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2f:{"id":"7b51129a2feec1d0","slug":"introducing-d3-regression","title":"Introducing d3-regression","thumbnail":"ad197e2e8eb5f9941be2886e71752dc89c1f877dfafd696d47b85e39606e516e","access_level":"public","create_time":"$D2019-03-26T13:24:07.721Z","update_time":"$D2026-07-10T16:27:31.413Z","view_time":null,"first_public_time":"$D2019-04-08T13:32:39.854Z","fork":false,"stars":121,"starred":false,"owner":{"type":"team","id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":"starter_2024"},"version":1357,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":null}],"members":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":60,"collection":{"id":"5c8e3662c8f2381d","slug":"d3-regression","title":"d3-regression","owner":{"id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens"}},"type":"notebook","body":{"title":"Introducing d3-regression","cells":[{"id":0,"value":"md`# Introducing d3-regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":258,"value":"md`[**d3-regression**](https://github.com/harrystevens/d3-regression) is a [D3.js](https://d3js.org/) module for calculating statistical regressions from two-dimensional data. It is dependency-free, and its API exposes configurable functions that transform input data, in the manner of other D3 modules.\n\nd3-regression can currently do the following types of regressions:\n- [Linear](#linear)\n- [Quadratic](#quadratic)\n- [Polynomial](#polynomial)\n- [Exponential](#exponential)\n- [Logarithmic](#logarithmic)\n- [Power law](#power)\n- [LOESS](#loess)\n- [Logistic](#logistic)\n- [Sigmoidal](#sigmoidal)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":179,"value":"linear = md`## Linear\n\nLinear regressions take the form ${tex`y = ax + b`}. Use d3.[regressionLinear()](https://github.com/HarryStevens/d3-regression#regressionLinear) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":58,"value":"linearRegression = d3.regressionLinear()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-1.7, 16]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":986,"value":"md`d3-regression's methods return configurable functions with x- and y- accessors (which default to d => d[0] and d => d[1], respectively). If you want the resulting line to extend beyond the extents of your input data, each generator (besides [LOESS](#loess)) lets you specify a domain.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":63,"value":"{\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${margin.left}, ${margin.top})`);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisLinear)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d == 0);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisLinear)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d == 0);\n\n g.selectAll(\"circle\")\n .data(dataLinear)\n .enter().append(\"circle\")\n .attr(\"r\", 3)\n .attr(\"cx\", d => xScaleLinear(d.x))\n .attr(\"cy\", d => yScaleLinear(d.y));\n\n g.append(\"line\")\n .attr(\"class\", \"regression\")\n .datum(resultLinear)\n .attr(\"x1\", d => xScaleLinear(d[0][0]))\n .attr(\"x2\", d => xScaleLinear(d[1][0]))\n .attr(\"y1\", d => yScaleLinear(d[0][1]))\n .attr(\"y2\", d => yScaleLinear(d[1][1]));\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":636,"value":"md`The regression shown above is described by the equation ${tex`y = ${resultLinear.a.toFixed(3)}x + ${resultLinear.b.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultLinear.rSquared.toFixed(3)}. This example comes from [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/line-of-best-fit).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":642,"value":"xScaleLinear = d3.scaleLinear()\n .domain([-4, 16])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":644,"value":"yScaleLinear = d3.scaleLinear()\n .domain([-4, 16])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":795,"value":"xAxisLinear = d3.axisBottom(xScaleLinear)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":797,"value":"yAxisLinear = d3.axisLeft(yScaleLinear)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1243,"value":"resultLinear = linearRegression(dataLinear)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":639,"value":"dataLinear = [{x: 8, y: 3}, {x: 2, y: 10}, {x: 11, y: 3}, {x: 6, y: 6}, {x: 5, y: 8}, {x: 4, y: 12}, {x: 12, y: 1}, {x: 9, y: 4}, {x: 6, y: 9}, {x: 1, y: 14}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":181,"value":"quadratic = md`## Quadratic\n\nQuadratic regressions take the form ${tex`y = ax^2 + bx + c`}. Use d3.[regressionQuad()](https://github.com/HarryStevens/d3-regression#regressionQuad) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"quadraticRegression = d3.regressionQuad()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-4, 4]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":963,"value":"md`When you pass data to the regression generator, you'll get back an array of points representing a curved line. You can use d3.