3e:null 3f:["$","title",null,{"children":"Linear models in Observable notebooks | Riia Järvenpää | Observable"}] 45:T94d,md`Following the [discussion about statistics in Observable notebooks](https://talk.observablehq.com/t/observable-for-research-advanced-statistics/4538), this notebook demonstrates how (multiple) linear regression models can be performed in JavaScript. ***The library used for the regression analysis is still in it's early development, so please leave comments/ideas/suggestions about changes in the API and/or the general implementation or approach!*** Currently, [ml-matrix](https://github.com/mljs/matrix) is used for the linear algebra. In the long run, the library aims to - provide reliable and accurate results, on par with R and python - feature a similiar interface to R's own [\`lm\`](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/lm) function, including the [\`summary\`](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/summary) function for reading and interpreting the results **Currently, the library supports:** - [x] standard linear regression - [x] multiple linear regression - [x] models without intercept - [x] models including weights ([weighted linear regression](https://en.wikipedia.org/wiki/Weighted_least_squares)) - [x] polynomial regressions (with and without orthogonal polygons) - [x] evaluating arithmetic expressions in the formula (e.g log(y) ~ a + log(x)) - [x] interaction terms - [x] \`summary\` function for models - [x] \`summary\` function for dataframes (array of objects) Please let me know if you encouter bugs, or have feature requests! ## Overview - Summary statistics - [\`Describing datasets using summary\`](#describingdatasets) - [\`Using summary on a dataset with non-numeric columns\`](#excursion) - Linear regression models - [\`(Simple) linear regression\`](#linearregression) - [\`Scaling, Interaction terms, arithmetic expressions\`](#scaling) - [\`Multiple linear regression\`](#multiplelinearregression) - [\`(Multiple) linear regression without intercept\`](#nointercept) - [\`Weighted (multiple) linear regression (WLS)\`](#wls) - [\`Polynomial regression (orthogonal/raw)\`](#polynomialRegression) - Extras - [\`Coding for categorial variables\`](#codingCategorialVars) - [\`Detecting multicollinearity (VIF)\`](#detectingMulticollinearity) - [\`Creating publication ready tables\`](#creatingTables) - [\`Can I trust the results? 🤔\`](#trust) `46:T2049,function stargazer(models, options = {}) { if (!models) throw TypeError("No model specified."); if (!Array.isArray(models)) models = [models]; const columns = models.length + 1; const columnsArray = [...new Array(columns)]; function checkPValue(value) { if (value < 0.01) { return "***"; } else if (value < 0.05) { return "**"; } else if (value < 0.1) { return "*"; } else { return ""; } } function pad(string) { if (!(string.startsWith("-") || string.startsWith("("))) { string = " " + string; } const curLength = string.length; const desired = 9; while (string.length < 9) { string += " "; } return string; } let htmlString = ` `; const dependentVars = {}; for (let i = 0; i < models.length; ++i) { let label = models[i].dependantVar.string; if (options.labels && options.labels[label]) { label = options.labels[label]; } if (dependentVars[label]) dependentVars[label] += 1; else dependentVars[label] = 1; } const independentVars = {}; for (let i = 0; i < models.length; ++i) { const curModel = models[i]; for (let j = 0; j < curModel.independantVars.length; ++j) { const predictor = curModel.independantVars[j].string; if (options.labels && options.labels[predictor]) { if (!independentVars[options.labels[predictor]]) { independentVars[options.labels[predictor]] = [predictor]; } else if ( independentVars[options.labels[predictor]].indexOf(predictor) === -1 ) { independentVars[options.labels[predictor]].push(predictor); } } else if (!independentVars[predictor]) { independentVars[predictor] = [predictor]; } } } // const independentVars = [...new Set(models.reduce((arr,cur) => (cur.independentVars.forEach(v => arr.push(v.string)), arr),[]))] // ToDo implement optional sorting htmlString += ` ${Object.keys(dependentVars) .map( (key, i) => `` ) .join("")} ${ options.modelTypes ? Object.keys(options.modelTypes) .map((key, i) => { return ``; }) .join("") : Object.keys(dependentVars) .map( (key, i) => `` ) .join("") } ${models .map( (m, i) => `` ) .join("")} ${Object.keys(independentVars) .map( (vLabel) => ` ${models .map((m) => { const possibleNames = independentVars[vLabel]; let varIndex = m.independantVars.findIndex( (v) => possibleNames.indexOf(v.string) > -1 ); if (varIndex !