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@kgryte
Created July 3, 2013 04:45
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Anscombe's Quartet + D3.js

Anscombe's Quartet

D3.js visualization of Anscombe's Quartet. Each dataset in the quartet is graphed separately along with its linear best fit. While all datasets have the same summary statistics (mean, variance, correlation, linear fit), their structures differ markedly.

Anscombe used the quartet in his seminal paper "Graphs in Statistical Analysis" to emphasize the importance of data visualization for exploratory data analysis. Such visualization exploration enables the analyst to make more informed analytical decisions and conclusions.

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{
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},
{
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{
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},
{
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},
{
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{
"x": 12,
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{
"x": 7,
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{
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[
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{
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{
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{
"x": 8,
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{
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]
]
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<!-- Stylesheets -->
<link href='http://fonts.googleapis.com/css?family=Cabin:500' rel='stylesheet' type='text/css'>
<link rel="stylesheet" type="text/css" href="reset.css">
<link rel="stylesheet" type="text/css" href="style.css">
<!-- Libraries -->
<script type="text/javascript" src="d3.min.js"></script>
<!-- Scripts -->
<script type="text/javascript" src="script.js"></script>
</head>
<body>
<h1>Anscombe's Quartet</h1>
<script type="text/javascript">
var scatter = Chart.scatter();
// Update settings:
scatter.xDomain( [3.5, 19] )
.yDomain( [2, 12.5] )
.yTicks( 5 );
// Load the JSON data:
d3.json( 'data.json', function( data ) {
var figure, width;
// For each dataset in 'data', create a figure and graph the dataset along with its linear fit:
for (var i = 0; i < data.length; i++) {
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figure = d3.select( 'body' )
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// Get the figure width:
width = parseInt( figure.style( 'width' ), 10 );
// Update the chart generator settings:
scatter.width( width )
.xLabel( 'x' + (i+1) )
.yLabel( 'y' + (i+1) );
// Append the data and generate a new chart:
figure.datum( data[i] )
.attr('class', 'chart')
.call( scatter );
// Compute the linear fit:
scatter.linearFit();
}; // end FOR i
});
</script>
</body>
</html>
/* http://meyerweb.com/eric/tools/css/reset/
v2.0 | 20110126
License: none (public domain)
*/
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del, dfn, em, img, ins, kbd, q, s, samp,
small, strike, strong, sub, sup, tt, var,
b, u, i, center,
dl, dt, dd, ol, ul, li,
fieldset, form, label, legend,
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article, aside, canvas, details, embed,
figure, figcaption, footer, header, hgroup,
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padding: 0;
border: 0;
font-size: 100%;
font: inherit;
vertical-align: baseline;
}
/* HTML5 display-role reset for older browsers */
article, aside, details, figcaption, figure,
footer, header, hgroup, menu, nav, section {
display: block;
}
body {
line-height: 1;
}
ol, ul {
list-style: none;
}
blockquote, q {
quotes: none;
}
blockquote:before, blockquote:after,
q:before, q:after {
content: '';
content: none;
}
table {
border-collapse: collapse;
border-spacing: 0;
}
/**
*
*
*
*
*
* @author Kristofer Gryte. http://www.kgryte.com
*
*
*/
var Chart = {};
Chart.scatter = function() {
var margin = {'top': 20, 'right': 20, 'bottom': 40, 'left': 80},
height = 300,
width = 760,
radius = 5,
xLabel = 'x',
yLabel = 'y',
xTicks, yTicks,
xValue = function(d) { return d.x; },
yValue = function(d) { return d.y; },
xScale = d3.scale.linear(),
yScale = d3.scale.linear(),
xAxis = d3.svg.axis().scale( xScale ).orient( 'bottom' ),
yAxis = d3.svg.axis().scale( yScale ).orient( 'left' ),
xDomain, yDomain,
line = d3.svg.line().x( X ).y( Y ),
linearFit,
canvas, graph, dataset, circles;
function chart( selection ) {
selection.each( function( data ) {
// Convert data to standard representation; needed for non-deterministic accessors:
data = data.map( function(d, i) {
return {
'x': xValue.call(data, d, i),
'y': yValue.call(data, d, i)
};
});
if (!xDomain) {
xDomain = d3.extent( data, function(d) { return d.x; });
};
if (!yDomain) {
yDomain = d3.extent( data, function(d) { return d.y; });
};
if (xTicks) {
xAxis.ticks( xTicks );
};
if (yTicks) {
yAxis.ticks( yTicks );
};
// Update the x-scale:
xScale
.domain( xDomain )
.range( [0, width - margin.left - margin.right] );
// Update the y-scale:
yScale
.domain( yDomain )
.range( [height - margin.top - margin.bottom, 0]);
// Create the SVG element:
