2a:T8ea,chart = { const svg = d3.select(DOM.svg(width, height)); const dataLegend = ([10, 100, 300]); const legend = svg.append("g") .attr("fill", "#000000") .attr("transform", "translate(100,125)") .attr("text-anchor", "middle") .style("font", "10px sans-serif") .selectAll("g") .data(dataLegend) .join("g"); legend.append("circle") .attr("fill" , "none") .attr("stroke" , "#aaa") .attr("cy" , d => -Math.sqrt(d)) .attr("cx" , margin.left) .attr("r" , d => Math.sqrt(d)); legend.append("text") .attr("y" , d => -2.1*Math.sqrt(d)) .attr("x" , margin.left) .attr("dy", "1.3em") .text(d3.format("")); svg.append("text") .attr("transform", "translate(100,125)") .attr("text-anchor", "middle") .style("font", "10px sans-serif") .attr("y" , d => -2.1*Math.sqrt(d3.max(dataLegend))) .attr("x" , margin.left) .text("Billion"); svg.append("g") .call(xAxis); svg.append("g") .call(yAxis); svg.append("path") .attr("fill", "#ccc") .attr("fill-opacity", 0.5) .attr("stroke", "none") .attr("d", area(intervalData)); svg.append("line") .datum([ [x.domain()[0], predict(x.domain()[0])], [x.domain()[1], predict(x.domain()[1])] ]) .attr("stroke", "#333") .attr("stroke-width", 1.5) .attr("x1", d => x(d[0][0])) .attr("x2", d => x(d[1][0])) .attr("y1", d => y(d[0][1])) .attr("y2", d => y(d[1][1])); svg.append("g") .selectAll(".chartCircle") .data(us) .join("circle") .attr("class" , "chartCircle") .attr("fill" , "steelblue") .attr("stroke" , "black") .attr("cx" , d => x(d.ppm)) .attr("cy" , d => y(d.disasters)) .attr("r" , d => Math.sqrt(d.costs)) const tooltip = svg.append("g"); svg .selectAll(".chartCircle") .on("touchmove mousemove", function(event, d) { tooltip.call( callout,`Year: ${d.year} Number Disasters: ${d.disasters} Cost: $${d.costs} Billion` ); tooltip.attr("transform", `translate(${d3.pointer(event, this)})`); }) .on("touchend mouseleave", function() { tooltip.call(callout, null); }); return svg.node(); }2b:Tc60,/** Returns the normal deviate Z corresponding to a given lower tail area of P; Z is accurate to about 1 part in 10**16. Wichura, M. J. (1988) Algorithm AS 241: The percentage points of the normal distribution. Applied Statistics, 37, 477–484. see also: J. D. Beasley, J. D./ Springer (1977), S. G., The percentage points of the NormalDistribution, Applied Statistics. 26, 118–121. Excel: NORMSINV(); R: qnorm() **/ function normdev(p) { if (p < 0 || p > 1) return false; if (p == 0) return -Infinity; if (p == 1) return Infinity; let a0 = 3.3871328727963666080e+0, a1 = 1.3314166789178437745e+2, a2 = 1.9715909503065514427e+3, a3 = 1.3731693765509461125e+4, a4 = 4.5921953931549871457e+4, a5 = 6.7265770927008700853e+4, a6 = 3.3430575583588128105e+4, a7 = 2.5090809287301226727e+3, b1 = 4.2313330701600911252e+1, b2 = 6.8718700749205790830e+2, b3 = 5.3941960214247511077e+3, b4 = 2.1213794301586595867e+4, b5 = 3.9307895800092710610e+4, b6 = 2.8729085735721942674e+4, b7 = 5.2264952788528545610e+3, c0 = 1.42343711074968357734e+0, c1 = 4.63033784615654529590e+0, c2 = 5.76949722146069140550e+0, c3 = 3.64784832476320460504e+0, c4 = 1.27045825245236838258e+0, c5 = 2.41780725177450611770e-1, c6 = 2.27238449892691845833e-2, c7 = 7.74545014278341407640e-4, d1 = 2.05319162663775882187e+0, d2 = 1.67638483018380384940e+0, d3 = 6.89767334985100004550e-1, d4 = 1.48103976427480074590e-1, d5 = 1.51986665636164571966e-2, d6 = 5.47593808499534494600e-4, d7 = 1.05075007164441684324e-9, e0 = 6.65790464350110377720e+0, e1 = 5.46378491116411436990e+0, e2 = 1.78482653991729133580e+0, e3 = 2.96560571828504891230e-1, e4 = 2.65321895265761230930e-2, e5 = 1.24266094738807843860e-3, e6 = 2.71155556874348757815e-5, e7 = 2.01033439929228813265e-7, f1 = 5.99832206555887937690e-1, f2 = 1.36929880922735805310e-1, f3 = 1.48753612908506148525e-2, f4 = 7.86869131145613259100e-4, f5 = 1.84631831751005468180e-5, f6 = 1.42151175831644588870e-7, f7 = 2.04426310338993978564e-15; let q = p - 0.5, r, z; // p close to 0.5 if (Math.abs(q) <= 0.425) { r = 0.180625 - q * q; z = q * (((((((a7 * r + a6) * r + a5) * r + a4) * r + a3) * r + a2) * r + a1) * r + a0) / (((((((b7 * r + b6) * r + b5) * r + b4) * r + b3) * r + b2) * r + b1) * r + 1); return z; } if (q > 0) r = 1 - p; else r = p; r = Math.sqrt(-Math.log(r)); // p neither close to 0.5 nor 0 or 1 if (r <= 5) { r += -1.6; z = (((((((c7 * r + c6) * r + c5) * r + c4) * r + c3) * r + c2) * r + c1) * r + c0) / (((((((d7 * r + d6) * r + d5) * r + d4) * r + d3) * r + d2) * r + d1) * r + 1); } // p near 0 or 1 else { r += -5; z = (((((((e7 * r + e6) * r + e5) * r + e4) * r + e3) * r + e2) * r + e1) * r + e0) / (((((((f7 * r + f6) * r + f5) * r + f4) * r + f3) * r + f2) * r + f1) * r + 1); } if (q < 0.0) z = -z; return z; }2c:T5f2,/* Hill's approximated inverse t-distribution calculates t given df and two-tail probability. Hill, G. W. (1970), Algorithm 396: Student's t-quantiles. Communications of the ACM, 13(10), 619–620. Hill, G. W. (1981) Remark on Algorithm 396, ACM Transactions on Mathematical Software, 7, 250–1. Excel: TINV(); R: qt() */ function inverseT(p, df) { const { sin, cos, sqrt, pow, exp, PI} = Math; let a, b, c, d, t, x, y; if (df == 1) return cos(p * PI / 2) / sin( p * PI / 2); if (df == 2) return sqrt(2 / (p * (2 - p)) - 2); a = 1 / (df - 0.5); b = 48 / (a * a); c = ((20700 * a / b - 98) * a - 16) * a + 96.36; d = ((94.5 / (b + c) - 3) / b + 1) * sqrt(a * PI * 0.5) * df; x = d * p; y = pow(x, 2 / df); if (y > 0.05 + a) { // The procedure normdev(p) is assumed to return a negative normal // deviate at the lower tail probability level p, e.g. -2.32 for p = 0.01. x = normdev(p / 2); y = x * x; if (df < 5) c = c + 0.3 * (df - 4.5) * (x + 0.6); c = (((0.05 * d * x - 5) * x - 7) * x - 2) * x + b + c; y = (((((0.4 * y + 6.3) * y + 36) * y + 94.5) / c - y - 3) / b + 1) * x; y = a * y * y; if (y > 0.002) y = exp(y) - 1; else y = 0.5 * y * y + y; // Remark on Algorithm 396 (used by R): // if (y > 0.1) y = exp(y) - 1; // else y = ((y + 4) * y + 12) * y * y / 24 + y; } else { y = ((1 / (((df + 6) / (df * y) - 0.089 * d - 0.822) * (df + 2) * 3) + 0.5 / (df + 4)) * y - 1) * (df + 1) / (df + 2) + 1 / y; } return sqrt(df * y); }2d:[{"id":"47c47186c63e08c3854c51d1f3f246cc2a1ed5373c218368aa23e45bb5069fe3c71aa776750c2024d63e3c38f876983ea5e0f130b8799b11f07afe4437ecede9","href":"https://static.observableusercontent.com/files/47c47186c63e08c3854c51d1f3f246cc2a1ed5373c218368aa23e45bb5069fe3c71aa776750c2024d63e3c38f876983ea5e0f130b8799b11f07afe4437ecede9","name":"USdisasters@3.csv","type":"text/csv","lastModified":1677513176185.489,"size":1084}] 29:{"title":"Billion Dollar Weather Disasters","cells":[{"id":718,"value":"md `# Billion Dollar Weather Disasters`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1151,"value":"Linear regression, where you draw a line down the middle of the data points, is sort of data analysis 101. But in the real world data is often more messy and you don't always see the analysis work out so neatly. In this case it does. The line explains the data really well, with an R-value of 0.76, meaning it explains 76 percent of the data. And it's statistically significant. \n\nAdjusted R squared = 0.7586 \n\nP-value: <0.0001\n\n[Weather Disaster](https://www.ncdc.noaa.gov/billions/mapping) and [CO2](https://gml.noaa.gov/webdata/ccgg/trends/co2/co2_annmean_mlo.txt) data from the National Oceanic and Atmospheric Administration","pinned":false,"hidden":false,"mode":"md"},{"id":39,"value":"$2a","pinned":false,"hidden":false,"mode":"ojs"},{"id":441,"value":"style = html`\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"us = d3.csvParse(await FileAttachment(\"USdisasters@3.csv\").text(), ({year, ppm, disasters, costs}) => ({year: +year, ppm: +ppm, disasters: +disasters, costs: +costs}))","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"x = d3.scaleLinear()\n .domain(d3.extent(us, d => d.ppm))\n .range([margin.left, width - margin.right])","pinned":false,"hidden":false,"mode":"ojs"},{"id":50,"value":"y = d3.scaleLinear()\n .domain(d3.extent(us, d => d.disasters))\n .range([height - margin.bottom, margin.top])","pinned":false,"hidden":false,"mode":"ojs"},{"id":42,"value":"xAxis = g => g\n .attr(\"transform\", `translate(0,${height - margin.bottom})`)\n .attr(\"class\" , \"ticks\")\n .call(d3.axisBottom(x).ticks(width/50).tickSizeOuter(0))\n .call(g => g.append(\"text\")\n .attr(\"class\" , \"label\")\n .attr(\"x\", width/2)\n .attr(\"y\", -4)\n .attr(\"text-anchor\", \"middle\")\n .attr(\"fill\", \"black\")\n .text(\"CO2 (Parts Per Million)\"))","pinned":false,"hidden":false,"mode":"ojs"},{"id":76,"value":"yAxis = g => g\n .attr(\"transform\", `translate(${margin.left},0)`)\n .attr(\"class\" , \"ticks\")\n .call(d3.axisLeft(y))\n .call(g => g.append(\"text\")\n .attr(\"class\" , \"label\")\n .attr(\"transform\", \"rotate(-90)\")\n .attr(\"y\", 15)\n .attr(\"x\" , -height/2+margin.top)\n .attr(\"text-anchor\", \"middle\")\n .attr(\"fill\", \"black\")\n .text(\"Number of Disasters\"))","pinned":false,"hidden":false,"mode":"ojs"},{"id":283,"value":"predict = linearRegression(us)","pinned":true,"hidden":false,"mode":"ojs"},{"id":318,"value":"interval = confidenceInterval(us, predict)","pinned":false,"hidden":false,"mode":"ojs"},{"id":303,"value":"$2b","pinned":false,"hidden":false,"mode":"ojs"},{"id":300,"value":"$2c","pinned":false,"hidden":false,"mode":"ojs"},{"id":299,"value":"function confidenceInterval(us, predict) {\n const mean = d3.sum(us, d => d.ppm) / us.length;\n let a = 0, b = 0;\n for (let i = 0; i < us.length; ++i) {\n a += Math.pow(us[i].ppm - mean, 2);\n b += Math.pow(us[i].disasters - predict(us[i].ppm), 2);\n }\n const sy = Math.sqrt(b / (us.length - 2));\n const t = inverseT(+0.05, us.length - 2) \n return function(x) {\n const Y = predict(x);\n const se = sy * Math.sqrt(1 / us.length + Math.pow(x - mean, 2) / a);\n return { x, left: Y - t * se, right: Y + t * se };\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":316,"value":"intervalData = {\n const domain = x.domain();\n const step = (domain[1] - domain[0]) / 100;\n return d3.range(domain[0], domain[1] + step, step).map(d => interval(d));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":281,"value":"function linearRegression(data) {\n let n = us.length, sumX = 0, sumY = 0, sumXY = 0, sumX2 = 0;\n for (let i = 0; i < us.length; ++i) {\n const xi = us[i].ppm;\n const yi = us[i].disasters;\n if (!Number.isFinite(xi) || !Number.isFinite(yi)) { --n; continue; }\n sumX += xi;\n sumY += yi;\n sumXY += xi * yi;\n sumX2 += xi * xi;\n }\n const slope = (n * sumXY - sumX * sumY) / (n * sumX2 - sumX * sumX);\n const intercept = (sumY - slope * sumX) / n;\n return x => slope * x + intercept;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":313,"value":"area = d3.area()\n .x(d => x(d.x))\n .y0(d => y(d.left))\n .y1(d => y(d.right))","pinned":true,"hidden":false,"mode":"ojs"},{"id":1117,"value":"callout = (g, value) => {\n if (!value) return g.style(\"display\", \"none\");\n\n g\n .style(\"display\", null)\n .style(\"pointer-events\", \"none\")\n .style(\"font\", \"12px sans-serif\");\n\n const path = g.selectAll(\"path\")\n .data([null])\n .join(\"path\")\n .attr(\"fill\", \"white\")\n .attr(\"stroke\", \"black\");\n\n const text = g.selectAll(\"text\")\n .data([null])\n .join(\"text\")\n .call(text => text\n .selectAll(\"tspan\")\n .data((value + \"\").split(/\\n/))\n .join(\"tspan\")\n .attr(\"x\", 0)\n .attr(\"y\", (d, i) => `${i * 1.5}em`)\n .style(\"font-weight\", (_, i) => i ? null : \"bold\")\n .text(d => d));\n\n const {x, y, width: w, height: h} = text.node().getBBox();\n\n text.attr(\"transform\", `translate(${-w / 2},${15 - y})`);\n path.attr(\"d\", `M${-w / 2 - 10},5H-5l5,-5l5,5H${w / 2 + 10}v${h + 20}h-${w + 20}z`);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"margin = ({top: 40, right: 75, bottom: 50, left: 75})","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"height = 600","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W2d","stdlib":"1","titling":"auto"}