== -1 && !m.modelWithoutIntercept) varIndex = varIndex + 1; if (varIndex > -1) { return ``; } else { return ""; } }) .join("")} ` ) .join("")} ${ models.some((m) => !m.modelWithoutIntercept) && `` + models .map((m) => { if (!m.modelWithoutIntercept) { return ``; } else { return ""; } }) .join("") + "" } ${models .map( (m, i) => `` ) .join("")} ${models .map( (m, i) => `` ) .join("")} ${models .map( (m, i) => `` ) .join("")} ${models .map( (m, i) => `` ) .join("")} ${models .map( (m, i) => `` ) .join("")} `; return html`${htmlString}`; //return dependentVars }47:T23c8,function summary(modelOrDataframe, options = {}) { if ( modelOrDataframe.hasOwnProperty("call") // && modelOrDataframe.hasOwnProperty('modelWithoutIntercept') ) { const model = modelOrDataframe; // perform a summary on the results of a regression model let htmlString = `Call:`; // add model call htmlString += `

lm(formula = ${model.call})

`; // add residual summary htmlString += `Residuals:
`; htmlString += `

	Dependent variable:
	${ options.labels && options.labels[key] ? options.labels[key] : key }
	${key}	OLS
	${ options.modelNames ? options.modelNames[i] + " " : `(${i + 1}) ` }
${vLabel}	${pad( `${m.coefficients[varIndex].toFixed(3)}${checkPValue( m.pValues[varIndex] )}` )} ${pad( `(${m.standardErrors[varIndex].toFixed(3)})` )}
Constant	${pad( `${m.coefficients[0].toFixed(3)}${checkPValue( m.pValues[0] )}` )} ${pad(`(${m.standardErrors[0].toFixed(3)})`)}
Observations	${m.dataframe.length.toString()}
R²	${m.rSquared.toFixed( 3 )}
Adjusted R²	${m.adjRSquared.toFixed( 3 )}
Residual Std. Error	${m.s.toFixed( 3 )}(df = ${m.rdf})
F Statistic	${m.f.toFixed( 3 )}${checkPValue(m.f)}(df = ${m.dfm};${m.rdf})
Note:	p<0.1; p<0.05; **p<0.01

Min	1Q	Median	3Q	Max
${round(d3.min(model.residuals), 4)}	${round( d3.quantile(model.residuals, 0.25), 4 )}	${round( d3.median(model.residuals), 4 )}	${round( d3.quantile(model.residuals, 0.75), 4 )}	${round(d3.max(model.residuals), 4)}

`; // add coefficients if (model.error && model.errorMessage === "LU matrix is singular") { htmlString += `Coefficients: (${model.removedVars.length} not defined because of singularities)
`; } else { htmlString += `Coefficients:
`; } htmlString += ` `; const significanceValues = [0.001, 0.01, 0.05, 0.1, 1]; const significanceCodes = ["***", "**", "*", ".", ""]; model.coefficients.forEach((value, i) => { let predictorName = model.independantVars[i]?.string; if (!model.modelWithoutIntercept) { if (i === 0) predictorName = "(Intercept)"; else predictorName = model.independantVars[i - 1].string; } if (model.removedVars && model.removedVars.indexOf(predictorName) > -1) { htmlString += ``; } else { const significanceIndex = significanceValues.findIndex( (sv) => model.pValues[i] < sv ); htmlString += ``; } }); if (model.removedVars) { model.removedVars.forEach((removedPredictor) => { if (model.coefficients.indexOf(removedPredictor) > -1) return; htmlString += ``; }); } htmlString += `

	Estimate	Std. Error	t value	Pr(>\|t\|)
${predictorName}	NA	NA	NA	NA
${predictorName}	${round(value, 4)}	${round(model.standardErrors[i], 4)}	${round(model.tValues[i], 3)}	${round( model.pValues[i], 4 )}	${ significanceIndex > -1 ? significanceCodes[significanceIndex] : "" }
${removedPredictor}	NA	NA	NA	NA
Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

`; //*/ htmlString += `Residual standard error: ${round(model.s, 4, false)} on ${ model.rdf } degrees of freedom
`; if (model.omittedRows && model.omittedRows.length) { htmlString += ` (${model.omittedRows.length} observations deleted due to missingness)
`; } htmlString += `Multiple R-squared: ${round( model.rSquared, 4, false )}, Adjusted R-squared: ${round(model.adjRSquared, 4, false)}
`; htmlString += `F-Statistics: ${round(model.f, 3, false)}, on ${ model.dfm } and ${model.rdf} DF, p-value: ${round(model.pValue, 3, false)}`; return html`

