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

ü         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

ü         数据是如何被离散化的

ü         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

 

Relationship Between X and Y Axis

r = + 1.0

Strong - Positive

As X goes up, Y always also goes up

r = + 0.5

Weak - Positive

As X goes up, Y tends to usually also go up

r = 0

- No Correlation -

X and Y are not correlated

r = - 0.5

Weak - Negative

As X goes up, Y tends to usually go down

r = - 1.0

Strong - Negative

As X goes up, Y always goes down

 

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; import java.awt.Color; import javax.swing.JPanel; import org.apache.commons.math.stat.descriptive.DescriptiveStatistics; import org.jfree.chart.ChartFactory; import org.jfree.chart.ChartPanel; import org.jfree.chart.JFreeChart; import org.jfree.chart.annotations.XYTextAnnotation; import org.jfree.chart.axis.NumberAxis; import org.jfree.chart.plot.PlotOrientation; import org.jfree.chart.plot.XYPlot; import org.jfree.chart.renderer.xy.XYLineAndShapeRenderer; import org.jfree.data.xy.DefaultXYDataset; import org.jfree.data.xy.XYDataset; import org.jfree.ui.ApplicationFrame; import org.jfree.ui.RefineryUtilities; // - http://en.wikipedia.org/wiki/Scatter_plot public class ScatterPlotDemo extends ApplicationFrame { /** * */ private static final long serialVersionUID = 1L; private static double[][] data; /** * A demonstration application showing a scatter plot. * * @param title the frame title. */ public ScatterPlotDemo(String title) { super(title); JPanel chartPanel = createDemoPanel(); chartPanel.setPreferredSize(new java.awt.Dimension(600, 400)); setContentPane(chartPanel); } private static JFreeChart createChart(XYDataset dataset) { JFreeChart chart = ChartFactory.createScatterPlot("Scatter Plot Demo", "lung capacity(ml)", "time holding breath(s)", dataset, PlotOrientation.VERTICAL, true, false, false); XYPlot plot = (XYPlot) chart.getPlot(); plot.setNoDataMessage("NO DATA"); plot.setDomainZeroBaselineVisible(true); plot.setRangeZeroBaselineVisible(true); XYLineAndShapeRenderer renderer = (XYLineAndShapeRenderer) plot.getRenderer(); renderer.setSeriesOutlinePaint(0, Color.black); renderer.setUseOutlinePaint(true); // x axis NumberAxis domainAxis = (NumberAxis) plot.getDomainAxis(); domainAxis.setAutoRange(true); // Y axis NumberAxis rangeAxis = (NumberAxis) plot.getRangeAxis(); rangeAxis.setAutoRange(true); XYTextAnnotation textAnnotation = new XYTextAnnotation("R = " + calculateCoefficient(data), 370, 25); // r value textAnnotation.setPaint(Color.BLUE); textAnnotation.setToolTipText("Correlation Coefficient"); plot.addAnnotation(textAnnotation); return chart; } /** * Creates a panel for the demo (used by SuperDemo.java). * * @return A panel. */ public static JPanel createDemoPanel() { JFreeChart chart = createChart(createXYDataset()); ChartPanel chartPanel = new ChartPanel(chart); chartPanel.setPopupMenu(null); chartPanel.setDomainZoomable(true); chartPanel.setRangeZoomable(true); return chartPanel; } public static XYDataset createXYDataset() { DefaultXYDataset xyDataset = new DefaultXYDataset(); data = new double[2][12]; // x axis data - lung capacity(ml) data[0] = new double[]{400,397,360,402,413,427,389,388,405,422,411,433}; // y axis data - time holding breath(s) 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}; xyDataset.addSeries("Research Data", data); System.out.println("Correlation Coefficient = " + calculateCoefficient(data)); return xyDataset; } public static double calculateCoefficient(double[][] data) { DescriptiveStatistics xDataSet = new DescriptiveStatistics(); for(int i=0; i