ChartDirector 6.1 (Java Edition)

Confidence Band




This example demonstrates adding confidence bands to a trend line. It also demonstrates how to display linear regression parameters on the chart.

In linear regression, the data points are assumed to be related by:

y = m * x + c + err

where m and c are constants, and err is a random variable. Linear regression estimates m, c and err based on available data.

As m and c are estimated values, the trend line y = m * x + c may be inaccurate. In ChartDirector, the uncertainties can be represented as a confidence band using TrendLayer.addConfidenceBand. For example, the 95% confidence band means there are 95% probability that the "real" trend line is in that band.

To predict a data point (infer y given x), we use y = m * x + c + err. As m, c and err are estimated values, the predicted data point may be inaccurate. In ChartDirector, the uncertainties can be represented as a prediction band using TrendLayer.addPredictionBand.

Note that the prediction band is always wider than the confidence band because of the extra uncertainties contributed by the err term.

In ChartDirector, the linear regression parameters slope, intercept, correlation coefficient and standard error can be obtained by using TrendLayer.getSlope, TrendLayer.getIntercept, TrendLayer.getCorrelation and TrendLayer.getStdError. (Please refer to appropriate statistics text books for explanation of these values.)

In this example, the linear regression parameters are formatted into a table using CDML, which is then added to the chart as custom text box using BaseChart.addText.

Source Code Listing

[JSP Version] jspdemo/confidenceband.jsp
<%@page import="ChartDirector.*" %>
<%
// The XY data of the first data series
double[] dataX = {50, 55, 37, 24, 42, 49, 63, 72, 83, 59};
double[] dataY = {3.6, 2.8, 2.5, 2.3, 3.8, 3.0, 3.8, 5.0, 6.0, 3.3};

// Create a XYChart object of size 450 x 420 pixels
XYChart c = new XYChart(450, 420);

// Set the plotarea at (55, 65) and of size 350 x 300 pixels, with white background and a light grey
// border (0xc0c0c0). Turn on both horizontal and vertical grid lines with light grey color
// (0xc0c0c0)
c.setPlotArea(55, 65, 350, 300, 0xffffff, -1, 0xc0c0c0, 0xc0c0c0, -1);

// Add a title to the chart using 18 point Times Bold Itatic font.
c.addTitle("Server Performance", "Times New Roman Bold Italic", 18);

// Add titles to the axes using 12pt Arial Bold Italic font
c.yAxis().setTitle("Response Time (sec)", "Arial Bold Italic", 12);
c.xAxis().setTitle("Server Load (TPS)", "Arial Bold Italic", 12);

// Set the axes line width to 3 pixels
c.yAxis().setWidth(3);
c.xAxis().setWidth(3);

// Add a scatter layer using (dataX, dataY)
ScatterLayer scatterLayer = c.addScatterLayer(dataX, dataY, "", Chart.DiamondSymbol, 11, 0x008000);

// tool tip for scatter layer
scatterLayer.setHTMLImageMap("", "", "title='Response time at {x} TPS: {value} sec'");

// Add a trend line layer for (dataX, dataY)
TrendLayer trendLayer = c.addTrendLayer2(dataX, dataY, 0x008000);

// Set the line width to 3 pixels
trendLayer.setLineWidth(3);

// Add a 95% confidence band for the line
trendLayer.addConfidenceBand(0.95, 0x806666ff);

// Add a 95% confidence band (prediction band) for the points
trendLayer.addPredictionBand(0.95, 0x8066ff66);

// tool tip for trend layer
trendLayer.setHTMLImageMap("", "",
    "title='Slope = {slope|4} sec/TPS; Intercept = {intercept|4} sec'");

// Add a legend box at (50, 30) (top of the chart) with horizontal layout. Use 10pt Arial Bold
// Italic font. Set the background and border color to Transparent.
LegendBox legendBox = c.addLegend(50, 30, false, "Arial Bold Italic", 10);
legendBox.setBackground(Chart.Transparent);

// Add entries to the legend box
legendBox.addKey("95% Line Confidence", 0x806666ff);
legendBox.addKey("95% Point Confidence", 0x8066ff66);

// Display the trend line parameters as a text table formatted using CDML
TextBox textbox = c.addText(56, 65, java.text.MessageFormat.format(
    "<*block*>Slope\nIntercept\nCorrelation\nStd Error<*/*>   <*block*>{0,number,#.####} " +
    "sec/tps\n{1,number,#.####} sec\n{2,number,#.####}\n{3,number,#.####} sec<*/*>", new Object[]{
    new Double(trendLayer.getSlope()), new Double(trendLayer.getIntercept()), new Double(
    trendLayer.getCorrelation()), new Double(trendLayer.getStdError())}), "Arial Bold", 8);

// Set the background of the text box to light grey, with a black border, and 1 pixel 3D border
textbox.setBackground(0xc0c0c0, 0, 1);

// Output the chart
String chart1URL = c.makeSession(request, "chart1");

