/// <summary>
/// Updates the given chart with the specified linear regression.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="lr">Linear Regression.</param>
/// <param name="predictorIndex">The predictor (independent) variable to plot on the x-axis.</param>
/// <exception cref="InvalidArgumentException">
/// Thrown if the given predictorIndex is outside the range of columns in lr.PredictorMatrix.
/// </exception>
/// <remarks>
/// The multidimensional linear regression fit is plotted projected onto the plane of the specified
/// predictor variable.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// The first two data series are replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, LinearRegression lr, int predictorIndex )
{
if( predictorIndex < 0 || predictorIndex > lr.PredictorMatrix.Cols )
{
throw new Core.IndexOutOfRangeException( predictorIndex );
}
List<string> titles = new List<string>()
{
"LinearRegression",
};
string xTitle = "Independent Variable " + predictorIndex;
string yTitle = "Dependent Variable";
// create version of predictor matrix with all other columns zeroed out
DoubleMatrix projection = new DoubleMatrix( lr.PredictorMatrix.Rows, lr.PredictorMatrix.Cols );
projection[Slice.All, predictorIndex] = lr.PredictorMatrix.Col( predictorIndex );
DoubleMatrix data = new DoubleMatrix( lr.NumberOfObservations, 3 );
data[Slice.All, 0] = lr.PredictorMatrix.Col( predictorIndex ); // x
data[Slice.All, 1] = lr.Observations; // y
data[Slice.All, 2] = lr.PredictedObservations( projection ); // y predicted
data = NMathFunctions.SortByColumn( data, 0 );
List<ChartSeries> series = new List<ChartSeries>()
{
BindXY( data.Col(0), data.Col(1), ChartSeriesType.Scatter, DefaultMarker ),
// only necessary to plot endpoints of line
BindXY( data.Col(0)[new Slice(0, 2, data.Rows - 1)], data.Col(2)[new Slice(0, 2, data.Rows - 1)], ChartSeriesType.Line, ChartSymbolShape.None )
};
series[0].Text = "Observed";
series[1].Text = "Predicted";
Update( ref chart, series, titles, xTitle, yTitle );
}
/// <summary>
/// Demonstrates linear reression in two dimensions.
/// </summary>
void LinearRegression()
{
// Set up example description
nRichDescription.Text = "A linear regression model is computed from the sample data containing random normal noise. \n\nA point is then predicted from the model with a 95% confidence interval - meaning the predicted point is expected to lie within the confidence interval 95% of the time.";
// First read in the independent (or predictor) values. This is a matrix
// with one column and a row for each amounts measurement.
DoubleVector raw_data = new DoubleVector(25, 0, 1);
DoubleMatrix measurements = new DoubleMatrix(raw_data);
// Next, read in the responses
// Build a linear polynomial and add noise for interest
RandomNumberGenerator rand = new RandGenNormal(0, noiselevel_);
Polynomial poly = new Polynomial(new DoubleVector("0, 1"));
DoubleVector responses = poly.Evaluate(raw_data) + new DoubleVector(raw_data.Length, rand); ;
// Construct a linear regression. If we want our regression to calculate a
// y-intercept we must send in true for the "addIntercept" parameter (the
// third paramameter in the constructor).
LinearRegression regression = new LinearRegression(measurements, responses, true);
DoubleVector residues = regression.Residuals;
// Use the linear regression class to make a prediction according to the model
DoubleVector xvalues = new DoubleVector("30"); // Use the model to predict the observation at 30.
Interval pi = regression.PredictionInterval(xvalues, 0.95);
// Build some data points along the regression line for display
DoubleMatrix abcissae = new DoubleMatrix(new DoubleVector(raw_data));
DoubleVector predicted_ys = regression.PredictedObservations(abcissae);
// Build the chart
SetupChartLayout("Linear Regression");
NChart chart = nChartControl1.Charts[0];
SetupChartAxes(chart);
// Set up the line series
NLineSeries line = new NLineSeries();
chart.Series.Add(line);
// tell the series to regard the X values
line.UseXValues = true;
// no data labels
line.DataLabelStyle.Visible = false;
// Set the line color
line.BorderStyle = new NStrokeStyle(2.0f, Color.Tomato);
// name data set
line.Name = "Linear Regression";
// Add the the Linear Regression line data to the line series
line.XValues.AddRange(abcissae.DataBlock.Data);
line.Values.AddRange(predicted_ys.DataBlock.Data);
// Draw the raw data points
NPointSeries point = new NPointSeries();
chart.Series.Add(point);
point.UseXValues = true;
point.DataLabelStyle.Visible = false;
// Set the point appearance properties
point.FillStyle = new NColorFillStyle(Color.SkyBlue);
point.BorderStyle = new NStrokeStyle(1.0f,Color.DarkGray);
point.PointShape = PointShape.Cross;
point.Size = new NLength(6.0f);
// Points must fit in the chart area
point.InflateMargins = true;
// Name point set
point.Name = "Observations";
// set the point data
point.Values.AddRange(responses.DataBlock.Data);
point.XValues.AddRange(measurements.DataBlock.Data);
double m = (pi.Min + pi.Max) / 2.0;
// Display the predicted value with an error bar series
NErrorBarSeries predicted_points = new NErrorBarSeries();
chart.Series.Add(predicted_points);
predicted_points.Name = "Predicted Point";
predicted_points.UseXValues = true;
predicted_points.InflateMargins = true;
predicted_points.FillStyle = new NColorFillStyle(Color.Crimson);
predicted_points.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
predicted_points.DataLabelStyle.Visible = false;
predicted_points.MarkerStyle.Visible = true;
predicted_points.MarkerStyle.FillStyle = new NColorFillStyle(Color.Crimson);
predicted_points.MarkerStyle.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
predicted_points.MarkerStyle.PointShape = PointShape.Bar;
predicted_points.MarkerStyle.Width = new NLength(5);
predicted_points.MarkerStyle.Height = new NLength(5);
predicted_points.SizeY = new NLength(5);
// Fill the data for the predicted point
predicted_points.XValues.AddRange(xvalues.DataBlock.Data);
predicted_points.Values.Add(m);
predicted_points.UpperErrorsY.Add(pi.Max - m);
predicted_points.LowerErrorsY.Add(m - pi.Min);
// Create a label to display the predicted value
NLabel label = new NLabel();
label.BoundsMode = BoundsMode.None;
label.ContentAlignment = ContentAlignment.BottomLeft;
label.Location = new NPointL(
new NLength(87, NRelativeUnit.ParentPercentage),
new NLength(3, NRelativeUnit.ParentPercentage));
label.TextStyle.TextFormat = TextFormat.XML;
label.TextStyle.FontStyle = new NFontStyle("Arial", 9);
label.TextStyle.StringFormatStyle.HorzAlign = Nevron.HorzAlign.Right;
label.TextStyle.BackplaneStyle.Visible = true;
label.TextStyle.BackplaneStyle.FillStyle = new NGradientFillStyle(GradientStyle.Horizontal, GradientVariant.Variant1, Color.FromArgb(130, 255, 255, 255), Color.FromArgb(130, 233, 233, 255));
label.TextStyle.BackplaneStyle.Shape = BackplaneShape.SmoothEdgeRectangle;
label.TextStyle.BackplaneStyle.StandardFrameStyle.InnerBorderColor = Color.White;
label.Text = "<font color = 'crimson'>" + m.ToString("0.###") + "</font> - predicted value with 95% confidence interval";
chart.ChildPanels.Add(label);
nChartControl1.Refresh();
}