canvas = d3.select( this ).append('svg:svg')
.attr('width', width)
.attr('height', height)
.attr('class', 'canvas');
// Create the graph element:
graph = canvas.append('svg:g')
.attr('class', 'graph')
.attr('transform', 'translate(' + margin.left + ',' + margin.top + ')');
// Create the dataset group:
dataset = graph.append('svg:g')
.attr('class', 'dataset');
// Create the circle marks:
circles = dataset.selectAll('.point')
.data( data )
.enter().append('svg:circle')
.attr('class', 'point')
.attr('cx', function(d) { return X(d);} )
.attr('cy', function(d) { return Y(d);} )
.attr('r', radius );
// Create the axes:
graph.append('svg:g')
.attr('class', 'x axis')
.attr('transform', 'translate(0,' + yScale.range()[0] + ')')
.call( xAxis )
.append('svg:text')
.attr('y', 40)
.attr('x', xScale.range()[1] / 2)
.attr('text-anchor', 'middle')
.attr('class', 'label')
.text( xLabel );
graph.append('svg:g')
.attr('class', 'y axis')
.call( yAxis )
.append('svg:text')
.attr('transform', 'rotate(-90)')
.attr('y', -74)
.attr('dy', '.71em')
.attr('x', -yScale.range()[0] / 2)
.attr('text-anchor', 'middle')
.attr('class', 'label')
.text( yLabel );
});
}; // end FUNCTION chart()
// x-accessor:
function X(d) {
return xScale( d.x );
};
// y-accessor:
function Y(d) {
return yScale( d.y );
};
// http://en.wikipedia.org/wiki/Simple_linear_regression
function linearRegression( data ){
var lr = {},
n = data.length,
sum_x = 0,
sum_y = 0,
sum_xy = 0,
sum_xx = 0,
sum_yy = 0;
for (var i = 0; i < data.length; i++) {
sum_x += data[i].x;
sum_y += data[i].y;
sum_xy += (data[i].x*data[i].y);
sum_xx += (data[i].x*data[i].x);
sum_yy += (data[i].y*data[i].y);
};
var XX = sum_x*sum_x,
XY = sum_x*sum_y,
YY = sum_y*sum_y,
nxy = n*sum_xy,
nxx = n*sum_xx,
nyy = n*sum_yy;
lr['slope'] = (nxy - XY) / (nxx - XX);
lr['intercept'] = (sum_y - lr.slope*sum_x) / n;
lr['r2'] = Math.pow( (nxy - XY) / Math.sqrt((nxx-XX)*(nyy-YY)), 2);
lr['fn'] = function(x) { return this.slope*x + this.intercept; };
return lr;
};
// Linear Regression: (best fit line)
chart.linearFit = function() {
// Initialize variables:
var data, _data, fit, domain, x, slope, intercept;
// Get the bound data:
data = circles.data();
// Perform the linear fit:
fit = linearRegression( data );
// Extract the fit statistics:
slope = Math.round( fit['slope'] * 10000) / 10000;
intercept = Math.round( fit['intercept'] * 10000 ) / 10000;
r2 = Math.round( fit['r2'] * 10000 ) / 10000;
// Generate the linear prediction based on a set of input values: 'x'
domain = xScale.domain();
x = d3.range( domain[0], domain[1]+0.5, 0.5)
_data = x.map( function(d, i) {
return {
'x': d,
'y': fit['fn']( d ) // evaluate the fit at a given 'x' value
};
});
// Generate the path:
graph.append('svg:path')
.data( [ _data ] )
.attr('class', 'line bestfit')
.attr('d', line)
.append('svg:title')
.text( 'Fit: y = ' + slope + 'x + ' + intercept + ' ; r2 = ' + r2 );
};
// Set/Get: margin
chart.margin = function( _ ) {
if (!arguments.length) return margin;
margin = _;
return chart;
};
// Set/Get: width
chart.width = function( _ ) {
if (!arguments.length) return width;
width = _;
return chart;
};
// Set/Get: height
chart.height = function( _ ) {
if (!arguments.length) return height;
height = _;
return chart;
};
// Set/Get: x
chart.x = function( _ ) {
if (!arguments.length) return xValue;
xValue = _;
return chart;
};
// Set/Get: y
chart.y = function( _ ) {
if (!arguments.length) return yValue;
yValue = _;
return chart;
};
// Set/Get: radius
chart.radius = function( _ ) {
if (!arguments.length) return radius;
radius = _;
return chart;
};
// Set/Get: xLabel
chart.xLabel = function( _ ) {
if (!arguments.length) return xLabel;
xLabel = _;
return chart;
};
// Set/Get: yLabel
chart.yLabel = function( _ ) {
if (!arguments.length) return yLabel;
yLabel = _;
return chart;
};
// Set/Get: xDomain
chart.xDomain = function( _ ) {
if (!arguments.length) return xDomain;
xDomain = _;
return chart;
};
// Set/Get: yDomain
chart.yDomain = function( _ ) {
if (!arguments.length) return yDomain;
yDomain = _;
return chart;
};
// Set/Get: xTicks
chart.xTicks = function( _ ) {
if (!arguments.length) return xTicks;
xTicks = _;
return chart;
};
// Set/Get: yTicks
chart.yTicks = function( _ ) {
if (!arguments.length) return yTicks;
yTicks = _;
return chart;
};
return chart;
}; // end FUNCTION scatterChart()
/* Apply a natural box layout model to all elements */
* {
-moz-box-sizing: border-box;
-webkit-box-sizing: border-box;
box-sizing: border-box;
}
body {
font-family: 'Cabin', sans-serif;
font-size: 14px;
font-weight: normal;
color: #474747;
width: 100%;
min-height: 100%;
}
h1 {
width: 70%;
margin: 0 auto;
margin-top: 20px;
margin-bottom: 20px;
text-align: center;
font-size: 24px;
}
figure {
position: relative;
float: left;
width: 50%;
}
.canvas {
font-family: 'Cabin', sans-serif;
font-size: 14px;
fill: #474747;
font-weight: normal;
}
.axis path, .axis line {
fill: none;
stroke: #aaa;
stroke-width: 1px;
shape-rendering: crispEdges;
}
.y.axis path {
stroke: none;
}
.point {
fill: rgb(255,166, 0);
stroke: rgb(227,121,0);
stroke-width: 2px;
}
.line {
fill: none;
stroke: steelblue;
stroke-width: 2px;
}
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