Data Analysis Mathematics Linear Algebra Statistics
New Version 8.0! QuickStart Samples

# Polynomial Regression QuickStart Sample (Visual Basic)

Illustrates how to fit data to polynomials using the PolynomialRegressionModel class in Visual Basic.

```Option Infer On

Imports System.Data
Imports Extreme.Mathematics
Imports Extreme.Statistics

Namespace Extreme.Numerics.QuickStart.VB
' Illustrates the use of the PolynomialRegressionModel class
' to perform polynomial regression.
Module PolynomialRegression

Sub Main()
' 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.
Dim deflection = Vector.Create(New Double() _
{
0.11019, 0.21956, 0.32949, 0.43899, 0.54803, 0.65694, 0.76562,
0.87487, 0.98292, 1.09146, 1.20001, 1.30822, 1.41599, 1.52399,
1.63194, 1.73947, 1.84646, 1.95392, 2.06128, 2.16844, 0.11052,
0.22018, 0.32939, 0.43886, 0.54798, 0.65739, 0.76596, 0.87474, 0.983,
1.0915, 1.20004, 1.30818, 1.41613, 1.52408, 1.63159, 1.73965,
1.84696, 1.95445, 2.06177, 2.16829
})
Dim load = Vector.Create(New Double() _
{
150000.0, 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
})

' Now create the regression model. We supply the dependent and independent
' variable, and the degree of the polynomial:
Dim 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")
For Each param As Parameter In model.Parameters
' Parameter objects have the following properties:
' - Name, usually the name of the variable:
' - Estimated value of the parameter:
' - Standard error:
' - The value of the t statistic for the hypothesis that the parameter
'    is zero.
' - Probability corresponding to the t statistic.
Console.WriteLine("{0,-19}{1,12:E4}{2,12:E2}{3,8:F2} {4,7:F4}", _
param.Name, _
param.Value, _
param.StandardError, _
param.Statistic, _
param.PValue)
Next
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.
Dim confidenceInterval As Interval = 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("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.WriteLine("Press Enter key to continue.")