${htmlString}

`; } else { const dataframe = modelOrDataframe; const set = new Set(); for (const row of dataframe) { for (const key of Object.keys(row)) set.add(key); } const columnNames = [...set]; const numericRows = [ "Min.", "1st Qu.", "Median", "Mean", "3rd Qu.", "Max." ]; let rows = numericRows.length; let containsNA = false; let summaryData = columnNames.map((column) => { let isNumeric = true; const mappedData = dataframe.map((r) => { if (r[column] !== undefined && isNaN(r[column])) isNumeric = false; return r[column]; }); if (isNumeric) { return { isNumeric: true, categories: [ d3.min(mappedData), d3.quantile(mappedData, 0.25), d3.median(mappedData), d3.mean(mappedData), d3.quantile(mappedData, 0.75), d3.max(mappedData), mappedData.filter((d) => d === null || d === undefined || isNaN(d)) .length ] }; } else { const keysWithCounts = mappedData.reduce((obj, cur) => { if (!obj[cur]) obj[cur] = 0; obj[cur] += 1; return obj; }, {}); const namesOfCategories = Object.keys(keysWithCounts); if (namesOfCategories.length > rows) rows = namesOfCategories.length; return { isNumeric: false, sortedKeys: namesOfCategories.sort(), categories: keysWithCounts }; } }); if ( summaryData.some((column) => column.isNumeric && column.categories[6] > 0) ) { containsNA = true; numericRows.push("NA's"); rows = numericRows.length; } if (options.ignoreNonNumeric) { const indecesToRemove = []; summaryData.forEach((column, i) => { if (!column.isNumeric) { indecesToRemove.push(i); } }); while (indecesToRemove.length) { columnNames.splice(indecesToRemove.pop(), 1); } summaryData = summaryData.filter((column) => column.isNumeric); rows = numericRows.length; } let htmlString = `

${columnNames .map((key, i) => ``) .join("")}`; for (let j = 0; j < rows; j++) { htmlString += `${columnNames .map((key, i) => { let padding = i > 0 ? 20 : 0; if (summaryData[i].isNumeric && numericRows[j]) { return ``; } else if ( !summaryData[i].isNumeric && summaryData[i].sortedKeys[j] ) { return ``; } else { return ``; } }) .join("")}`; } return html`${htmlString}`; } }48:[{"id":"e47b2d6937ff57b12bdded94cad1f55c985dc5c900d1476a3e100b13416f016b35ab752163b07685652441e4c2a2dcbefe7e00ce5cfec082b9f2ff4346081850","href":"https://static.observableusercontent.com/files/e47b2d6937ff57b12bdded94cad1f55c985dc5c900d1476a3e100b13416f016b35ab752163b07685652441e4c2a2dcbefe7e00ce5cfec082b9f2ff4346081850","name":"freeny.csv","type":"text/csv","lastModified":1683363945862.525,"size":1614},{"id":"ccd41e7902c50e2ce8d3852b212de2a727b137a460b870b09ffe952da4dbdcb40a089f9eec3a5f5a35f4fa1389ddb743a90e7cd878de60b9751e81898432a7ce","href":"https://static.observableusercontent.com/files/ccd41e7902c50e2ce8d3852b212de2a727b137a460b870b09ffe952da4dbdcb40a089f9eec3a5f5a35f4fa1389ddb743a90e7cd878de60b9751e81898432a7ce","name":"hsb2.csv","type":"text/csv","lastModified":1683363945862.525,"size":5976},{"id":"20abd1368e7b85da88c933f0b8c324499ac8dc8563797925fdc6c5ff7f339852b4d9be388e884ee90360d2a16bea6526fdcc5cd7ba658aff68b61a5b85892584","href":"https://static.observableusercontent.com/files/20abd1368e7b85da88c933f0b8c324499ac8dc8563797925fdc6c5ff7f339852b4d9be388e884ee90360d2a16bea6526fdcc5cd7ba658aff68b61a5b85892584","name":"linear-models.esm@50.js","type":"application/javascript","lastModified":1683363945862.525,"size":128372}] 43:{"id":"a8e2f5364bf56eb4","slug":null,"title":"Linear models in Observable notebooks","thumbnail":"e86395f03f5b71d96eb1ad19de06154de7c5b9b3eb16627ef5e7bf6bad91bc31","access_level":"public","create_time":"$D2023-05-06T09:05:45.862Z","update_time":"$D2023-05-06T09:05:45.862Z","view_time":null,"first_public_time":"$D2023-05-06T09:05:45.862Z","has_unpublished_edits":null,"fork":{"id":"c3ef6d4e928e9ece","slug":"linear-models-in-observable-notebooks","title":"Linear models in Observable notebooks","owner":{"id":"d2dc6c8d94d1ea2c","login":"chrispahm","name":"Christoph Pahmeyer"}},"stars":0,"starred":false,"owner":{"type":"team","id":"1a7853441e3c211d","login":"rialistic","name":"Riia Järvenpää","avatar_url":"https://avatars-next.observableusercontent.com/b4c8ff27583b2087427edc32f10cb51d0ca63b15edff86fe2bb5e15692bcf867","tier":"starter_2024","bio":"Trying to be a social data researcher. Kallio, Helsinki, Finland. I like to