一：什么是散點圖 - What is a scatter plot

任何數據分析的第一步是圖形化曲線顯示數據，根據相互關系，圖形曲線被稱為散點圖。散點圖可以表示兩個變量之間真實的關系強度，關系的趨勢，是否存在 Outliers

二：散點圖的目的是什么

ü 觀察變量之間的關系，發現統計數據中是否存在問題，或者特殊值和感興趣的數據

ü 數據是如何被離散化的

ü 通過眼睛觀察是否存在 Outliers

三：示例說明

一個人的肺活量和屏住呼吸時間的研究，一個人能屏住呼吸多久，一個研究者選擇一組人作為研究對象，測量每個人的肺活量作為第一個變量，屏住呼吸時間作為第二個變量，研究者將使用散點圖來描述數據，假設肺活量作為水平軸，屏住呼吸時間做為垂直軸。

四：代碼實現

基于 Java 開源的數據圖形顯示組件 -JFreeChart 已經實現了離散圖，只要我們提供數據即可

基于上面描述的演示如下：

五：相關性系數 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 值為 0.9814324978439516, 顯然肺活量跟屏住呼吸時間長短有很強的正相關性。

以下為源代碼：

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<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>

【gloomyfish】【原創】數據分析之 – 散點圖