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.

The following is the command line version of the code in "cppdemo/confidenceband". The MFC version of the code is in "mfcdemo/mfcdemo". The Qt Widgets version of the code is in "qtdemo/qtdemo". The QML/Qt Quick version of the code is in "qmldemo/qmldemo".

#include "chartdir.h"
#include <stdio.h>

int main(int argc, char *argv[])
{
    char buffer[1024];

    // The XY data of the first data series
    double dataX[] = {50, 55, 37, 24, 42, 49, 63, 72, 83, 59};
    const int dataX_size = (int)(sizeof(dataX)/sizeof(*dataX));
    double dataY[] = {3.6, 2.8, 2.5, 2.3, 3.8, 3.0, 3.8, 5.0, 6.0, 3.3};
    const int dataY_size = (int)(sizeof(dataY)/sizeof(*dataY));

    // 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)
    c->addScatterLayer(DoubleArray(dataX, dataX_size), DoubleArray(dataY, dataY_size), "",
        Chart::DiamondSymbol, 11, 0x008000);

    // Add a trend line layer for (dataX, dataY)
    TrendLayer* trendLayer = c->addTrendLayer(DoubleArray(dataX, dataX_size), DoubleArray(dataY,
        dataY_size), 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);

    // 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
    sprintf(buffer,
        "<*block*>Slope\nIntercept\nCorrelation\nStd Error<*/*>   <*block*>%.4f sec/tps\n%.4f sec\n"
        "%.4f\n%.4f sec<*/*>", trendLayer->getSlope(), trendLayer->getIntercept(),
        trendLayer->getCorrelation(), trendLayer->getStdError());
    TextBox* textbox = c->addText(56, 65, buffer, "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
    c->makeChart("confidenceband.png");

    //free up resources
    delete c;

    return 0;
}