data, but been mostly doing raw communications so far.","following":false},"version":1562,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"02643ec94659c257","login":"rialistic","name":"Riia Järvenpää","avatar_url":"https://avatars-next.observableusercontent.com/b4c8ff27583b2087427edc32f10cb51d0ca63b15edff86fe2bb5e15692bcf867","tier":null,"bio":"Trying to be a social data researcher. Kallio, Helsinki, Finland. I like to data, but been mostly doing raw communications so far.","following":false}],"members":[{"type":"individual","id":"02643ec94659c257","login":"rialistic","name":"Riia Järvenpää","avatar_url":"https://avatars-next.observableusercontent.com/b4c8ff27583b2087427edc32f10cb51d0ca63b15edff86fe2bb5e15692bcf867","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Linear models in Observable notebooks","cells":[{"id":0,"value":"md`# Linear models in Observable notebooks`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":220,"value":"$45","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":547,"value":"describingdatasets = md`### Describing datasets`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":250,"value":"md`The following examples will use \"Freeny's data on quarterly revenue and explanatory variables\" dataset ([source](https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/freeny.html)). In R, the dataset is available under the variable \\`freeny\\`. `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":207,"value":"freeny = FileAttachment('freeny.csv').csv({ typed: true })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":257,"value":"md`In order to get an overview of the data, we can use the \\`summary\\` function to describe the dataset. Just like in R!`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":217,"value":"summary(freeny)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":801,"value":"md`By importing the [\\`pairplot\\`](https://observablehq.com/@chrispahm/plotting-pairwise-relationships-in-a-dataset) function, `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":736,"value":"import { pairplot } from '@chrispahm/plotting-pairwise-relationships-in-a-dataset'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":714,"value":"pairplot(freeny, { width: 600, height: 450, spacing: -10 })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":185,"value":"linearregression = md`### Linear regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":265,"value":"md`In order to fit a linear model on our dataset, we can use the \\`lm\\` function just like we would do in R. The first argument in the \\`lm\\` function takes the models formula as a string. The \\`~\\` operator is basic in the formation of such models. An expression of the form \\`y ~ model\\` is interpreted as a specification that the response \\`y\\` is modelled by a linear predictor specified symbolically by \\`model\\` (or \\`income.level\\` in our specific example).\n\nBear in mind that the names of the linear predictors need to **exactly match** the names of the properties of the dataframe (array of objects) that are passed to the \\`lm\\` function as the second argument.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":276,"value":"md`Now that we fit our model, we can inspect and analyze it using the \\`summary\\` function`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":739,"value":"linear_model = lm('y ~ income.level', freeny)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":741,"value":"summary(linear_model)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":191,"value":"multiplelinearregression = md`### Multiple linear regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"multiple_regression = lm('market.potential ~ price.index + income.level', freeny)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":215,"value":"summary(multiple_regression)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":670,"value":"scaling = md`### Scaling`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":766,"value":"multiple_regression_scaled = lm(\n 'scale(market.potential) ~ scale(price.index) + scale(income.level) - 1',\n freeny\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":769,"value":"summary(multiple_regression_scaled)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":776,"value":"interactionTerms = md`### Interaction terms`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":771,"value":"multiple_regression_interaction = lm(\n 'market.potential ~ price.index + income.level + income.level * price.index',\n freeny\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":773,"value":"summary(multiple_regression_interaction)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":792,"value":"arithmeticExpression = md`### Arithmetic expressions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":779,"value":"multiple_regression_arithmetic = lm(\n 'log(market.potential) ~ price.index + log(income.level)',\n freeny\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":782,"value":"summary(multiple_regression_arithmetic)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":204,"value":"nointercept = md`### Models without intercept`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":177,"value":"regression_wo_intercept = lm(\n 'market.potential ~ price.index + income.level - 1',\n freeny\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":180,"value":"summary(regression_wo_intercept)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":478,"value":"wls = md`### Weighted linear regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":482,"value":"md`This simple example was taken from the [R source code tests of the \\`lm\\` function](https://github.com/wch/r-source/blob/trunk/tests/lm-tests.R)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":485,"value":"roller = {\n const weight = [1.9, 3.1, 3.3, 4.8, 5.3, 6.1, 6.4, 7.6, 9.8, 12.4];\n const depression = [2, 1, 5, 5, 20, 20, 23, 10, 30, 25];\n return weight.map((w, i) => {\n return {\n weight: w,\n depression: depression[i],\n w: i + 1\n };\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":488,"value":"rlm = lm('weight ~ depression', roller, {\n weights: roller.map(r => r.w)\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":490,"value":"summaryStatisticsReg = summary(rlm)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1002,"value":"polynomialRegression = md`### Polynomial regression`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1014,"value":"md`#### Using orthogonal polygons`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1008,"value":"polyReg = lm('y ~ poly(income.level, 6)', freeny)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1011,"value":"summary(polyReg)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1020,"value":"md`#### Using 'raw' polygons`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1026,"value":"summary(lm(\"y ~ income.level + I(income.level^2)\", freeny))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1036,"value":"codingCategorialVars = md`### Coding for categorial variables`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1213,"value":"md`Following this UCLA tutorial on coding for categorial variables: https://stats.idre.ucla.edu/r/modules/coding-for-categorical-variables-in-regression-models/`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1039,"value":"hsb2 = FileAttachment(\"hsb2.csv\").csv({ typed: true })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1061,"value":"hsb_with_factor = hsb2.map(r => {\n const factor = 'race';\n // get uniqe factor levels\n const factorLevels = [...new Set(hsb2.map(r => r[factor]))];\n const sortedLevels = factorLevels.sort();\n // for each factor level, add a new column to our dataframe\n // e.g. race.f1, race.f2 ...\n sortedLevels.forEach(\n level => (r[factor + '.f' + level] = r[factor] === level ? 