28:null 29:["$","title",null,{"children":"Median Splits of Two Predictor Variables | Gary McClelland | Observable"}] 2e:[] 2c:{"id":"5a241d747930c920","slug":null,"title":"Median Splits of Two Predictor Variables","thumbnail":"b03edcf72adc6deeeda7848ddb35aea278777149a18e39136b3594944dcf6cd8","access_level":"public","create_time":"$D2023-01-10T23:53:29.491Z","update_time":"$D2023-01-19T23:16:46.858Z","view_time":null,"first_public_time":"$D2023-01-19T23:07:48.175Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"8e902c6c168a5327","login":"mcclella","name":"Gary McClelland","avatar_url":"https://avatars-next.observableusercontent.com/5fb0f9ce97ef2ff380c45d797b84b995cfeccb679fa1fcc25ae40f1a1b81414b","tier":"starter_2024"},"version":427,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"bb02701f3bca15dc","login":"mcclella","name":"Gary 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Plot.ruleX([xMed]),\n \n Plot.dot(wtData, {x: \"x\", y: \"y\", fill: \"grp\", r: 2 + 5*wt}),\n \n Plot.text(counts, {x: \"xLoc\", y: 'yLoc', text: 'count', fontSize: 16}),\n Plot.text([{x: 0, y: 3}], {\n x: \"x\",\n y: \"y\",\n text: [\"r = \" + jStat.corrcoeff(x,y).toFixed(2)],\n dy: -20,\n fill: 'red',\n fontSize: 24\n })\n ],\n color: {type: 'categorical', scheme: 'tableau10'},\n marginTop: 50\n \n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":298,"value":"viewof rho = Inputs.range([-0.99, 0.99], {value: 0, step: 0.01, label: \"Rho\"})\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"viewof wt = Inputs.range([0,1], {value: 0, step: 0.01, label: \"Weight\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":287,"value":"Plot.plot({\n x: {domain: [-3,3]},\n y: {domain: [-3,3]},\n marks: [\n Plot.ruleY([yMed]),\n Plot.ruleX([xMed]),\n \n Plot.dot(dummyData, {x: \"x\", y: \"y\", fill: \"grp\", r: 2 + 5*wt}),\n \n Plot.text(counts, {x: \"xLoc\", y: 'yLoc', text: 'count', fontSize: 16}),\n Plot.text([{x: 0, y: 3}], {\n x: \"x\",\n y: \"y\",\n text: [\"r = \" + jStat.corrcoeff(xd,yd).toFixed(2)],\n dy: -20,\n fill: 'red',\n fontSize: 24\n })\n ],\n color: {type: 'categorical', scheme: 'tableau10'},\n marginTop: 50\n \n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":394,"value":"### Model for Generating the Data\n#### Z = 3 + 0.9 X + 0.1 Y + N(0,1) where N(0,1) is random standard normal deviate","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":387,"value":"### Regression using original continuous predictors\n#### Z = ${mrCont.coef[0].toFixed(2)} + ${mrCont.coef[1].toFixed(2)} X + ${mrCont.coef[2].toFixed(2)} Y \n#### ${tex`R^2 = `}${mrCont.R2.toFixed(2)}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":369,"value":"### Regression using cell means as codes (\"proper\" median split)\n#### Z = ${mr.coef[0].toFixed(2)} + ${mr.coef[1].toFixed(2)} X + ${mr.coef[2].toFixed(2)} Y \n#### ${tex`R^2 = `}${mr.R2.toFixed(2)}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":372,"value":"### Regression using equal cell codes (traditional median splits)\n#### Z = ${mrDummy.coef[0].toFixed(2)} + ${mrDummy.coef[1].toFixed(2)} X + ${mrDummy.coef[2].toFixed(2)} Y\n#### ${tex`R^2 = `}${mrDummy.R2.toFixed(2)}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":412,"value":"Next","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":389,"value":"---\n## Support Functions and Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"n = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"nu = Math.sqrt(1-rho*rho)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"temp = {let x=[]; for(let i=0; i<=n-1; i++) x.push(jStat.normal.sample(0,1)); // generate bivariate normal sample of size n\n let d = []; for(let i=0; i<=n-1; i++) d.push({x: x[i], y: rho*x[i] + nu*jStat.normal.sample(0,1)}); return d}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"xMed = d3.median(temp, d => d.x)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":61,"value":"yMed = d3.median(temp, d=> d.y)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"data = {let d = []; \n for(let i=0; i< temp.length; i++) { // use 0 = LL, 1 = LH, 2 = HL, 3 = HH\n let grp = 0; let x = temp[i].x; let y = temp[i].y;\n if(x <= xMed && y > yMed) grp = 1; else if(x > xMed && y <= yMed) grp = 2; else if(x > xMed && y > yMed) grp=3;\n d.push({x: temp[i].x, y: temp[i].y, grp: grp})\n }\n return d;}\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":104,"value":"wtData = {let d = [];\n for(let i=0; i d.grp == i), d => d.x),\n xLoc: 3*dummyMeans[i].xMean, yLoc: 3*dummyMeans[i].yMean});\n return m\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":305,"value":"means = {let m = []; //compute the means for the four quadrants defined by median splits\n for(let i=0; i <= 3; i++)\n m.push({xMean: d3.mean(data.filter(d => d.grp == i), d => d.x),\n yMean: d3.mean(data.filter(d => d.grp == i), d=> d.y), grp: i});\n return m\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"x = {let x = []; // extract x as a vector for use in stat functions. surely there is a better way but this works\n for(let i =0; i < wtData.length; i++) x.push(wtData[i].x); return x;}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"y = {let y = []; for(let i=0; // extract y as a vector for use in stat functions. surely there is a better way but this works\n i < wtData.length; i++) y.push(wtData[i].y); return y;}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":275,"value":"xd = {let x = []; // extract x as a vector for use in stat functions. surely there is a better way but this works\n for(let i =0; i < dummyData.length; i++) x.push(dummyData[i].x); return x;}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":273,"value":"yd = {let y = []; for(let i=0; // extract y as a vector for use in stat functions. surely there is a better way but this works\n i < dummyData.length; i++) y.push(dummyData[i].y); return y;}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"jStat = require('jStat')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"v = 1 // variance of the model error term","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":321,"value":"z = {let z=[]; for(let i=0; i< data.length; i++)\n z.push(3 + 0.9*data[i].x + 0.1*data[i].y + v*jStat.normal.sample(0,1));\n return z;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":319,"value":"mod = {let m = []; for(let i=0; i < wtData.length; i++)\n m.push([1, wtData[i].x, wtData[i].y])\n return m;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":336,"value":"modDummy = {let m = []; for(let i=0; i < wtData.length; i++)\n m.push([1, dummyData[i].x, dummyData[i].y])\n return m;\n }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":381,"value":"modCont = {let m = []; for(let i=0; i < data.length; i++)\n m.push([1, data[i].x, data[i].y])\n return m;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":324,"value":"mr = jStat.models.ols(z,mod)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":338,"value":"mrDummy = jStat.models.ols(z,modDummy)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":383,"value":"mrCont = jStat.models.ols(z,modCont)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":364,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2e","stdlib":"1"}} 2d:"$2c:body"