学步园

 一：什么是散点图
- What is a scatter plot

任何数据分析的第一步是图形化曲线显示数据，根据相互关系，图形曲线被称为散点图。散点图可以表示两个变量之间真实的关系强度，关系的趋势，是否存在Outliers

二：散点图的目的是什么

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观察变量之间的关系，发现统计数据中是否存在问题，或者特殊值和感兴趣的数据

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数据是如何被离散化的

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通过眼睛观察是否存在Outliers

三：示例说明

一个人的肺活量和屏住呼吸时间的研究，一个人能屏住呼吸多久，一个研究者选择一组人作为研究对象，测量每个人的肺活量作为第一个变量，屏住呼吸时间作为第二个变量，研究者将使用散点图来描述数据，假设肺活量作为水平轴，屏住呼吸时间做为垂直轴。

四：代码实现

基于Java开源的数据图形显示组件-JFreeChart已经实现了离散图，只要我们提供数据即可

基于上面描述的演示如下：

五：相关性系数 correlation coefficient – R/r

本例中的r值为0.9814324978439516,显然肺活量跟屏住呼吸时间长短有很强的正相关性。

以下为源代码：

package com.dataanalysis.plots;</p> <p>import java.awt.Color;</p> <p>import javax.swing.JPanel;</p> <p>import org.apache.commons.math.stat.descriptive.DescriptiveStatistics;<br /> import org.jfree.chart.ChartFactory;<br /> import org.jfree.chart.ChartPanel;<br /> import org.jfree.chart.JFreeChart;<br /> import org.jfree.chart.annotations.XYTextAnnotation;<br /> import org.jfree.chart.axis.NumberAxis;<br /> import org.jfree.chart.plot.PlotOrientation;<br /> import org.jfree.chart.plot.XYPlot;<br /> import org.jfree.chart.renderer.xy.XYLineAndShapeRenderer;<br /> import org.jfree.data.xy.DefaultXYDataset;<br /> import org.jfree.data.xy.XYDataset;<br /> import org.jfree.ui.ApplicationFrame;<br /> import org.jfree.ui.RefineryUtilities;</p> <p>// - http://en.wikipedia.org/wiki/Scatter_plot</p> <p>public class ScatterPlotDemo extends ApplicationFrame {</p> <p> /**<br /> *<br /> */<br /> private static final long serialVersionUID = 1L;<br /> private static double[][] data;<br /> /**<br /> * A demonstration application showing a scatter plot.<br /> *<br /> * @param title the frame title.<br /> */<br /> public ScatterPlotDemo(String title) {<br /> super(title);<br /> JPanel chartPanel = createDemoPanel();<br /> chartPanel.setPreferredSize(new java.awt.Dimension(600, 400));<br /> setContentPane(chartPanel);<br /> }</p> <p> private static JFreeChart createChart(XYDataset dataset) {<br /> JFreeChart chart = ChartFactory.createScatterPlot("Scatter Plot Demo",<br /> "lung capacity(ml)", "time holding breath(s)", dataset, PlotOrientation.VERTICAL, true, false, false);</p> <p> XYPlot plot = (XYPlot) chart.getPlot();<br /> plot.setNoDataMessage("NO DATA");<br /> plot.setDomainZeroBaselineVisible(true);<br /> plot.setRangeZeroBaselineVisible(true);</p> <p> XYLineAndShapeRenderer renderer = (XYLineAndShapeRenderer) plot.getRenderer();<br /> renderer.setSeriesOutlinePaint(0, Color.black);<br /> renderer.setUseOutlinePaint(true);</p> <p> // x axis<br /> NumberAxis domainAxis = (NumberAxis) plot.getDomainAxis();<br /> domainAxis.setAutoRange(true);</p> <p> // Y axis<br /> NumberAxis rangeAxis = (NumberAxis) plot.getRangeAxis();<br /> rangeAxis.setAutoRange(true);</p> <p> XYTextAnnotation textAnnotation =<br /> new XYTextAnnotation("R = " + calculateCoefficient(data),<br /> 370, 25); // r value<br /> textAnnotation.setPaint(Color.BLUE);<br /> textAnnotation.setToolTipText("Correlation Coefficient");</p> <p> plot.addAnnotation(textAnnotation);</p> <p> return chart;<br /> }</p> <p> /**<br /> * Creates a panel for the demo (used by SuperDemo.java).<br /> *<br /> * @return A panel.<br /> */<br /> public static JPanel createDemoPanel() {<br /> JFreeChart chart = createChart(createXYDataset());<br /> ChartPanel chartPanel = new ChartPanel(chart);<br /> chartPanel.setPopupMenu(null);<br /> chartPanel.setDomainZoomable(true);<br /> chartPanel.setRangeZoomable(true);<br /> return chartPanel;<br /> }</p> <p> public static XYDataset createXYDataset() {<br /> DefaultXYDataset xyDataset = new DefaultXYDataset();<br /> data = new double[2][12];</p> <p> // x axis data - lung capacity(ml)<br /> data[0] = new double[]{400,397,360,402,413,427,389,388,405,422,411,433};</p> <p> // y axis data - time holding breath(s)<br /> data[1] = new double[]{21.7,20.7,17.7,21.9,23.7,25.7,20.4,20.1,22.9,24.8,22.5,25.9};</p> <p> xyDataset.addSeries("Research Data", data);<br /> System.out.println("Correlation Coefficient = " + calculateCoefficient(data));<br /> return xyDataset;<br /> }</p> <p> public static double calculateCoefficient(double[][] data) {<br /> DescriptiveStatistics xDataSet = new DescriptiveStatistics();<br /> for(int i=0; i<data i="" xdataset="" descriptivestatistics="" ydataset="new" for="" double="" n="yDataSet.getValues().length;" xysum="0.0d;" xpowsum="0.0d;" ypowsum="0.0d;" math="" s1="xySum" xs="xPowSum" ys="yPowSum" s2="Math.sqrt(xS" return="" starting="" point="" the="" demonstration="" application="" args="" ignored="" public="" static="" void="" main="" scatterplotdemo="" demo="new" plot="" refineryutilities=""></data>