31:[] 2f:{"title":"Quadratic Regression","cells":[{"id":0,"value":"md`# Quadratic Regression\n\nQuadratic regressions take the form ${tex`y = ax^2 + bx + c`}. Use [d3-regression](https://github.com/HarryStevens/d3-regression)'s d3.[regressionQuad()](https://github.com/HarryStevens/d3-regression#regressionQuad) like this:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":16,"value":"regressionGenerator = d3.regressionQuad()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-4, 3.1]);","pinned":true,"hidden":false,"mode":"ojs"},{"id":418,"value":"md`d3.regressionQuad() returns a configurable function with x- and y- accessors (which default to d => d[0] and d => d[1], respectively). If you want the resulting line to extend beyond the extents of your input data, you can specify a domain.\n\nWhen you pass data to the regression generator, you'll get back an array of points representing a curved line. You can use a d3.[line()](https://github.com/d3/d3-shape#line) to render it in SVG or Canvas:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":118,"value":"lineGenerator = d3.line()\n .x(d => xScale(d[0]))\n .y(d => yScale(d[1]));","pinned":true,"hidden":false,"mode":"ojs"},{"id":74,"value":"chart = {\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n .style(\"overflow\", \"visible\");\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${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"},{"id":421,"value":"md`This example comes from [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/quadratic-regression). The regression is described by the equation ${tex`y = ${regressionGenerator(data).a.toFixed(3)}x^2 + ${regressionGenerator(data).b.toFixed(3)}x + ${regressionGenerator(data).c.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${regressionGenerator(data).rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":192,"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"},{"id":92,"value":"md`## Data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2,"value":"data = [{x: -3, y: 7.5}, {x: -2, y: 3}, {x: -1, y: 0.5}, {x: 0, y: 1}, {x: 1, y: 3}, {x: 2, y: 6}, {x: 3, y: 14}]","pinned":false,"hidden":false,"mode":"ojs"},{"id":75,"value":"md`## Dimensions`","pinned":false,"hidden":false,"mode":"ojs"},{"id":78,"value":"margin = ({left: 30, right: 9, top: 20, bottom: 21})","pinned":false,"hidden":false,"mode":"ojs"},{"id":80,"value":"base = Math.min(width, 400)","pinned":false,"hidden":false,"mode":"ojs"},{"id":81,"value":"innerWidth = base - margin.left - margin.right","pinned":false,"hidden":false,"mode":"ojs"},{"id":83,"value":"innerHeight = base - margin.top - margin.bottom","pinned":false,"hidden":false,"mode":"ojs"},{"id":86,"value":"md`## Scales`","pinned":false,"hidden":false,"mode":"ojs"},{"id":98,"value":"xScale = d3.scaleLinear()\n .domain([-4, 4])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs"},{"id":100,"value":"yScale = d3.scaleLinear()\n .domain([-2, 14])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs"},{"id":102,"value":"md`## Axes`","pinned":false,"hidden":false,"mode":"ojs"},{"id":104,"value":"xAxisGenerator = d3.axisBottom(xScale)\n .tickSize(innerHeight + 10)","pinned":false,"hidden":false,"mode":"ojs"},{"id":106,"value":"yAxisGenerator = d3.axisLeft(yScale)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"md`## Styles`","pinned":false,"hidden":false,"mode":"ojs"},{"id":96,"value":"style = html`\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":90,"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). To curve the regression line between points, I used [d3-shape](https://github.com/d3/d3-selection). 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"},{"id":88,"value":"d3 = require(\"d3-axis@3\", \"d3-regression@2\", \"d3-scale@4\", \"d3-shape@3\", \"d3-selection@3\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":146,"value":"md`## References\n\n- [EasyCalculation.com](https://www.easycalculation.com/statistics/learn-quadratic-regression.php)\n- [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/quadratic-regression)\n- [Arizona Department of Health Services](https://www.azdhs.gov/documents/preparedness/state-laboratory/lab-licensure-certification/technical-resources/calibration-training/12-quadratic-least-squares-regression-calib.pdf)\n`","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}