Simple Regression in F# QuickStart Sample

Illustrates how to perform a simple linear regression using the SimpleRegressionModel class in F#.

This sample is also available in: C#, Visual Basic, IronPython.

Overview

This QuickStart sample demonstrates how to perform simple linear regression analysis using the SimpleRegressionModel class in Numerics.NET.

The sample shows two different regression scenarios using data from the National Institute of Standards and Technology’s Statistical Reference Datasets (NIST StRD). The first example demonstrates a no-intercept model using the ‘NoInt1’ dataset, while the second uses the ‘Norris’ dataset with an intercept term.

For each model, the sample shows how to:

Create and populate the dependent and independent variable data
Construct and configure the SimpleRegressionModel
Fit the model to the data
Access key regression statistics including:
- Parameter estimates and standard errors
- Residual standard error
- R-squared and adjusted R-squared values
- F-statistic
- ANOVA table results

The code illustrates different ways to input data, including using simple arrays and Vector objects. It also demonstrates how to control model properties like the intercept term.

The code

//=====================================================================
//
//  File: simple-regression.fs
//
//---------------------------------------------------------------------
//
//  This file is part of the Numerics.NET Code Samples.
//
//  Copyright (c) 2004-2025 ExoAnalytics Inc. All rights reserved.
//
//=====================================================================

module SimpleRegression

#light

open System

open Numerics.NET
open Numerics.NET.Statistics

// The license is verified at runtime. We're using a 30 day trial key here.
// For more information, see:
//     https://numerics.net/trial-key
let licensed = Numerics.NET.License.Verify("your-trial-key-here")

// Illustrates the use of the SimpleRegressionModel class
// to perform multiple linear regression.

// 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.
let yData1 = Vector.Create(
                [|130.0; 131.0; 132.0; 133.0; 134.0; 135.0;
                136.0; 137.0; 138.0; 139.0; 140.0|])
let xData1 = Vector.Create(
                [|60.0; 61.0; 62.0; 63.0; 64.0; 65.0;
                 66.0; 67.0; 68.0; 69.0; 70.0|])

// Next, we create the regression model. We can pass the data arrays directly.
let model1 = SimpleRegressionModel(yData1, xData1)
model1.NoIntercept <- true
model1.Fit()

for parameter in model1.Parameters do
    printfn "%O" parameter
printfn "Residual standard error: %.2f" model1.StandardError
printfn "R-Squared: %.3f" model1.RSquared
printfn "Adjusted R-Squared: %.3f" model1.AdjustedRSquared
printfn "F-statistic: %.3f" model1.FStatistic

printfn "%O" model1.AnovaTable

// Model 2 uses the 'Norris' dataset.

printfn "\n\nModel 2"
let 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|])
let 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:
let model2 = SimpleRegressionModel(dependent2, independent2)
model2.Fit()

for parameter in model2.Parameters do
    printfn "%O" parameter
printfn "Residual standard error: %.8f" model2.StandardError
printfn "R-Squared: %.8f" model2.RSquared
printfn "Adjusted R-Squared: %.8f" model2.AdjustedRSquared
printfn "F-statistic: %.3f" model2.FStatistic

printfn "%O" model2.AnovaTable

// The data can also be supplied as two Vector objects.
// This is not illustrated here.

printf "Press any key to exit."
Console.ReadLine() |> ignore