28:null 29:["$","title",null,{"children":"The Sigmoid Function | Charles Redmond | Observable"}] 2e:T468,{ const svgDims = [600,300] const svg = d3.select(DOM.svg(svgDims[0],svgDims[1])).attr("style","background:white;border:1px solid white") const xScale = d3.scaleLinear().domain([-10,10]).range([30,570]) const yScale = d3.scaleLinear().domain([-1,1]).range([270,30]) const xAxis = svg.append("g").attr("transform",`translate(0,${yScale(0)})`).call(d3.axisBottom(xScale)) const yAxis = svg.append("g").attr("transform",`translate(${xScale(0)},0)`).call(d3.axisLeft(yScale).ticks(5)) for(let i = 0;i xScale(d)).y(d => yScale(slope*d+intercept))(data) svg.append("path").attr("d",pathData).attr("fill","none").attr("stroke","black") yield svg.node() }2f:T46d,{ const svgDims = [600,300] const svg = d3.select(DOM.svg(svgDims[0],svgDims[1])).attr("style","background:white;border:1px solid white") const xScale = d3.scaleLinear().domain([-10,10]).range([30,570]) const yScale = d3.scaleLinear().domain([-1,1]).range([270,30]) const xAxis = svg.append("g").attr("transform",`translate(0,${yScale(0)})`).call(d3.axisBottom(xScale)) const yAxis = svg.append("g").attr("transform",`translate(${xScale(0)},0)`).call(d3.axisLeft(yScale).ticks(5)) for(let i = 0;i xScale(d)).y(d => yScale(exp(slope*d+intercept)))(data) svg.append("path").attr("d",pathData).attr("fill","none").attr("stroke","black") yield svg.node() }30:T4a2,{ const svgDims = [600,300] const svg = d3.select(DOM.svg(svgDims[0],svgDims[1])).attr("style","background:white;border:1px solid white") const xScale = d3.scaleLinear().domain([-10,10]).range([30,570]) const yScale = d3.scaleLinear().domain([-1,1]).range([270,30]) const xAxis = svg.append("g").attr("transform",`translate(0,${yScale(0)})`).call(d3.axisBottom(xScale)) const yAxis = svg.append("g").attr("transform",`translate(${xScale(0)},0)`).call(d3.axisLeft(yScale).ticks(5)) const f = (d) => { return exp(slope*d+intercept) } for(let i = 0;i xScale(d)).y(d => yScale(f(d)/(1+f(d))))(data) svg.append("path").attr("d",pathData).attr("fill","none").attr("stroke","black") yield svg.node() }31:[] 2c:{"id":"c095b619f5c0b29c","slug":"the-sigmoid-function","title":"The Sigmoid Function","thumbnail":"8fb0a12e064e9ed5eb12a4a5f384936c162963c486d69b1dd393b3699f9cdac2","access_level":"public","create_time":"$D2020-06-25T13:42:35.830Z","update_time":"$D2020-11-09T21:43:41.886Z","view_time":null,"first_public_time":"$D2020-06-25T16:15:26.072Z","has_unpublished_edits":null,"fork":false,"stars":3,"starred":false,"owner":{"type":"team","id":"66151b62b45d9fca","login":"credmond","name":"Charles Redmond","avatar_url":"https://avatars-next.observableusercontent.com/50425ed9f407a7b47d1c471a09963f335e0652ab9acc237869e2d7949fb04a77","tier":"starter_2024"},"version":165,"publish_version":165,"role":null,"authored":false,"authors":[{"type":"individual","id":"37a987477e8b6db3","login":"credmond","name":"Charles Redmond","avatar_url":"https://avatars-next.observableusercontent.com/50425ed9f407a7b47d1c471a09963f335e0652ab9acc237869e2d7949fb04a77","tier":null}],"members":[{"type":"individual","id":"37a987477e8b6db3","login":"credmond","name":"Charles Redmond","avatar_url":"https://avatars-next.observableusercontent.com/50425ed9f407a7b47d1c471a09963f335e0652ab9acc237869e2d7949fb04a77","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":4,"collection":{"id":"1e9b5b6f5aa0f2d4","slug":"logistic-regression","title":"Logistic Regression","owner":{"id":"66151b62b45d9fca","login":"credmond","name":"Charles Redmond"}},"type":"notebook","body":{"title":"The Sigmoid Function","cells":[{"id":0,"value":"md`# The Sigmoid Function`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"viewof slope = slider({min:0,max:1,step:.01,description: \"set slope\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":67,"value":"viewof intercept = slider({min:-1,max:1,step:.01,description:\"set intercept\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":92,"value":"html`

log-odds of red given x

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"{\n if(slope == 1){\n var a = \"x\"\n }else if(slope == -1){\n var a = \"-x\"\n }else if(slope == 0){\n var a = \"\"\n }else{\n var a = `${slope}x`\n }\n\n if(intercept == 0 && slope == 0 ){\n return tex`y = 0`\n }else if(intercept == 0 ){\n return tex`y = ${a}`\n }else if(intercept > 0 && slope == 0){\n return tex`y = ${intercept}`\n }else if(intercept > 0){\n return tex`y = ${a} + ${intercept}`\n }else if(intercept < 0 ){\n return tex`y = ${a} - ${-1*intercept}`\n }else{\n return tex``\n }\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"$2e","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"html`

odds of red given x

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"tex`y = ${odds}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"html`

probability of red given x

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"tex`y = \\dfrac{${odds}}{1+${odds}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"html`

Variables and Code

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"data = {\n const data = []\n for(var i = -10; i <= 10; i = i + .01){\n data.push(i)\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":46,"value":"blue = {\n const blue = []\n for(let i = 0;i < 30;i++){\n blue.push({x:normal(-4,3),y:0})\n }\n return blue\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"red = {\n const red = []\n for(let i = 0;i < 30;i++){\n red.push({x:normal(4,3),y:1})\n }\n return red\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"odds = {\n if(slope == 1){\n var a = \"x\"\n }else if(slope == -1){\n var a = \"-x\"\n }else if(slope == 0){\n var a = \"\"\n }else{\n var a = `${slope}x`\n }\n\n if(intercept == 0 && slope == 0 ){\n return `e^{0}`\n }else if(intercept == 0 ){\n return `e^{${a}}`\n }else if(intercept > 0 && slope == 0){\n return ` e^{${intercept}}`\n }else if(intercept > 0){\n return `e^{${a} + ${intercept}}`\n }else if(intercept < 0 ){\n return ` e^{${a} - ${-1*intercept}}`\n }else{\n return ``\n }\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"html`

Libraries

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"import {slider,button,select,text,radio,checkbox,number} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"stdlib = require( \"https://unpkg.com/@stdlib/stdlib@0.0.32/dist/stdlib-flat.min.js\" )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"normal = stdlib.base.random.normal","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"ss = require(\"https://unpkg.com/simple-statistics@6.1.0/dist/simple-statistics.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"exp = stdlib.base.exp","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2d:"$2c:body"