2a:null 2b:["$","title",null,{"children":"Correlation | Harry Stevens | Observable"}] 30:[] 2e:{"id":"6907be2377f291ab","slug":"correlation","title":"Correlation","thumbnail":"ec277e78bbf0fc7e119d988f2e62bd1fe5dc8f40482f98b20f9641c6cd2fa643","access_level":"public","create_time":"$D2020-06-16T19:22:40.362Z","update_time":"$D2021-09-03T18:02:42.684Z","view_time":null,"first_public_time":"$D2020-06-16T20:07:10.293Z","fork":false,"stars":6,"starred":false,"owner":{"type":"team","id":"be420f6a83563b92","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":"starter_2024"},"version":245,"publish_version":245,"role":null,"authored":false,"authors":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":null}],"members":[{"type":"individual","id":"61e2153e05789733","login":"harrystevens","name":"Harry Stevens","avatar_url":"https://avatars-next.observableusercontent.com/bc9bae4b7e30062b343ae978a13454e29cd3f2daf3a800d0024043686ddf094b","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Correlation","cells":[{"id":0,"value":"md`# Correlation\n\nThis notebook includes a function to calculate the [correlation coefficient](https://en.wikipedia.org/wiki/bivariate_correlation) for two variables in a data array. To use it in your notebook:\n\n~~~js\nimport { Correlation } from \"@harrystevens/correlation\";\n~~~`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":171,"value":"toc({selector: \"h2\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":76,"value":"md`## API Reference`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":79,"value":"md`Correlation()\n\nCreates a new correlation coefficient generator with default x- and y-accessors.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":89,"value":"myCorrelationGenerator = Correlation();","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":102,"value":"// Total positive correlation\nmyCorrelationGenerator([\n [1, 1],\n [2, 2]\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":108,"value":"// Total negative correlation\nmyCorrelationGenerator([\n [1, 2],\n [2, 1]\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":223,"value":"// Ignores pairs with null or non-numeric values\nmyCorrelationGenerator([\n [1, 1],\n [2, 2],\n [null, 3],\n [4, \"foobar\"]\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":234,"value":"// true and false evaluate to 1 and 0, respectively\nmyCorrelationGenerator([\n [false, true],\n [true, false]\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":110,"value":"// Sample dataset from https://memory.psych.mun.ca/tech/js/correlation.shtml\nmyCorrelationGenerator([\n [50, 58],\n [80, 97],\n [95, 81],\n [33, 51],\n [61, 67],\n [43, 15],\n [55, 61],\n [48, 24],\n [50, 75],\n [5, 16]\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":96,"value":"md`correlation.x([x])\n\nIf x is specified, sets the x-accessor, which is passed the current datum (d), the current index (i), and the entire data array (data). If x is not specified, returns the current x-accessor, which defaults to:\n\n~~~js\nfunction x(d, i, data) {\n return d[0];\n}\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":127,"value":"md`correlation.y([y])\n\nIf y is specified, sets the y-accessor, which is passed the current datum (d), the current index (i), and the entire data array (data). If y is not specified, returns the current y-accessor, which defaults to:\n\n~~~js\nfunction y(d, i, data) {\n return d[1];\n}\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":130,"value":"yourCorrelationGenerator = Correlation()\n .x(d => d.sales)\n .y(d => d.temperature);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":148,"value":"// Total positive correlation\nyourCorrelationGenerator([\n {sales: 10, temperature: 50},\n {sales: 20, temperature: 60}\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":153,"value":"// Total negative correlation\nyourCorrelationGenerator([\n {sales: 20, temperature: 50},\n {sales: 10, temperature: 60}\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":143,"value":"// Same sample dataset but with objects instead of arrays\nyourCorrelationGenerator([\n {\"sales\": 50, \"temperature\": 58},\n {\"sales\": 80, \"temperature\": 97},\n {\"sales\": 95, \"temperature\": 81},\n {\"sales\": 33, \"temperature\": 51},\n {\"sales\": 61, \"temperature\": 67},\n {\"sales\": 43, \"temperature\": 15},\n {\"sales\": 55, \"temperature\": 61},\n {\"sales\": 48, \"temperature\": 24},\n {\"sales\": 50, \"temperature\": 75},\n {\"sales\": 5, \"temperature\": 16}\n]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":44,"value":"md`## Code`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"function Correlation(){\n let x = d => d[0],\n y = d => d[1];\n \n function correlation(data){\n let l = data.length,\n n = 0,\n xSum = 0,\n ySum = 0,\n xySum = 0,\n x2Sum = 0,\n y2Sum = 0;\n \n for (let i = 0; i < l; i++){\n const d = data[i],\n dx = x(d, i, data),\n dy = y(d, i, data);\n \n if (dx != null && isFinite(dx) && dy != null && isFinite(dy)) {\n xSum += dx;\n ySum += dy;\n xySum += dx * dy;\n x2Sum += dx * dx;\n y2Sum += dy * dy;\n n++;\n }\n\n }\n \n return (n * xySum - xSum * ySum) / Math.sqrt((n * x2Sum - xSum * xSum) * (n * y2Sum - ySum * ySum));\n }\n\n correlation.x = function(fn){ return arguments.length ? (x = fn, correlation) : x; }\n correlation.y = function(fn){ return arguments.length ? (y = fn, correlation) : y; }\n \n return correlation;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":194,"value":"md`## Sources\n- [Wikipedia](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient)\n- [Ian Neath](https://memory.psych.mun.ca/tech/js/correlation.shtml)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":74,"value":"import { toc} from \"@harrystevens/toc\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2f:"$2e:body"