ChartDirector 6.2 (.NET 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

[Windows Forms - C# version] NetWinCharts\CSharpWinCharts\confidenceband.cs
 ```using System; using ChartDirector; namespace CSharpChartExplorer { public class confidenceband : DemoModule { //Name of demo module public string getName() { return "Confidence Band"; } //Number of charts produced in this demo module public int getNoOfCharts() { return 1; } //Main code for creating chart. //Note: the argument chartIndex is unused because this demo only has 1 chart. public void createChart(WinChartViewer 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, unchecked((int)0x806666ff)); // Add a 95% confidence band (prediction band) for the points trendLayer.addPredictionBand(0.95, unchecked((int)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", unchecked((int)0x806666ff)); legendBox.addKey("95% Point Confidence", unchecked((int)0x8066ff66)); // Display the trend line parameters as a text table formatted using CDML ChartDirector.TextBox textbox = c.addText(56, 65, String.Format( "<*block*>Slope\nIntercept\nCorrelation\nStd Error<*/*> <*block*>{0:0.0000} " + "sec/tps\n{1:0.0000} sec\n{2:0.0000}\n{3:0.0000} sec<*/*>", trendLayer.getSlope(), trendLayer.getIntercept(), trendLayer.getCorrelation(), 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.Chart = c; // include tool tip for the chart viewer.ImageMap = c.getHTMLImageMap("clickable"); } } }```

[Windows Forms - VB Version] NetWinCharts\VBNetWinCharts\confidenceband.vb
 ```Imports System Imports Microsoft.VisualBasic Imports ChartDirector Public Class confidenceband Implements DemoModule 'Name of demo module Public Function getName() As String Implements DemoModule.getName Return "Confidence Band" End Function 'Number of charts produced in this demo module Public Function getNoOfCharts() As Integer Implements DemoModule.getNoOfCharts Return 1 End Function 'Main code for creating chart. 'Note: the argument chartIndex is unused because this demo only has 1 chart. Public Sub createChart(viewer As WinChartViewer, chartIndex As Integer) _ Implements DemoModule.createChart ' The XY data of the first data series Dim dataX() As Double = {50, 55, 37, 24, 42, 49, 63, 72, 83, 59} Dim dataY() As Double = {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 Dim c As XYChart = 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, &Hffffff, -1, &Hc0c0c0, &Hc0c0c0, -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) Dim scatterLayer As ScatterLayer = c.addScatterLayer(dataX, dataY, "", _ Chart.DiamondSymbol, 11, &H008000) ' tool tip for scatter layer scatterLayer.setHTMLImageMap("", "", "title='Response time at {x} TPS: {value} sec'") ' Add a trend line layer for (dataX, dataY) Dim trendLayer As TrendLayer = c.addTrendLayer2(dataX, dataY, &H008000) ' Set the line width to 3 pixels trendLayer.setLineWidth(3) ' Add a 95% confidence band for the line trendLayer.addConfidenceBand(0.95, &H806666ff) ' Add a 95% confidence band (prediction band) for the points trendLayer.addPredictionBand(0.95, &H8066ff66) ' 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. Dim legendBox As 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", &H806666ff) legendBox.addKey("95% Point Confidence", &H8066ff66) ' Display the trend line parameters as a text table formatted using CDML Dim textbox As ChartDirector.TextBox = c.addText(56, 65, _ "<*block*>Slope<*br*>Intercept<*br*>Correlation<*br*>Std Error<*/*> <*block*>" & _ FormatNumber(trendLayer.getSlope(), 4) & " sec/tps<*br*>" & FormatNumber( _ trendLayer.getIntercept(), 4) & " sec<*br*>" & FormatNumber(trendLayer.getCorrelation( _ ), 4) & "<*br*>" & FormatNumber(trendLayer.getStdError(), 4) & " sec<*/*>", _ "Arial Bold", 8) ' Set the background of the text box to light grey, with a black border, and 1 pixel 3D ' border textbox.setBackground(&Hc0c0c0, 0, 1) ' Output the chart viewer.Chart = c ' include tool tip for the chart viewer.ImageMap = c.getHTMLImageMap("clickable") End Sub End Class```

[WPF - C#] NetWPFCharts\confidenceband.cs
 ```using System; using ChartDirector; namespace CSharpWPFDemo { public class confidenceband : DemoModule { //Name of demo module public string getName() { return "Confidence Band"; } //Number of charts produced in this demo module public int getNoOfCharts() { return 1; } //Main code for creating chart. //Note: the argument chartIndex is unused because this demo only has 1 chart. public void createChart(WPFChartViewer 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, unchecked((int)0x806666ff)); // Add a 95% confidence band (prediction band) for the points trendLayer.addPredictionBand(0.95, unchecked((int)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", unchecked((int)0x806666ff)); legendBox.addKey("95% Point Confidence", unchecked((int)0x8066ff66)); // Display the trend line parameters as a text table formatted using CDML ChartDirector.TextBox textbox = c.addText(56, 65, String.Format( "<*block*>Slope\nIntercept\nCorrelation\nStd Error<*/*> <*block*>{0:0.0000} " + "sec/tps\n{1:0.0000} sec\n{2:0.0000}\n{3:0.0000} sec<*/*>", trendLayer.getSlope(), trendLayer.getIntercept(), trendLayer.getCorrelation(), 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.Chart = c; // include tool tip for the chart viewer.ImageMap = c.getHTMLImageMap("clickable"); } } }```

[ASP.NET Web Forms - C# version] NetWebCharts\CSharpASP\confidenceband.aspx
 ```<%@ Page Language="C#" Debug="true" %> <%@ Import Namespace="ChartDirector" %> <%@ Register TagPrefix="chart" Namespace="ChartDirector" Assembly="netchartdir" %> ```

[ASP.NET Web Forms - VB Version] NetWebCharts\VBNetASP\confidenceband.aspx
 ```<%@ Page Language="VB" Debug="true" %> <%@ Import Namespace="ChartDirector" %> <%@ Register TagPrefix="chart" Namespace="ChartDirector" Assembly="netchartdir" %> ```
 ```using System; using System.Web.Mvc; using ChartDirector; namespace NetMvcCharts.Controllers { public class ConfidencebandController : Controller { // // Default Action // public ActionResult Index() { ViewBag.Title = "Confidence Band"; createChart(ViewBag.Viewer = new RazorChartViewer(HttpContext, "chart1")); return View("~/Views/Shared/ChartView.cshtml"); } // // Create chart // private void createChart(RazorChartViewer viewer) { // 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, unchecked((int)0x806666ff)); // Add a 95% confidence band (prediction band) for the points trendLayer.addPredictionBand(0.95, unchecked((int)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", unchecked((int)0x806666ff)); legendBox.addKey("95% Point Confidence", unchecked((int)0x8066ff66)); // Display the trend line parameters as a text table formatted using CDML ChartDirector.TextBox textbox = c.addText(56, 65, String.Format( "<*block*>Slope\nIntercept\nCorrelation\nStd Error<*/*> <*block*>{0:0.0000} " + "sec/tps\n{1:0.0000} sec\n{2:0.0000}\n{3:0.0000} sec<*/*>", trendLayer.getSlope(), trendLayer.getIntercept(), trendLayer.getCorrelation(), 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.Image = c.makeWebImage(Chart.PNG); // include tool tip for the chart viewer.ImageMap = c.getHTMLImageMap(""); } } }```
 ```@{ Layout = null; } @ViewBag.Title