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2d:{"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":"$D2019-04-08T13:32:39.854Z","has_unpublished_edits":null,"fork":false,"stars":122,"starred":false,"owner":{"type":"team","id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":"starter_2024"},"version":1357,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry 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d3-regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":258,"value":"md`[**d3-regression**](https://github.com/harrystevens/d3-regression) is a [D3.js](https://d3js.org/) module for calculating statistical regressions from two-dimensional data. It is dependency-free, and its API exposes configurable functions that transform input data, in the manner of other D3 modules.\n\nd3-regression can currently do the following types of regressions:\n- [Linear](#linear)\n- [Quadratic](#quadratic)\n- [Polynomial](#polynomial)\n- [Exponential](#exponential)\n- [Logarithmic](#logarithmic)\n- [Power law](#power)\n- [LOESS](#loess)\n- [Logistic](#logistic)\n- [Sigmoidal](#sigmoidal)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"linearRegression = d3.regressionLinear()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-1.7, 16]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":986,"value":"md`d3-regression's methods return configurable functions with x- and y- accessors (which default to d => d[0] and d => d[1], respectively). If you want the resulting line to extend beyond the extents of your input data, each generator (besides [LOESS](#loess)) lets you specify a domain.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"{\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${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","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":642,"value":"xScaleLinear = d3.scaleLinear()\n .domain([-4, 16])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":644,"value":"yScaleLinear = d3.scaleLinear()\n .domain([-4, 16])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":795,"value":"xAxisLinear = d3.axisBottom(xScaleLinear)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":797,"value":"yAxisLinear = d3.axisLeft(yScaleLinear)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1243,"value":"resultLinear = linearRegression(dataLinear)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":639,"value":"dataLinear = [{x: 8, y: 3}, {x: 2, y: 10}, {x: 11, y: 3}, {x: 6, y: 6}, {x: 5, y: 8}, {x: 4, y: 12}, {x: 12, y: 1}, {x: 9, y: 4}, {x: 6, y: 9}, {x: 1, y: 14}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"quadraticRegression = d3.regressionQuad()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-4, 4]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":963,"value":"md`When you pass data to the regression generator, you'll get back an array of points representing a curved line. You can use d3.[line()](https://github.com/d3/d3-shape#line) to render it in SVG or Canvas:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":674,"value":"lineGenerator = d3.line()\n .x(d => xScaleQuadratic(d[0]))\n .y(d => yScaleQuadratic(d[1]));","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1301,"value":"chart(xAxisQuadratic, yAxisQuadratic, dataQuadratic, resultQuadratic, xScaleQuadratic, yScaleQuadratic, lineGenerator)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":668,"value":"xScaleQuadratic = d3.scaleLinear()\n .domain([-4, 4])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":670,"value":"yScaleQuadratic = d3.scaleLinear()\n .domain([-2, 14])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":772,"value":"xAxisQuadratic = d3.axisBottom(xScaleQuadratic)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":775,"value":"yAxisQuadratic = d3.axisLeft(yScaleQuadratic)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1248,"value":"resultQuadratic = quadraticRegression(dataQuadratic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":663,"value":"dataQuadratic = [{x: -3, y: 7.5}, {x: -2, y: 3}, {x: -1, y: 0.5}, {x: 0, y: 1}, {x: 1, y: 3}, {x: 2, y: 6}, {x: 3, y: 14}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1018,"value":"polynomialRegression = d3.regressionPoly()\n .x(d => d.x)\n .y(d => d.y)\n .order(3);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1051,"value":"md`I've specified an order above just to show how it works, but order defaults to 3 (i.e. a cubic regression), so that line of code is unnecessary. If order is set to 4, the regression generator will perform a fourth-degree polynomial regression. Likewise, if order is set to 2, the regression generator will perform a quadratic regression.