1 : 0)\n );\n return r;\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1051,"value":"summary(lm('write ~ race.f2 + race.f3 + race.f4', hsb_with_factor))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1202,"value":"detectingMulticollinearity = md`### Detecting multicollinearity in a regression model`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1216,"value":"md`The \\`vif\\` function calculates the VIF values for all predictors in the regression model. Please read the following excellent UCLA tutorial on detecting multicollinearity in regression models for details: http://www.sthda.com/english/articles/39-regression-model-diagnostics/160-multicollinearity-essentials-and-vif-in-r/`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1206,"value":"vifValues = vif(multiple_regression)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1208,"value":"View(vifValues)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1416,"value":"creatingTables = md`### Creating publication ready tables from regression outputs`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1420,"value":"md`The \\`stargazer\\` function can be used to create well-formatted (HTML) tables that hold regression analysis results from several models side-by-side. \nYou can copy & paste these tables in a Google Docs or Word document, which will preserve its structure. \nThe function is heavily inspired by the R [stargazer](https://www.rdocumentation.org/packages/stargazer/versions/5.2.2/topics/stargazer) package.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1400,"value":"publicationTable = stargazer(\n [multiple_regression, multiple_regression_scaled],\n {\n labels: {\n \"market.potential\": \"Market potential\",\n \"scale(market.potential)\": \"Market potential, scaled\",\n \"price.index\": \"Price index\",\n \"income.level\": \"Income level\",\n \"scale(price.index,2)\": \"Price index, scaled\",\n \"scale(income.level,1)\": \"Income level, scaled\"\n },\n modelNames: [\"OLS\", \"Scaled OLS\"],\n modelTypes: {} // { OLS: 2}\n }\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1472,"value":"trust = md`### Can I trust the results? 🤔 \n\nWhile the \\`lm\\` function is validated with the results of R's lm for a few datasets, **you should still validate your individual results before publishing**. \nFor this purpose, the result of a call to \\`lm\\` exports a \\`toR\\` method, which returns the equivalent R code for your lm function call as a string. Passing \\`true\\` as an argument in the \\`toR\\` method (aka \\`toR(true)\\`) will also include the accompanying dataframe used in the call.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1477,"value":"rCodeString = multiple_regression.toR(true)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1523,"value":"md`The resulting R code may either be run locally, or using OpenCPU (see https://observablehq.com/@bryangingechen/hello-r-on-opencpu, as done below):`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1489,"value":"{\n const pre = html`

`;\n  const code = html``;\n  pre.appendChild(code);\n  //arguments\n  const mysnippet = new ocpu.Snippet(rCodeString);\n\n  // use the public base server\n  ocpu.seturl(\"//public.opencpu.org/ocpu/library/base/R\");\n\n  //perform the request\n  const req = ocpu.call(\n    \"identity\",\n    {\n      x: mysnippet\n    },\n    function (session) {\n      session.getConsole(function (outtxt) {\n        code.innerText = outtxt;\n      });\n    }\n  );\n\n  //if R returns an error, put the error message\n  req.fail(function () {\n    const err = \"Server error: \" + req.responseText;\n    code.innerText = err;\n  });\n\n  return pre;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1526,"value":"md`For comparison, here's the result of the (JS) \\`lm\\` function presented in this notebook: `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1518,"value":"summary(multiple_regression)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1494,"value":"import { ocpu } from \"@bryangingechen/hello-r-on-opencpu\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":511,"value":"excursion = md`### Using \\`summary\\` on a dataframe with non-numeric columns`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":518,"value":"summary([{ m: 1, n: 2, c: 'red' }])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":569,"value":"md`In case you only want to focus on numerical columns, you may pass the \\`ignoreNonNumeric\\` flag in the options object (*second argument*):`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":574,"value":"summary([{ c: 'red', m: 1, n: 2 }], { ignoreNonNumeric: true })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":529,"value":"md`You can use the slider below in order to test the performance of the \\`summary\\` function depending on the dataframes length.