[line()](https://github.com/d3/d3-shape#line) to render it in SVG or Canvas:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":674,"value":"lineGenerator = d3.line()\n .x(d => xScaleQuadratic(d[0]))\n .y(d => yScaleQuadratic(d[1]));","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":661,"value":"md`The regression shown below is described by the equation ${tex`y = ${resultQuadratic.a.toFixed(3)}x^2 + ${resultQuadratic.b.toFixed(3)}x + ${resultQuadratic.c.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultQuadratic.rSquared.toFixed(3)}. This example is from [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/quadratic-regression). `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1301,"value":"chart(xAxisQuadratic, yAxisQuadratic, dataQuadratic, resultQuadratic, xScaleQuadratic, yScaleQuadratic, lineGenerator)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":668,"value":"xScaleQuadratic = d3.scaleLinear()\n .domain([-4, 4])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":670,"value":"yScaleQuadratic = d3.scaleLinear()\n .domain([-2, 14])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":772,"value":"xAxisQuadratic = d3.axisBottom(xScaleQuadratic)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":775,"value":"yAxisQuadratic = d3.axisLeft(yScaleQuadratic)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1248,"value":"resultQuadratic = quadraticRegression(dataQuadratic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":663,"value":"dataQuadratic = [{x: -3, y: 7.5}, {x: -2, y: 3}, {x: -1, y: 0.5}, {x: 0, y: 1}, {x: 1, y: 3}, {x: 2, y: 6}, {x: 3, y: 14}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1012,"value":"polynomial = md`## Polynomial\n\nPolynomial regressions take the form ${tex`y = a_nx^n + … + a_1x + a_0`}, where ${tex`n`} is the order of the polynomial. Use d3.[regressionPoly()](https://github.com/harrystevens/d3-regression#regressionPoly) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1018,"value":"polynomialRegression = d3.regressionPoly()\n .x(d => d.x)\n .y(d => d.y)\n .order(3);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1051,"value":"md`I've specified an order above just to show how it works, but order defaults to 3 (i.e. a cubic regression), so that line of code is unnecessary. If order is set to 4, the regression generator will perform a fourth-degree polynomial regression. Likewise, if order is set to 2, the regression generator will perform a quadratic regression.\n\nBe careful about attempting to fit your data with higher order polynomials; though the regression line will fit your data with a high determination coefficient, it will likely have little predictive power for data outside of your domain.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1020,"value":"chart(xAxisPolynomial, yAxisPolynomial, dataPolynomial, resultPolynomial, xScalePolynomial, yScalePolynomial, linePolynomial)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1053,"value":"md`The regression shown above is described by the equation ${tex`y = ${resultPolynomial.coefficients.slice().reverse().map((d, i, arr) => {\n const deg = arr.length - i - 1;\n return d.toFixed(2) + (deg > 0 ? \"x\" : \"\") + (deg > 1 ? `^{${deg}}` : \"\");\n}).join(\"+\")}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultPolynomial.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1025,"value":"xScalePolynomial = d3.scaleLinear()\n .domain([0, 8])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1028,"value":"yScalePolynomial = d3.scaleLinear()\n .domain([140, 180])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1031,"value":"linePolynomial = d3.line()\n .x(d => xScalePolynomial(d[0]))\n .y(d => yScalePolynomial(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1035,"value":"xAxisPolynomial = d3.axisBottom(xScalePolynomial)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1038,"value":"yAxisPolynomial = d3.axisLeft(yScalePolynomial)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1253,"value":"resultPolynomial = polynomialRegression(dataPolynomial)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1022,"value":"dataPolynomial = [{\"x\":0,\"y\":140},{\"x\":1,\"y\":149},{\"x\":2,\"y\":159.6},{\"x\":3,\"y\":159},{\"x\":4,\"y\":155.9},{\"x\":5,\"y\":169},{\"x\":6,\"y\":162.9},{\"x\":7,\"y\":169},{\"x\":8,\"y\":180}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":465,"value":"exponential = md`## Exponential\n\nExponential regressions take the form ${tex`y = ae^{bx}`}, where ${tex`e`} is [Euler's number](https://en.wikipedia.org/wiki/Eulers_number). Use d3.[regressionExp()](https://github.com/HarryStevens/d3-regression#regressionExp) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":486,"value":"exponentialRegression = d3.regressionExp()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-2, 5.06]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":682,"value":"md`The below example comes from [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/exponential-regression). The regression is described by the equation ${tex`y = ${resultExponential.a.toFixed(3)}e^{${resultExponential.b.toFixed(3)}x}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultExponential.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":534,"value":"chart(xAxisExponential, yAxisExponential, dataExponential, resultExponential, xScaleExponential, yScaleExponential, lineExponential)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":684,"value":"xScaleExponential = d3.scaleLinear()\n .domain([-2, 10])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":686,"value":"yScaleExponential = d3.scaleLinear()\n .domain([-10, 100])\n .range([innerHeight, 0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":691,"value":"lineExponential = d3.line()\n .x(d => xScaleExponential(d[0]))\n .y(d => yScaleExponential(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":761,"value":"xAxisExponential = d3.axisBottom(xScaleExponential)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":765,"value":"yAxisExponential = d3.axisLeft(yScaleExponential)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1258,"value":"resultExponential = exponentialRegression(dataExponential)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":688,"value":"dataExponential = [{x: 0, y: 3}, {x: 1, y: 7}, {x: 2, y: 10}, {x: 3, y: 24}, {x: 4, y: 50}, {x: 5, y: 95}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":697,"value":"logarithmic = md`## Logarithmic\n\nLogarithmic regressions take the form ${tex`y = a{\\cdot} {\\ln}(x) + b`}. Use d3.[regressionLog()](https://github.com/HarryStevens/d3-regression#regressionLog) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":699,"value":"logarithmicRegression = d3.regressionLog()\n .x(d => d.x)\n .y(d => d.y)\n .domain([.81, 35]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":704,"value":"md`The below example comes from [PTC](http://support.ptc.com/help/mathcad/en/index.html#page/PTC_Mathcad_Help%2Fexample_logarithmic_regression.html%23). The regression is described by the equation ${tex`y = ${resultLogarithmic.a.toFixed(3)} {\\cdot} {\\ln}(x) + ${resultLogarithmic.b.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultLogarithmic.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":715,"value":"chart(xAxisLogarithmic, yAxisLogarithmic, dataLogarithmic, resultLogarithmic, xScaleLogarithmic, yScaleLogarithmic, lineLogarithmic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":708,"value":"xScaleLogarithmic = d3.scaleLinear()\n .domain([0, 35])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":710,"value":"yScaleLogarithmic = d3.scaleLinear()\n .domain([4, 8])\n .range([innerHeight, 0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":712,"value":"lineLogarithmic = d3.line()\n .x(d => xScaleLogarithmic(d[0]))\n .y(d => yScaleLogarithmic(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":752,"value":"xAxisLogarithmic = d3.axisBottom(xScaleLogarithmic)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":755,"value":"yAxisLogarithmic = d3.axisLeft(yScaleLogarithmic)\n .tickSize(innerWidth + 10)\n .tickValues(d3.range(4, 9))\n .tickFormat(d => d)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1127,"value":"resultLogarithmic = logarithmicRegression(dataLogarithmic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":706,"value":"dataLogarithmic = [{x: 1, y: 4.181}, {x: 2, y: 4.665}, {x: 3, y: 5.296}, {x: 4, y: 5.365}, {x: 5, y: 5.448}, {x: 6, y: 5.744}, {x: 7, y: 5.653}, {x: 8, y: 5.844}, {x: 9, y: 6.362}, {x: 10, y: 6.38}, {x: 11, y: 6.311}, {x: 12, y: 6.457}, {x: 13, y: 6.479}, {x: 14, y: 6.59}, {x: 15, y: 6.74}, {x: 16, y: 6.58}, {x: 17, y: 6.852}, {x: 18, y: 6.531}, {x: 19, y: 6.682}, {x: 20, y: 7.013}, {x: 21, y: 6.82}, {x: 22, y: 6.647}, {x: 23, y: 6.951}, {x: 24, y: 7.121}, {x: 25, y: 7.143}, {x: 26, y: 6.914}, {x: 27, y: 6.941}, {x: 28, y: 7.226}, {x: 29, y: 6.898}, {x: 30, y: 7.392}, {x: 31, y: 6.938}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":893,"value":"power = md`## Power law\n\nPower law regressions take the form ${tex`y = ax^b`}. Use d3.[regressionPow()](https://github.com/HarryStevens/d3-regression#regressionPow) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":898,"value":"powerRegression = d3.regressionPow()\n .x(d => d.rank)\n .y(d => d.sales);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":915,"value":"md`The below example comes from [\"Power Law in Popular Media\"](https://medium.com/@michaeltauberg/power-law-in-popular-media-7d7efef3fb7c) by Michael Tauberg. The regression is described by the equation ${tex`y = ${resultPower.a.toFixed(3)}x^{${resultPower.b.toFixed(3)}}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultPower.