25:["$","title",null,{"children":"Introducing d3-regression | mheard03 | Observable"}] 49:T400,{ const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom)) const g = svg.append("g") .attr("transform", `translate(${margin.left}, ${margin.top})`); g.append("g") .attr("class", "axis") .call(xAxisLinear) .selectAll(".tick") .classed("baseline", d => d == 0); g.append("g") .attr("class", "axis") .attr("transform", `translate(${innerWidth})`) .call(yAxisLinear) .selectAll(".tick") .classed("baseline", d => d == 0); g.selectAll("circle") .data(dataLinear) .enter().append("circle") .attr("r", 3) .attr("cx", d => xScaleLinear(d.x)) .attr("cy", d => yScaleLinear(d.y)); g.append("line") .attr("class", "regression") .datum(linearRegression(dataLinear)) .attr("x1", d => xScaleLinear(d[0][0])) .attr("x2", d => xScaleLinear(d[1][0])) .attr("y1", d => yScaleLinear(d[0][1])) .attr("y2", d => yScaleLinear(d[1][1])); return svg.node(); 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29:{"id":"cf0c939cf442c21a","slug":null,"title":"Introducing d3-regression","thumbnail":"49e3b8e7b5c25c76853ac31b4ed41e895e2facb91573182f4e68e995d0ccb899","access_level":"public","create_time":"$D2023-08-14T11:17:50.514Z","update_time":"$D2023-10-16T17:38:33.001Z","view_time":null,"first_public_time":"$D2023-08-14T11:17:50.514Z","has_unpublished_edits":null,"fork":{"id":"7b51129a2feec1d0","slug":"introducing-d3-regression","title":"Introducing d3-regression","owner":{"id":"be420f6a83563b92","login":"harrystevens","name":"Harry 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d3-regression","cells":[{"id":0,"value":"md`# Introducing d3-regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"$49","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":636,"value":"md`The regression shown above is described by the equation ${tex`y = ${linearRegression(dataLinear).a.toFixed(3)}x + ${linearRegression(dataLinear).b.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${linearRegression(dataLinear).rSquared.toFixed(3)}. This example comes from [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/line-of-best-fit).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":797,"value":"yAxisLinear = d3.axisLeft(yScaleLinear)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":674,"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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":661,"value":"md`The regression shown below is described by the equation ${tex`y = ${quadraticRegression(dataQuadratic).a.toFixed(3)}x^2 + ${quadraticRegression(dataQuadratic).b.toFixed(3)}x + ${quadraticRegression(dataQuadratic).c.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${quadraticRegression(dataQuadratic).rSquared.toFixed(3)}. This example is from [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/quadratic-regression). `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"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}, ${margin.top})`);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisQuadratic)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisQuadratic)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.selectAll(\"circle\")\n .data(dataQuadratic)\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(quadraticRegression(dataQuadratic))\n .attr(\"d\", lineGenerator);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":668,"value":"xScale = d3.scaleLinear()\n .domain([-4, 4])\n .range([0, innerWidth])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":670,"value":"yScale = d3.scaleLinear()\n .domain([-2, 14])\n .range([innerHeight, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":772,"value":"xAxisQuadratic = d3.axisBottom(xScale)\n .tickSize(innerHeight + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":775,"value":"yAxisQuadratic = d3.axisLeft(yScale)\n .tickSize(innerWidth + 10);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1186,"value":"{\n const pr = polynomialRegression(dataPolynomial);\n return d3.range(...xScalePolynomial.domain()).map(x => [x, pr.predict(x), dataPolynomial.find(d => d.x >= x)]);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1020,"value":"{\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${margin.left}, ${margin.top})`);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisPolynomial)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisPolynomial)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.selectAll(\"circle\")\n .data(dataPolynomial)\n .enter().append(\"circle\")\n .attr(\"r\", 3)\n .attr(\"cx\", d => xScalePolynomial(d.x))\n .attr(\"cy\", d => yScalePolynomial(d.y));\n\n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(polynomialRegression(dataPolynomial))\n .attr(\"d\", linePolynomial);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1053,"value":"md`The regression shown above is described by the equation ${tex`y = ${polynomialRegression(dataPolynomial).coefficients.reverse().map((d, i) => {\n const deg = Math.abs(polynomialRegression(dataPolynomial).coefficients.