\n\nBe careful about attempting to fit your data with higher order polynomials; though the regression line will fit your data with a high determination coefficient, it will likely have little predictive power for data outside of your domain.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1020,"value":"chart(xAxisPolynomial, yAxisPolynomial, dataPolynomial, resultPolynomial, xScalePolynomial, yScalePolynomial, linePolynomial)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1025,"value":"xScalePolynomial = d3.scaleLinear()\n .domain([0, 8])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1028,"value":"yScalePolynomial = d3.scaleLinear()\n .domain([140, 180])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1031,"value":"linePolynomial = d3.line()\n .x(d => xScalePolynomial(d[0]))\n .y(d => yScalePolynomial(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1035,"value":"xAxisPolynomial = d3.axisBottom(xScalePolynomial)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1038,"value":"yAxisPolynomial = d3.axisLeft(yScalePolynomial)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1253,"value":"resultPolynomial = polynomialRegression(dataPolynomial)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1022,"value":"dataPolynomial = [{\"x\":0,\"y\":140},{\"x\":1,\"y\":149},{\"x\":2,\"y\":159.6},{\"x\":3,\"y\":159},{\"x\":4,\"y\":155.9},{\"x\":5,\"y\":169},{\"x\":6,\"y\":162.9},{\"x\":7,\"y\":169},{\"x\":8,\"y\":180}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":486,"value":"exponentialRegression = d3.regressionExp()\n .x(d => d.x)\n .y(d => d.y)\n .domain([-2, 5.06]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":534,"value":"chart(xAxisExponential, yAxisExponential, dataExponential, resultExponential, xScaleExponential, yScaleExponential, lineExponential)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":684,"value":"xScaleExponential = d3.scaleLinear()\n .domain([-2, 10])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":686,"value":"yScaleExponential = d3.scaleLinear()\n .domain([-10, 100])\n .range([innerHeight, 0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":691,"value":"lineExponential = d3.line()\n .x(d => xScaleExponential(d[0]))\n .y(d => yScaleExponential(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":761,"value":"xAxisExponential = d3.axisBottom(xScaleExponential)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":765,"value":"yAxisExponential = d3.axisLeft(yScaleExponential)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1258,"value":"resultExponential = exponentialRegression(dataExponential)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":688,"value":"dataExponential = [{x: 0, y: 3}, {x: 1, y: 7}, {x: 2, y: 10}, {x: 3, y: 24}, {x: 4, y: 50}, {x: 5, y: 95}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":699,"value":"logarithmicRegression = d3.regressionLog()\n .x(d => d.x)\n .y(d => d.y)\n .domain([.81, 35]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":715,"value":"chart(xAxisLogarithmic, yAxisLogarithmic, dataLogarithmic, resultLogarithmic, xScaleLogarithmic, yScaleLogarithmic, lineLogarithmic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":708,"value":"xScaleLogarithmic = d3.scaleLinear()\n .domain([0, 35])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":710,"value":"yScaleLogarithmic = d3.scaleLinear()\n .domain([4, 8])\n .range([innerHeight, 0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":712,"value":"lineLogarithmic = d3.line()\n .x(d => xScaleLogarithmic(d[0]))\n .y(d => yScaleLogarithmic(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":752,"value":"xAxisLogarithmic = d3.axisBottom(xScaleLogarithmic)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":755,"value":"yAxisLogarithmic = d3.axisLeft(yScaleLogarithmic)\n .tickSize(innerWidth + 10)\n .tickValues(d3.range(4, 9))\n .tickFormat(d => d)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1127,"value":"resultLogarithmic = logarithmicRegression(dataLogarithmic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":706,"value":"dataLogarithmic = [{x: 1, y: 4.181}, {x: 2, y: 4.665}, {x: 3, y: 5.296}, {x: 4, y: 5.365}, {x: 5, y: 5.448}, {x: 6, y: 5.744}, {x: 7, y: 5.653}, {x: 8, y: 5.844}, {x: 9, y: 6.362}, {x: 10, y: 6.38}, {x: 11, y: 6.311}, {x: 12, y: 6.457}, {x: 13, y: 6.479}, {x: 14, y: 6.59}, {x: 15, y: 6.74}, {x: 16, y: 6.58}, {x: 17, y: 6.852}, {x: 18, y: 6.531}, {x: 19, y: 6.682}, {x: 20, y: 7.013}, {x: 21, y: 6.82}, {x: 22, y: 6.647}, {x: 23, y: 6.951}, {x: 24, y: 7.121}, {x: 25, y: 7.143}, {x: 26, y: 6.914}, {x: 27, y: 6.941}, {x: 28, y: 7.226}, {x: 29, y: 6.898}, {x: 30, y: 7.392}, {x: 31, y: 6.938}]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":898,"value":"powerRegression = d3.regressionPow()\n .x(d => d.rank)\n .y(d => d.sales);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":917,"value":"chart(xAxisPower, yAxisPower, dataPower, resultPower, xScalePower, yScalePower, linePower, \"rank\", \"sales\", 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":905,"value":"xScalePower = d3.scaleLinear()\n .domain([0, 5e3])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":907,"value":"yScalePower = d3.scaleLinear()\n .domain([100, 0])\n .range([0, innerHeight])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":909,"value":"xAxisPower = d3.axisBottom(xScalePower)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(0, 6e3, 1e3))\n .tickFormat(d => d >= 1e3 ? `${d / 1e3}k` : d)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":911,"value":"yAxisPower = d3.axisLeft(yScalePower)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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","output":"$undefined","database":"$undefined"},{"id":1263,"value":"resultPower = powerRegression(dataPower)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":902,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":189,"value":"loess = md`## LOESS\n\nd3-regression's implementation of the LOESS regression was adapted with very little modification from Jason Davies's [science.js](https://github.com/jasondavies/science.js), with the main difference that this API returns a configurable function with x- and y-accessors similar to other D3.js modules.\n\nUse d3.[regressionLoess()](https://github.com/HarryStevens/d3-regression#regressionLoess) like this:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"loessRegression = d3.regressionLoess()\n .x(d => d.year)\n .y(d => d.temperature)\n .bandwidth(bandwidth);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":721,"value":"md`The chart below displays the average annual temperature in California from 1900 to 2017. You can [download the data from NOAA](https://www.ncdc.noaa.gov/cag/statewide/time-series). A prettier version of this chart was published in Axios on Nov. 15, 2018, under the headline [\"Humans are a wildfire threat multiplier\"](https://www.axios.com/humans-are-a-wildfire-threat-multiplier-f8f9afb3-a91f-449e-af10-9fa2011a8f81.html).\n\nAdjust the slider below to see how the smoothing line changes with the bandwidth, also called the \"smoothing parameter,\" which is the fraction of all points used to calculate each local fit. Higher bandwidths produce smoother lines, and vice versa.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":723,"value":"viewof bandwidth = Inputs.range([.02, 1], {\n label: \"Bandwidth\",\n step: .01,\n value: .25\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":55,"value":"chart(xAxisLoess, yAxisLoess, dataLoess, resultLoess, xScaleLoess, yScaleLoess, lineLoess, \"year\", \"temperature\", 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":732,"value":"xScaleLoess = d3.scaleLinear()\n .domain([1900, 2020])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":736,"value":"yScaleLoess = d3.scaleLinear()\n .domain([55, 62])\n .range([innerHeight, 0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":739,"value":"lineLoess = d3.line()\n .x(d => xScaleLoess(d[0]))\n .y(d => yScaleLoess(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":741,"value":"xAxisLoess = d3.axisBottom(xScaleLoess)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(1900, 2040, 20))\n .tickFormat(d => d % 100 === 0 ? d : \"`\" + d.toString().slice(2, 4))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":745,"value":"yAxisLoess = d3.axisLeft(yScaleLoess)\n .tickSize(innerWidth + 10)\n .tickValues(d3.range(55, 63))\n .tickFormat(d => d);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1268,"value":"resultLoess = loessRegression(dataLoess)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":728,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1104,"value":"logisticRegression = d3.regressionLogistic()\n .x(d => d.x)\n .y(d => d.y);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1146,"value":"chart(xAxisLogistic, yAxisLogistic, dataLogistic, resultLogistic, xScaleLogistic, yScaleLogistic, lineLogistic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1148,"value":"xScaleLogistic = d3.scaleLinear()\n .domain(d3.extent(dataLogistic, d => d.x))\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1152,"value":"yScaleLogistic = d3.scaleLinear()\n .domain(d3.extent(dataLogistic, d => d.y))\n .range([innerHeight, 0])\n .nice();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1174,"value":"lineLogistic = d3.line()\n .x(d => xScaleLogistic(d[0]))\n .y(d => yScaleLogistic(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1162,"value":"xAxisLogistic = d3.axisBottom(xScaleLogistic)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(-6, 8, 2))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1168,"value":"yAxisLogistic = d3.axisLeft(yScaleLogistic)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1120,"value":"resultLogistic = logisticRegression(dataLogistic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1106,"value":"dataLogistic = [\n {x: -6, y: 0.9},\n {x: -5, y: 0.7},\n {x: -4, y: 3.8},\n {x: -3, y: 5.9},\n {x: -2, y: 17.4},\n {x: -1, y: 28.6},\n {x: 0, y: 55.8},\n {x: 1, y: 69.1},\n {x: 2, y: 89.7},\n {x: 3, y: 91.5},\n {x: 4, y: 99.4},\n {x: 5, y: 96.8},\n {x: 6, y: 101.2}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1190,"value":"sigmoidalRegression = d3.regressionSigmoidal()\n .x(d => d.x)\n .y(d => d.y);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1224,"value":"chart(xAxisSigmoidal, yAxisSigmoidal, dataSigmoidal, resultSigmoidal, xScaleSigmoidal, yScaleSigmoidal, lineSigmoidal)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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":"$undefined","output":"$undefined","database":"$undefined"},{"id":1222,"value":"xScaleSigmoidal = d3.scaleLinear()\n .domain(d3.extent(dataSigmoidal, d => d.x))\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1220,"value":"yScaleSigmoidal = d3.scaleLinear()\n .domain(d3.extent(dataSigmoidal, d => d.y))\n .range([innerHeight, 0])\n .nice();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1218,"value":"lineSigmoidal = d3.line()\n .x(d => xScaleSigmoidal(d[0]))\n .y(d => yScaleSigmoidal(d[1]));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1216,"value":"xAxisSigmoidal = d3.axisBottom(xScaleSigmoidal)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(-6, 8, 2))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1214,"value":"yAxisSigmoidal = d3.axisLeft(yScaleSigmoidal)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1197,"value":"resultSigmoidal = sigmoidalRegression(dataSigmoidal)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1192,"value":"dataSigmoidal = [\n {x: -6, y: 20.1},\n {x: -5, y: 17.6},\n {x: -4, y: 22.8},\n {x: -3, y: 24.2},\n {x: -2, y: 36.9},\n {x: -1, y: 47.3},\n {x: 0, y: 74.8},\n {x: 1, y: 88.2},\n {x: 2, y: 109.5},\n {x: 3, y: 111.1},\n {x: 4, y: 120.8},\n {x: 5, y: 116.9},\n {x: 6, y: 121.7}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1312,"value":"## Graphic","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$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","output":"$undefined","database":"$undefined"},{"id":66,"value":"md`## Dimensions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"margin = ({left: 29, right: 8, top: 13, bottom: 24});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"base = Math.min(width, 400);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"innerWidth = base - margin.left - margin.right;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"innerHeight = base - margin.top - margin.bottom;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"md`## Styles`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"html`\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$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","output":"$undefined","database":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2e:"$2d:body"