// include tool tip for the chart
String imageMap1 = c.getHTMLImageMap("");
%>
<html>
<body style="margin:5px 0px 0px 5px">
<div style="font-size:18pt; font-family:verdana; font-weight:bold">
    Confidence Band
</div>
<hr color="#000080">
<div style="font-size:10pt; font-family:verdana; margin-bottom:1.5em">
    <a href="viewsource.jsp?file=<%=request.getServletPath()%>">View Source Code</a>
</div>
<img src='<%=response.encodeURL("getchart.jsp?"+chart1URL)%>'
    usemap="#map1" border="0">
<map name="map1"><%=imageMap1%></map>
</body>
</html>

[Java Version] javademo/confidenceband.java
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import ChartDirector.*;

public class confidenceband implements DemoModule
{
    //Name of demo program
    public String toString() { return "Confidence Band"; }

    //Number of charts produced in this demo
    public int getNoOfCharts() { return 1; }

    //Main code for creating charts
    public void createChart(ChartViewer viewer, int chartIndex)
    {
        // The XY data of the first data series
        double[] dataX = {50, 55, 37, 24, 42, 49, 63, 72, 83, 59};
        double[] dataY = {3.6, 2.8, 2.5, 2.3, 3.8, 3.0, 3.8, 5.0, 6.0, 3.3};

        // Create a XYChart object of size 450 x 420 pixels
        XYChart c = new XYChart(450, 420);

        // Set the plotarea at (55, 65) and of size 350 x 300 pixels, with white background and a
        // light grey border (0xc0c0c0). Turn on both horizontal and vertical grid lines with light
        // grey color (0xc0c0c0)
        c.setPlotArea(55, 65, 350, 300, 0xffffff, -1, 0xc0c0c0, 0xc0c0c0, -1);

        // Add a title to the chart using 18 point Times Bold Itatic font.
        c.addTitle("Server Performance", "Times New Roman Bold Italic", 18);

        // Add titles to the axes using 12pt Arial Bold Italic font
        c.yAxis().setTitle("Response Time (sec)", "Arial Bold Italic", 12);
        c.xAxis().setTitle("Server Load (TPS)", "Arial Bold Italic", 12);

        // Set the axes line width to 3 pixels
        c.yAxis().setWidth(3);
        c.xAxis().setWidth(3);

        // Add a scatter layer using (dataX, dataY)
        ScatterLayer scatterLayer = c.addScatterLayer(dataX, dataY, "", Chart.DiamondSymbol, 11,
            0x008000);

        // tool tip for scatter layer
        scatterLayer.setHTMLImageMap("", "", "title='Response time at {x} TPS: {value} sec'");

        // Add a trend line layer for (dataX, dataY)
        TrendLayer trendLayer = c.addTrendLayer2(dataX, dataY, 0x008000);

        // Set the line width to 3 pixels
        trendLayer.setLineWidth(3);

        // Add a 95% confidence band for the line
        trendLayer.addConfidenceBand(0.95, 0x806666ff);

        // Add a 95% confidence band (prediction band) for the points
        trendLayer.addPredictionBand(0.95, 0x8066ff66);

        // tool tip for trend layer
        trendLayer.setHTMLImageMap("", "",
            "title='Slope = {slope|4} sec/TPS; Intercept = {intercept|4} sec'");

        // Add a legend box at (50, 30) (top of the chart) with horizontal layout. Use 10pt Arial
        // Bold Italic font. Set the background and border color to Transparent.
        LegendBox legendBox = c.addLegend(50, 30, false, "Arial Bold Italic", 10);
        legendBox.setBackground(Chart.Transparent);

        // Add entries to the legend box
        legendBox.addKey("95% Line Confidence", 0x806666ff);
        legendBox.addKey("95% Point Confidence", 0x8066ff66);

        // Display the trend line parameters as a text table formatted using CDML
        TextBox textbox = c.addText(56, 65, java.text.MessageFormat.format(
            "<*block*>Slope\nIntercept\nCorrelation\nStd Error<*/*>   <*block*>{0,number,#.####} " +
            "sec/tps\n{1,number,#.####} sec\n{2,number,#.####}\n{3,number,#.####} sec<*/*>",
            new Object[]{new Double(trendLayer.getSlope()), new Double(trendLayer.getIntercept()),
            new Double(trendLayer.getCorrelation()), new Double(trendLayer.getStdError())}),
            "Arial Bold", 8);

        // Set the background of the text box to light grey, with a black border, and 1 pixel 3D
        // border
        textbox.setBackground(0xc0c0c0, 0, 1);

        // Output the chart
        viewer.setChart(c);

        // include tool tip for the chart
        viewer.setImageMap(c.getHTMLImageMap("clickable"));
    }

    //Allow this module to run as standalone program for easy testing
    public static void main(String[] args)
    {
        //Instantiate an instance of this demo module
        DemoModule demo = new confidenceband();

        //Create and set up the main window
        JFrame frame = new JFrame(demo.toString());
        frame.addWindowListener(new WindowAdapter() {
            public void windowClosing(WindowEvent e) {System.exit(0);} });
        frame.getContentPane().setBackground(Color.white);

        // Create the chart and put them in the content pane
        ChartViewer viewer = new ChartViewer();
        demo.createChart(viewer, 0);
        frame.getContentPane().add(viewer);

        // Display the window
        frame.pack();
        frame.setVisible(true);
    }
}