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 randam 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 using
TrendLayer.getSlope,
TrendLayer.getIntercept,
TrendLayer.getCorrelation and
TrendLayer.getStdError. (Please refer to appropriate statistics text books on 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.
[File: phpdemo/confidenceband.php".]
| <![CDATA[<?php
require_once("../lib/phpchartdir.php");
#The XY data of the first data series
$dataX = array(50, 55, 37, 24, 42, 49, 63, 72, 83, 59);
$dataY = array(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
$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", "timesbi.ttf", 18);
#Add a title to the y axis using 12 pts Arial Bold Italic font
$c->yAxis->setTitle("Response Time (sec)", "arialbi.ttf", 12);
#Set the y axis line width to 3 pixels
$c->yAxis->setWidth(3);
#Set the y axis label format to show 1 decimal point
$c->yAxis->setLabelFormat("{value|1}");
#Add a title to the x axis using 12 pts Arial Bold Italic font
$c->xAxis->setTitle("Server Load (TPS)", "arialbi.ttf", 12);
#Set the x axis line width to 3 pixels
$c->xAxis->setWidth(3);
#Add a scatter layer using (dataX, dataY)
$c->addScatterLayer($dataX, $dataY, "", DiamondSymbol, 11, 0x8000);
#Add a trend line layer for (dataX, dataY)
$trendLayer = $c->addTrendLayer2($dataX, $dataY, 0x8000);
#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 10
#pts Arial Bold Italic font. Set the background and border color to Transparent.
$legendBox = $c->addLegend(50, 30, false, "arialbi.ttf", 10);
$legendBox->setBackground(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 = $c->addText(56, 65, sprintf(
"<*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()), "arialbd.ttf", 8);
#Set the background of the text box to light grey, with a black border, and 1
#pixel 3D border
$textbox->setBackground(0xc0c0c0, 0, 1);
#output the chart
header("Content-type: image/png");
print($c->makeChart2(PNG));
?>]]> |
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