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":917,"value":"chart(xAxisPower, yAxisPower, dataPower, resultPower, xScalePower, yScalePower, linePower, \"rank\", \"sales\", 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":905,"value":"xScalePower = d3.scaleLinear()\n .domain([0, 5e3])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":907,"value":"yScalePower = d3.scaleLinear()\n .domain([100, 0])\n .range([0, innerHeight])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":909,"value":"xAxisPower = d3.axisBottom(xScalePower)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(0, 6e3, 1e3))\n .tickFormat(d => d >= 1e3 ? `${d / 1e3}k` : d)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":911,"value":"yAxisPower = d3.axisLeft(yScalePower)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":913,"value":"linePower = d3.line()\n .x(d => xScalePower(d[0]))\n .y(d => yScalePower(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1263,"value":"resultPower = powerRegression(dataPower)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":902,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":189,"value":"loess = md`## LOESS\n\nd3-regression's implementation of the LOESS regression was adapted with very little modification from Jason Davies's [science.js](https://github.com/jasondavies/science.js), with the main difference that this API returns a configurable function with x- and y-accessors similar to other D3.js modules.\n\nUse d3.[regressionLoess()](https://github.com/HarryStevens/d3-regression#regressionLoess) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":160,"value":"loessRegression = d3.regressionLoess()\n .x(d => d.year)\n .y(d => d.temperature)\n .bandwidth(bandwidth);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":721,"value":"md`The chart below displays the average annual temperature in California from 1900 to 2017. You can [download the data from NOAA](https://www.ncdc.noaa.gov/cag/statewide/time-series). A prettier version of this chart was published in Axios on Nov. 15, 2018, under the headline [\"Humans are a wildfire threat multiplier\"](https://www.axios.com/humans-are-a-wildfire-threat-multiplier-f8f9afb3-a91f-449e-af10-9fa2011a8f81.html).\n\nAdjust the slider below to see how the smoothing line changes with the bandwidth, also called the \"smoothing parameter,\" which is the fraction of all points used to calculate each local fit. Higher bandwidths produce smoother lines, and vice versa.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":723,"value":"viewof bandwidth = Inputs.range([.02, 1], {\n label: \"Bandwidth\",\n step: .01,\n value: .25\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":55,"value":"chart(xAxisLoess, yAxisLoess, dataLoess, resultLoess, xScaleLoess, yScaleLoess, lineLoess, \"year\", \"temperature\", 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":732,"value":"xScaleLoess = d3.scaleLinear()\n .domain([1900, 2020])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":736,"value":"yScaleLoess = d3.scaleLinear()\n .domain([55, 62])\n .range([innerHeight, 0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":739,"value":"lineLoess = d3.line()\n .x(d => xScaleLoess(d[0]))\n .y(d => yScaleLoess(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":741,"value":"xAxisLoess = d3.axisBottom(xScaleLoess)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(1900, 2040, 20))\n .tickFormat(d => d % 100 === 0 ? d : \"`\" + d.toString().slice(2, 4))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":745,"value":"yAxisLoess = d3.axisLeft(yScaleLoess)\n .tickSize(innerWidth + 10)\n .tickValues(d3.range(55, 63))\n .tickFormat(d => d);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1268,"value":"resultLoess = loessRegression(dataLoess)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":728,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1100,"value":"logistic = md`## Logistic\n\nLogistic regressions take the form ${tex`y = \\frac{a}{1 + e^{-b(x - c)}}`}. Use d3.[regressionLogistic()](https://github.com/HarryStevens/d3-regression#regressionLogistic) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1104,"value":"logisticRegression = d3.regressionLogistic()\n .x(d => d.x)\n .y(d => d.y);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1133,"value":"md`The regression shown below is described by the equation ${tex`y = \\frac{${resultLogistic.a.toFixed(3)}}{1 + e^{-${resultLogistic.b.toFixed(3)}(x - ${resultLogistic.c.toFixed(3)})}}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultLogistic.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1146,"value":"chart(xAxisLogistic, yAxisLogistic, dataLogistic, resultLogistic, xScaleLogistic, yScaleLogistic, lineLogistic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1148,"value":"xScaleLogistic = d3.scaleLinear()\n .domain(d3.extent(dataLogistic, d => d.x))\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1152,"value":"yScaleLogistic = d3.scaleLinear()\n .domain(d3.extent(dataLogistic, d => d.y))\n .range([innerHeight, 0])\n .nice();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1174,"value":"lineLogistic = d3.line()\n .x(d => xScaleLogistic(d[0]))\n .y(d => yScaleLogistic(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1162,"value":"xAxisLogistic = d3.axisBottom(xScaleLogistic)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(-6, 8, 2))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1168,"value":"yAxisLogistic = d3.axisLeft(yScaleLogistic)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1120,"value":"resultLogistic = logisticRegression(dataLogistic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1106,"value":"dataLogistic = [\n {x: -6, y: 0.9},\n {x: -5, y: 0.7},\n {x: -4, y: 3.8},\n {x: -3, y: 5.9},\n {x: -2, y: 17.4},\n {x: -1, y: 28.6},\n {x: 0, y: 55.8},\n {x: 1, y: 69.1},\n {x: 2, y: 89.7},\n {x: 3, y: 91.5},\n {x: 4, y: 99.4},\n {x: 5, y: 96.8},\n {x: 6, y: 101.2}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1182,"value":"sigmoidal = md`## Sigmoidal\n\nSigmoidal regressions take the form ${tex`y = a + \\frac{b}{1 + e^{-c(x - d)}}`}. Use d3.[regressionSigmoidal()](https://github.com/HarryStevens/d3-regression#regressionSigmoidal) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1190,"value":"sigmoidalRegression = d3.regressionSigmoidal()\n .x(d => d.x)\n .y(d => d.y);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1224,"value":"chart(xAxisSigmoidal, yAxisSigmoidal, dataSigmoidal, resultSigmoidal, xScaleSigmoidal, yScaleSigmoidal, lineSigmoidal)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1209,"value":"md`The regression shown below is described by the equation ${tex`y = ${resultSigmoidal.a.toFixed(3)} + \\frac{${resultSigmoidal.b.toFixed(3)}}{1 + e^{-${resultSigmoidal.c.toFixed(3)}(x - ${resultSigmoidal.d.toFixed(3)})}}`}. The coefficient of determination, or ${tex`R^2`}, is ${resultSigmoidal.rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1222,"value":"xScaleSigmoidal = d3.scaleLinear()\n .domain(d3.extent(dataSigmoidal, d => d.x))\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1220,"value":"yScaleSigmoidal = d3.scaleLinear()\n .domain(d3.extent(dataSigmoidal, d => d.y))\n .range([innerHeight, 0])\n .nice();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1218,"value":"lineSigmoidal = d3.line()\n .x(d => xScaleSigmoidal(d[0]))\n .y(d => yScaleSigmoidal(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1216,"value":"xAxisSigmoidal = d3.axisBottom(xScaleSigmoidal)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(-6, 8, 2))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1214,"value":"yAxisSigmoidal = d3.axisLeft(yScaleSigmoidal)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1197,"value":"resultSigmoidal = sigmoidalRegression(dataSigmoidal)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1192,"value":"dataSigmoidal = [\n {x: -6, y: 20.1},\n {x: -5, y: 17.6},\n {x: -4, y: 22.8},\n {x: -3, y: 24.2},\n {x: -2, y: 36.9},\n {x: -1, y: 47.3},\n {x: 0, y: 74.8},\n {x: 1, y: 88.2},\n {x: 2, y: 109.5},\n {x: 3, y: 111.1},\n {x: 4, y: 120.8},\n {x: 5, y: 116.9},\n {x: 6, y: 121.7}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1312,"value":"## Graphic","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":1285,"value":"chart = (xAxis, yAxis, data, result, xScale, yScale, lineGenerator, xVar = \"x\", yVar = \"y\", r = 3) => {\n const svg = d3.create(\"svg\")\n .attr(\"width\", innerWidth + margin.left + margin.right)\n .attr(\"height\", innerHeight + margin.top + margin.bottom);\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${margin.left}, ${margin.top})`);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxis)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxis)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.selectAll(\"circle\")\n .data(data)\n .enter().append(\"circle\")\n .attr(\"r\", r)\n .attr(\"cx\", d => xScale(d[xVar]))\n .attr(\"cy\", d => yScale(d[yVar]));\n\n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(result)\n .attr(\"d\", lineGenerator);\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":66,"value":"md`## Dimensions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":12,"value":"margin = ({left: 29, right: 8, top: 13, bottom: 24});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":16,"value":"base = Math.min(width, 400);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":18,"value":"innerWidth = base - margin.left - margin.right;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":20,"value":"innerHeight = base - margin.top - margin.bottom;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":73,"value":"md`## Styles`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":41,"value":"html`\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":77,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":6,"value":"d3 = require(\"d3-array@3\", \"d3-axis@3\", \"d3-regression@2.2\", \"d3-scale@4\", \"d3-shape@3\", \"d3-selection@3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 30:"$2f:body"