# Simple Regression QuickStart Sample (Visual Basic)

Illustrates how to perform a simple linear regression using the SimpleRegressionModel class in Visual Basic.

View this sample in: C# F# IronPython

``````Option Infer On

Imports Extreme.DataAnalysis
Imports Extreme.Mathematics
Imports Extreme.Statistics

' Illustrates the use of the SimpleRegressionModel class for performing
' simple linear regression..
Module SimpleRegression

Sub Main()
' The license is verified at runtime. We're using
' https://www.extremeoptimization.com/trial-key

' Simple linear regression can be performed using
' the SimpleRegressionModel class. There are some special constructors
' for simple linear regression, with only one independent variable.
'
' 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!

' Model 1 uses the 'NoInt1' dataset. The model has no intercept.

' First, we construct Double arrays containing the data for
' the dependent and independent variables.
Dim yData1 As Double() = {130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140}
Dim xData1 As Double() = {60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70}

' Next, we create the regression model. We can pass the data arrays directly.
Dim model1 As New SimpleRegressionModel(yData1, xData1)
model1.NoIntercept = True
model1.Fit()

For Each param As Parameter(Of Double) In model1.Parameters
Console.WriteLine(param.ToString())
Next
Console.WriteLine("Residual standard error: {0:F2}", model1.StandardError)
Console.WriteLine("R-Squared: {0:F3}", model1.RSquared)
Console.WriteLine("F-statistic: {0:F3}", model1.FStatistic)

Console.WriteLine(model1.AnovaTable.ToString())

' Model 2 uses the 'Norris' dataset.

Console.WriteLine(Environment.NewLine + "" + Environment.NewLine + "Model 2")
Dim dependent2 = Vector.Create(0.1, 338.8, 118.1, 888.0, 9.2, 228.1, 668.5, 998.5,
449.1, 778.9, 559.2, 0.3, 0.1, 778.1, 668.8, 339.3,
448.9, 10.8, 557.7, 228.3, 998.0, 888.8, 119.6, 0.3,
0.6, 557.6, 339.3, 888.0, 998.5, 778.9, 10.2, 117.6,
228.9, 668.4, 449.2, 0.2)
Dim independent2 = Vector.Create(0.2, 337.4, 118.2, 884.6, 10.1, 226.5, 666.3, 996.3,
448.6, 777.0, 558.2, 0.4, 0.6, 775.5, 666.9, 338.0,
447.5, 11.6, 556.0, 228.1, 995.8, 887.6, 120.2, 0.3,
0.3, 556.8, 339.1, 887.2, 999.0, 779.0, 11.1, 118.3,
229.2, 669.1, 448.9, 0.5)

' Next, we create the regression model, using the NumericalVariable objects
' we just created:
Dim model2 As New SimpleRegressionModel(dependent2, independent2)
model2.Fit()

For Each param As Parameter(Of Double) In model2.Parameters
Console.WriteLine(param.ToString())
Next
Console.WriteLine("Residual standard error: {0:F8}", model2.StandardError)
Console.WriteLine("R-Squared: {0:F8}", model2.RSquared)