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 ${polynomialRegression(dataPolynomial).rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1025,"value":"xScalePolynomial = getXScale(dataPolynomial, \"x\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1028,"value":"yScalePolynomial = getYScale(dataPolynomial, \"y\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1035,"value":"xAxisPolynomial = getXAxis(xScalePolynomial);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1038,"value":"yAxisPolynomial = getYAxis(yScalePolynomial);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1221,"value":"dataExponential.map(d => ({ x: 2**d.x, y: d.y }));","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1022,"value":"dataPolynomial = arcStatsMetaFull","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1287,"value":"d3.regressionExp()( [[0.75,0.0008322048187316205],[0.5,0.002950193881990022],[0.25,0.013783049583435358],[0.125,0.04848795175552207],[0.0625,0.14894719541065593],[0.03125,0.4342218506336344],[0.015625,1.1765973861516719],[0.0078125,3.1163323602081308],[0.00390625,7.376351052224644],[0.001953125,14.473160939529752],[0.0009765625,33.616200305708034],[0.00048828125,65.89583139608975],[0.000244140625,195.2348298878895],[0.0001220703125,384.9595503351178],[0.00006103515625,666.0828711250322],[0.000030517578125,2138.1863559873227],[0.0000152587890625,4245.4559120226995]].map(v => [1-v[0], v[1]]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":486,"value":"exponentialRegression = d3.regressionExp()\n .x(d => d.x)\n .y(d => d.y);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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 = ${exponentialRegression(dataExponential).a.toFixed(3)}e^{${exponentialRegression(dataExponential).b.toFixed(3)}x}`}. The coefficient of determination, or ${tex`R^2`}, is ${exponentialRegression(dataExponential).rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1275,"value":"{\n const slope = 1;\n const reg = exponentialRegression(dataExponential);\n return Math.log(slope * 1/(reg.a*reg.b))/reg.b\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":534,"value":"{\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${margin.left}, ${margin.top})`);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisExponential)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisExponential)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n\n g.selectAll(\"circle\")\n .data(dataExponential)\n .enter().append(\"circle\")\n .attr(\"r\", 3)\n .attr(\"cx\", d => xScaleExponential(d.x))\n .attr(\"cy\", d => yScaleExponential(d.y));\n\n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(exponentialRegression(dataExponential))\n .attr(\"d\", lineExponential);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":684,"value":"xScaleExponential = getXScale(dataExponential, \"x\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":686,"value":"yScaleExponential = getYScale(dataExponential, \"y\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":761,"value":"xAxisExponential = getXAxis(xScaleExponential);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":765,"value":"yAxisExponential = getYAxis(yScaleExponential);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":688,"value":"dataExponential = {\n const quantileValues = [[0.75,0.0008322048187316205],[0.5,0.002950193881990022],[0.25,0.013783049583435358],[0.125,0.04848795175552207],[0.0625,0.14894719541065593],[0.03125,0.4342218506336344],[0.015625,1.1765973861516719],[0.0078125,3.1163323602081308],[0.00390625,7.376351052224644],[0.001953125,14.473160939529752],[0.0009765625,33.616200305708034],[0.00048828125,65.89583139608975],[0.000244140625,195.2348298878895],[0.0001220703125,384.9595503351178],[0.00006103515625,666.0828711250322],[0.000030517578125,2138.1863559873227],[0.0000152587890625,4245.4559120226995]];\n return quantileValues.map(v => ({x: 100 * (1-v[0]), y: v[1] }));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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 = ${logarithmicRegression(dataLogarithmic).a.toFixed(3)} {\\cdot} {\\ln}(x) + ${logarithmicRegression(dataLogarithmic).b.toFixed(3)}`}. The coefficient of determination, or ${tex`R^2`}, is ${logarithmicRegression(dataLogarithmic).rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":715,"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}, ${margin.top})`)\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisLogarithmic)\n .selectAll(\".tick\")\n .classed(\"baseline\", d => d === 0);\n \n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisLogarithmic);\n\n g.selectAll(\"circle\")\n .data(dataLogarithmic)\n .enter().append(\"circle\")\n .attr(\"r\", 3)\n .attr(\"cx\", d => xScaleLogarithmic(d.x))\n .attr(\"cy\", d => yScaleLogarithmic(d.y))\n\n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(logarithmicRegression(dataLogarithmic))\n .attr(\"d\", lineLogarithmic);\n\n return svg.node()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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 = ${powerRegression(dataPower).a.toFixed(3)}x^{${powerRegression(dataPower).b.toFixed(3)}}`}. The coefficient of determination, or ${tex`R^2`}, is ${powerRegression(dataPower).rSquared.toFixed(3)}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":917,"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}, ${margin.top})`)\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisPower)\n .selectAll(\".tick line\")\n .classed(\"baseline\", d => d === 0);\n \n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisPower)\n .selectAll(\".tick line\")\n .classed(\"baseline\", d => d === 0);\n\n g.selectAll(\"circle\")\n .data(dataPower)\n .enter().append(\"circle\")\n .attr(\"r\", 