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QuickStart Samples

Polynomial Regression QuickStart Sample (C#)

Illustrates how to fit data to polynomials using the PolynomialRegressionModel class in C#.

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using System;

using Extreme.Mathematics;
using Extreme.Statistics;

namespace Extreme.Numerics.QuickStart.CSharp
{
    /// <summary>
    /// Illustrates the use of the PolynomialRegressionModel class
    /// to perform polynomial regression.
    /// </summary>
    class PolynomialRegression
    {
        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main(string[] args)
        {
            // Polynomial regression can be performed using 
            // the PolynomialRegressionModel class.
            //
            // This QuickStart sample uses data from the National Institute
            // for Standards and Technology's Statistical Reference Datasets
            // library at http://www.itl.nist.gov/div898/strd/.

            // Note that, due to round-off error, the results here will not be exactly
            // the same as the NIST results, which were calculated using 500 digits
            // of precision!

            // We use the 'Pontius' dataset, which contains measurement data
            // from the calibration of load cells. The independent variable is the load.
            // The dependent variable is the deflection.
            double[] deflectionData = 
            {
                .11019, .21956, .32949, .43899, .54803, .65694, .76562, 
                .87487, .98292, 1.09146, 1.20001, 1.30822, 1.41599, 1.52399,
                1.63194, 1.73947, 1.84646, 1.95392, 2.06128, 2.16844, .11052,
                .22018, .32939, .43886, .54798, .65739, .76596, .87474, .98300,
                1.09150, 1.20004, 1.30818, 1.41613, 1.52408, 1.63159, 1.73965,
                1.84696, 1.95445, 2.06177, 2.16829
            };
            double[] loadData =
            {
                150000, 300000, 450000, 600000, 750000, 900000, 
                1050000, 1200000, 1350000, 1500000, 1650000, 1800000,
                1950000, 2100000, 2250000, 2400000, 2550000, 2700000,
                2850000, 3000000, 150000, 300000, 450000, 600000, 
                750000, 900000, 1050000, 1200000, 1350000, 1500000,
                1650000, 1800000, 1950000, 2100000, 2250000, 2400000,
                2550000, 2700000, 2850000, 3000000
            };
            var deflection = Vector.Create(deflectionData);
            var load = Vector.Create(loadData);

            // Now create the regression model. We supply the dependent and independent
            // variable, and the degree of the polynomial:
            var model = new PolynomialRegressionModel(deflection, load, 2);

            // The Compute method performs the actual regression analysis.
            model.Compute();

            // The Parameters collection contains information about the regression 
            // parameters.
            Console.WriteLine("Variable                  Value    Std.Error  t-stat  p-Value");
            foreach(Parameter parameter in model.Parameters)
            {
                // Parameter objects have the following properties:
                Console.WriteLine("{0,-19}{1,12:E4}{2,12:E2}{3,8:F2} {4,7:F4}",
                    // Name, usually the name of the variable:
                    parameter.Name, 
                    // Estimated value of the parameter:
                    parameter.Value, 
                    // Standard error:
                    parameter.StandardError,
                    // The value of the t statistic for the hypothesis that the parameter
                    // is zero.
                    parameter.Statistic, 
                    // Probability corresponding to the t statistic.
                    parameter.PValue);
            }
            Console.WriteLine();

            // In addition to these properties, Parameter objects have a GetConfidenceInterval
            // method that returns a confidence interval at a specified confidence level.
            // Notice that individual parameters can be accessed using their numeric index.
            // Parameter 0 is the intercept, if it was included.
            Interval confidenceInterval = model.Parameters[0].GetConfidenceInterval(0.95);
            Console.WriteLine("95% confidence interval for constant term: {0:E4} - {1:E4}",
                confidenceInterval.LowerBound, confidenceInterval.UpperBound);
            Console.WriteLine();
            
            // There is also a wealth of information about the analysis available
            // through various properties of the LinearRegressionModel object:
            Console.WriteLine("Residual standard error: {0:E3}", model.StandardError);
            Console.WriteLine("R-Squared:               {0:F4}", model.RSquared);
            Console.WriteLine("Adjusted R-Squared:      {0:F4}", model.AdjustedRSquared);
            Console.WriteLine("F-statistic:             {0:F4}", model.FStatistic);
            Console.WriteLine("Corresponding p-value:   {0:E5}", model.PValue);
            Console.WriteLine();

            // Much of this data can be summarized in the form of an ANOVA table:
            Console.WriteLine(model.AnovaTable.ToString());

            Console.Write("Press any key to exit.");
            Console.ReadLine();
        }
    }
}