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":524,"value":"viewof noOfRows = Range([1, 1000000], {\n  value: 100,\n  label: \"Number of rows\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":521,"value":"{\n  const data = [];\n  const colors = [\n    'blue',\n    'green',\n    'red',\n    'orange',\n    'pink',\n    'yellow',\n    'black',\n    'grey'\n  ];\n  for (let i = 0; i < noOfRows; i++) {\n    data.push({\n      m: Math.round(Math.random() * 100),\n      n: Math.round(Math.random() * 100),\n      c: colors[d3.randomInt(0, colors.length)()]\n    });\n  }\n  return summary(data);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":533,"value":"md`### Technical appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1397,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1191,"value":"import { View } from '2e82ed5d6839b1de'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1224,"value":"ml = require('ml-matrix')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1166,"value":"function vif(model) {\n  const vifResults = {};\n  model.independantVars.forEach(predictor => {\n    const dependent = predictor;\n    const independentVars = model.independantVars.filter(v => v !== predictor);\n    const reg = lm(\n      `${predictor.string} ~ ${independentVars.map(v => v.string).join(' + ')}`,\n      model.dataframe\n    );\n    vifResults[predictor.string] = 1 / (1 - reg.rSquared);\n  });\n  return vifResults;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":954,"value":"function appendZeroesScientific(value) {\n  const string = value.toString();\n  let e = 'e-';\n  let elements = string.split('e-');\n  if (!elements[1]) {\n    elements = string.split('e');\n    e = 'e';\n  }\n  let number = elements[1];\n  if (!number) return string;\n  // count digits\n  const digits = number.length;\n  if (digits === 1) {\n    return elements[0] + e + '0' + number;\n  }\n  return string;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":427,"value":"import { Range } from \"@observablehq/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"function round(value, decimals, enforceDecimals = true) {\n  if (value === 0) return '<2e-16';\n  // check if number rounds to integer given a precision of 1e-07,\n  // which is R's default value\n  const rounded16 = roundAccurately(value, 16);\n  if (countDecimals(rounded16) < decimals && !isNaN(rounded16))\n    return rounded16;\n  if (\n    value > Number(`-0.${new Array(decimals).join('0')}9`) &&\n    value < Number(`0.${new Array(decimals).join('0')}9`)\n  )\n    return appendZeroesScientific(value.toExponential(2));\n  const roundedVal = roundAccurately(value, decimals);\n  //return roundedVal;\n  return enforceDecimals ? roundedVal.toFixed(decimals) : roundedVal;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":838,"value":"function roundAccurately(number, decimalPlaces) {\n  if (number.toString().includes(\"e\")) {\n    return (\n      Math.round(number * Math.pow(10, decimalPlaces)) /\n      Math.pow(10, decimalPlaces)\n    );\n  } else {\n    return Number(\n      Math.round(number + \"e\" + decimalPlaces) + \"e-\" + decimalPlaces\n    );\n  }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":818,"value":"function countDecimals(value) {\n  let text = value.toString();\n  // verify if number 0.000005 is represented as \"5e-6\"\n  if (text.indexOf('e-') > -1) {\n    let [base, trail] = text.split('e-');\n    let deg = parseInt(trail, 10);\n    return deg;\n  }\n  // count decimals for number in representation like \"0.123456\"\n  try {\n    if (Math.floor(value) !== value) {\n      return value.toString().split(\".\")[1].length || 0;\n    }\n  } catch (e) {\n    console.log(e, value);\n    //\n  }\n\n  return 0;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"lm = (await import(await FileAttachment(\"linear-models.esm@50.js\").url()))\n  .default","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"d3 = require('d3')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W48","stdlib":"1"}}
44:"$43:body"

${key}
${ numericRows[j] }	${ numericRows[j] === "NA's" ? summaryData[i].categories[j] : summaryData[i].categories[j].toFixed(3) }	${ summaryData[i].sortedKeys[j] }	${summaryData[ i ].categories[summaryData[i].sortedKeys[j]].toString()}