Data Analysis Mathematics Linear Algebra Statistics
New Version 8.1!

Supports .NET 6.0. Try it for free with our fully functional 60-day trial version.

QuickStart Samples

# Multiple Linear Regression QuickStart Sample (C#)

Illustrates how to use the LinearRegressionModel class to perform a multiple linear regression in C#.

```using System;
using System.Data;
using System.IO;

using Extreme.DataAnalysis;
using Extreme.Mathematics;
using Extreme.Statistics;

namespace Extreme.Numerics.QuickStart.CSharp
{
/// <summary>
/// Illustrates building multiple linear regression models using
/// the LinearRegressionModel class in the
/// Extreme.Statistics namespace of the Extreme
/// Optimization Numerical Libraries for .NET.
/// </summary>
class MultipleRegression
{
/// <summary>
/// The main entry point for the application.
/// </summary>
static void Main(string[] args)
{
// Multiple linear regression can be performed using
// the LinearRegressionModel class.
//
//

// This QuickStart sample uses data test scores of 200 high school
// students, including science, math, and reading.

// First, read the data from a file into a data frame.

// Now create the regression model. Parameters are the data frame,
// the name of the dependent variable, and a string array containing
// the names of the independent variables.
var model = new LinearRegressionModel(data,
"science", new string[] {"math", "female", "socst", "read"});

// Alternatively, we can use a formula to describe the variables
// in the model. The dependent variable goes on the left, the
// independent variables on the right of the ~:
var model2 = new LinearRegressionModel(data,
"science ~ math + female + socst + read");

// We can set model options now, such as whether to exclude
// the constant term:
// model.NoIntercept = false;

// 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,-20}{1,10:F6}{2,10:F6}{3,8:F2} {4,7:F5}",
// 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 intercept: {0:F4} - {1:F4}",
confidenceInterval.LowerBound, confidenceInterval.UpperBound);

// Parameters can also be accessed by name:
confidenceInterval = model.Parameters.Get("math").GetConfidenceInterval(0.95);
Console.WriteLine("95% confidence interval for 'math': {0:F4} - {1:F4}",
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:F3}", model.StandardError);
Console.WriteLine("R-Squared:               {0:F4}", model.RSquared);
Console.WriteLine("F-statistic:             {0:F4}", model.FStatistic);
Console.WriteLine("Corresponding p-value:   {0:F5}", model.PValue);
Console.WriteLine();

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

// All this information can be printed using the Summarize method.
// You will also see summaries using the library in C# interactive.
Console.WriteLine(model.Summarize());

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