一：什么是散點(diǎn)圖 - What is a scatter plot

任何數(shù)據(jù)分析的第一步是圖形化曲線顯示數(shù)據(jù)，根據(jù)相互關(guān)系，圖形曲線被稱為散點(diǎn)圖。散點(diǎn)圖可以表示兩個(gè)變量之間真實(shí)的關(guān)系強(qiáng)度，關(guān)系的趨勢(shì)，是否存在 Outliers

二：散點(diǎn)圖的目的是什么

ü 觀察變量之間的關(guān)系，發(fā)現(xiàn)統(tǒng)計(jì)數(shù)據(jù)中是否存在問題，或者特殊值和感興趣的數(shù)據(jù)

ü 數(shù)據(jù)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(gè)人的肺活量和屏住呼吸時(shí)間的研究，一個(gè)人能屏住呼吸多久，一個(gè)研究者選擇一組人作為研究對(duì)象，測(cè)量每個(gè)人的肺活量作為第一個(gè)變量，屏住呼吸時(shí)間作為第二個(gè)變量，研究者將使用散點(diǎn)圖來描述數(shù)據(jù)，假設(shè)肺活量作為水平軸，屏住呼吸時(shí)間做為垂直軸。

四：代碼實(shí)現(xiàn)

基于 Java 開源的數(shù)據(jù)圖形顯示組件 -JFreeChart 已經(jīng)實(shí)現(xiàn)了離散圖，只要我們提供數(shù)據(jù)即可

基于上面描述的演示如下：

五：相關(guān)性系數(shù) 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(shí)間長(zhǎng)短有很強(qiáng)的正相關(guān)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(chuàng)】數(shù)據(jù)分析之 – 散點(diǎn)圖