2)\n .attr(\"cx\", d => xScalePower(d.rank))\n .attr(\"cy\", d => yScalePower(d.sales))\n\n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(powerRegression(dataPower))\n .attr(\"d\", linePower);\n\n return svg.node()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":905,"value":"xScalePower = d3.scaleLinear()\n .domain([0, 2048])\n .range([0, innerWidth]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":907,"value":"yScalePower = d3.scaleLinear()\n .domain([0, 90000])\n .range([0, innerHeight])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":909,"value":"xAxisPower = d3.axisBottom(xScalePower)\n .tickSize(innerHeight + 10)\n .tickFormat(d => d >= 1e3 ? `${d / 1e3}k` : d)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":911,"value":"yAxisPower = d3.axisLeft(yScalePower)\n .tickSize(innerWidth + 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":902,"value":"dataPower = {\n return arcStatsMeta3.map(m => ({ rank: 2**m.value, sales: m.coordCounts }));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1102,"value":"arcStatsMeta2 ={\n const max = _.maxBy(arcStatsMeta, \"coordCounts\").coordCounts;\n const minDelta = 5000;\n const last = arcStatsMeta.at(-1);\n return arcStatsMeta.filter(m => m == last || m.coordCounts > last.coordCounts * 1);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1130,"value":"arcStatsMeta3 = arcStatsMeta.map(m => ({ value: Math.log2(m.value), coordCounts: m.coordCounts }));","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1226,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1094,"value":"import { arcStats, arcStatsMeta } from \"053fea843f886be5\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$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":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":55,"value":"{\n const svg = d3.select(DOM.svg(innerWidth + margin.left + margin.right, innerHeight + margin.top + margin.bottom))\n \n const g = svg.append(\"g\")\n .attr(\"transform\", `translate(${margin.left}, ${margin.top})`);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .call(xAxisLoess);\n\n g.append(\"g\")\n .attr(\"class\", \"axis\")\n .attr(\"transform\", `translate(${innerWidth})`)\n .call(yAxisLoess);\n\n g.selectAll(\"circle\")\n .data(dataLoess)\n .enter().append(\"circle\")\n .attr(\"r\", 2)\n .attr(\"cx\", d => xScaleLoess(d.year))\n .attr(\"cy\", d => yScaleLoess(d.temperature));\n\n g.append(\"path\")\n .attr(\"class\", \"regression\")\n .datum(loessRegression(dataLoess))\n .attr(\"d\", lineLoess);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1138,"value":"function getXScale(data, field) {\n return d3.scaleLinear()\n .domain([_.minBy(data, field)[field], _.maxBy(data, field)[field]])\n .range([0, innerWidth]);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1141,"value":"function getYScale(data, field) {\n return d3.scaleLinear()\n .domain([_.minBy(data, field)[field], _.maxBy(data, field)[field]])\n .range([innerHeight, 0]);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1148,"value":"yScaleLoess.range()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1153,"value":"function getXAxis(xScale) {\n return d3.axisBottom(xScale)\n .tickSize(innerHeight + 10)\n .tickValues(d3.range(...xScale.domain()));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1146,"value":"function getYAxis(yScale) {\n return d3.axisLeft(yScale)\n .tickSize(innerWidth + 10);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":732,"value":"xScaleLoess = getXScale(dataLoess, \"year\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":736,"value":"yScaleLoess = getYScale(dataLoess, \"temperature\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$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","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":741,"value":"xAxisLoess = getXAxis(xScaleLoess)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":745,"value":"yAxisLoess = getYAxis(yScaleLoess)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":728,"value":"dataLoess = arcStatsMeta3.map(m => ({ year: m.value, temperature: m.coordCounts }));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"md`## Dimensions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"margin = ({left: 60, right: 8, top: 13, bottom: 24});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"base = Math.max(width, 400);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"innerWidth = base - margin.left - margin.right;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"innerHeight = base - margin.top - margin.bottom;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"md`## Styles`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"html`\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"md`## Imports\n\nTo make the scatterplot, I used [d3-axis](https://github.com/d3/d3-axis), [d3-scale](https://github.com/d3/d3-scale), and [d3-selection](https://github.com/d3/d3-selection). To draw the regression line, I used [d3-shape](https://github.com/d3/d3-selection). I also am loading [d3-regression](https://github.com/HarryStevens/d3-regression) with the rest of the D3.js modules.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"d3 = require(\"d3-array@3\", \"d3-axis@3\", \"d3-regression@1\", \"d3-scale@4\", \"d3-shape@3\", \"d3-selection@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4b","stdlib":"1"}} 24:null