},{"type":"team","id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":"starter_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"5c8e3662c8f2381d","slug":"d3-regression","title":"d3-regression","owner":{"id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens"}},"type":"notebook","body":{"title":"Sigmoidal Regression","cells":[{"id":0,"value":"md`# Sigmoidal Regression\n\nSigmoidal regressions take the form ${tex`y = a + \\frac{b}{1 + e^{-c(x - d)}}`}. Use [d3-regression](https://github.com/HarryStevens/d3-regression)'s d3.[regressionLogistic()](https://github.com/HarryStevens/d3-regression#regressionLogistic) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"regressionGenerator = d3.regressionSigmoidal()\n .x(d => d.x)\n .y(d => d.y);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":315,"value":"result = regressionGenerator(data)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":221,"value":"md`d3.regressionSigmoidal() returns a configurable function with x- and y- accessors (which default to d => d[0] and d => d[1], respectively). If you want the resulting line to extend beyond the extents of your input data, you can specify a domain.\n\nWhen you pass data to the regression generator, you'll get back an array of points representing a curved line. You can use a d3.[line()](https://github.com/d3/d3-shape#line) to render it in SVG or Canvas:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"lineGenerator = d3.line()\n .x(d => xScale(d[0]))\n .y(d => yScale(d[1]));","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":92,"value":"{\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${margin.left}, ${margin.top})`)\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisGenerator)\n .selectAll(\".tick line\")\n .classed(\"baseline\", d => d === 0);\n \n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisGenerator)\n .selectAll(\".tick line\")\n .classed(\"baseline\", d => d === 0);\n\n g.selectAll(\"circle\")\n .data(data)\n .enter().append(\"circle\")\n .attr(\"r\", 3)\n .attr(\"cx\", d => xScale(d.x))\n .attr(\"cy\", d => yScale(d.y))\n \n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(regressionGenerator(data))\n .attr(\"d\", lineGenerator);\n\n return svg.node()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"md`The regression shown above is described by the equation ${tex`y = ${result.a.toFixed(3)} + \\frac{${result.b.toFixed(3)}}{1 + e^{-${result.c.toFixed(3)}(x - ${result.d.toFixed(3)})}}`}. The coefficient of determination, or ${tex`R^2`}, is ${result.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"md`[**d3-regression**](https://github.com/harrystevens/d3-regression) is a [D3.js](https://d3js.org/) module for calculating statistical regressions from two-dimensional data. It is dependency-free, and its API exposes configurable functions that transform input data, in the manner of other D3 modules.\n\nFor an explanation of all of d3-regression's capabilities, see [this tutorial](https://observablehq.com/d/7b51129a2feec1d0).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"md`## Data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"data = [\n {x: -6, y: 20.1},\n {x: -5, y: 17.6},\n {x: -4, y: 22.8},\n {x: -3, y: 24.2},\n {x: -2, y: 36.9},\n {x: -1, y: 47.3},\n {x: 0, y: 74.8},\n {x: 1, y: 88.2},\n {x: 2, y: 109.5},\n {x: 3, y: 111.1},\n {x: 4, y: 120.8},\n {x: 5, y: 116.9},\n {x: 6, y: 121.7}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"md`## Dimensions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"margin = ({left: 29, right: 8, top: 11, bottom: 26});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"base = Math.min(width, 400)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"innerWidth = base - margin.left - margin.right;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"innerHeight = base - margin.top - margin.bottom;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"md`## Scales`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":46,"value":"xScale = d3.scaleLinear()\n .domain(d3.extent(data, d => d.x))\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"yScale = d3.scaleLinear()\n .domain(d3.extent(data, d => d.y))\n .range([innerHeight, 0])\n .nice();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"md`## Axes`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"xAxisGenerator = d3.axisBottom(xScale)\n .tickSize(innerHeight + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"yAxisGenerator = d3.axisLeft(yScale)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"md`## Styles`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"html`\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"md`## Imports\n\nTo make the scatterplot, I used [d3-axis](https://github.com/d3/d3-axis), [d3-scale](https://github.com/d3/d3-scale), and [d3-selection](https://github.com/d3/d3-selection), and [d3-shape](https://github.com/d3/d3-shape). I also am loading [d3-regression](https://github.com/HarryStevens/d3-regression) with the rest of the D3.js modules.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"d3 = require(\"d3-array@3\", \"d3-axis@3\", \"d3-regression@2\", \"d3-scale@4\", \"d3-shape@3\", \"d3-selection@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 32:"$31:body"