Fitting

Summary: this tutorial will walk through several ways of fitting data with FSharp.Stats.

Linear Regression

In Linear Regression a linear system of equations is generated. The coefficients obtained by the solution to this equation system minimize the squared distances from the regression curve to the data points. These distances are also known as residuals (or least squares).

Summary

With the FSharp.Stats.Fitting.LinearRegression module you can apply various regression methods. A LinearRegression type provides many common methods for fitting two- or multi dimensional data. These include

Simple linear regression (fitting a straight line to the data)
Polynomial regression (fitting a polynomial of specified order/degree) to the data
Robust regression (fitting a straight line to the data and ignoring outliers)

The following code snippet summarizes many regression methods. In the following sections, every method is discussed in detail!

open Plotly.NET
open FSharp.Stats
open FSharp.Stats.Fitting

let testDataX = vector [|1. .. 10.|]

let testDataY = vector [|0.;-1.;0.;0.;0.;0.;1.;1.;3.;3.5|]


let coefSimpL    = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.SimpleLinear) // simple linear regression with a straight line through the data
let coefSimpLRTO = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.SimpleLinear,Constraint = Constraint.RegressionThroughOrigin) // simple linear regression with a straight line through the origin (0,0)
let coefSimpLXY  = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.SimpleLinear,Constraint = Constraint.RegressionThroughXY (9.,1.)) // simple linear regression with a straight line through the coordinate 9,1.
let coefPoly_1   = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.Polynomial 1) // fits a polynomial of degree 1 (equivalent to simple linear regression)
let coefPoly_2   = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.Polynomial 2) // fits a quadratic polynomial
let coefPoly_3   = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.Polynomial 3) // fits a cubic polynomial
let coefPoly_3w  = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.Polynomial 3, Weighting = (vector [1.;1.;1.;1.;2.;2.;2.;10.;1.;1.])) // fits a cubic polynomial with weighted points
let coefRobTh    = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.Robust RobustEstimator.Theil) // fits a straight line that is insensitive to outliers
let coefRobThSen = LinearRegression.fit(testDataX, testDataY, FittingMethod = Method.Robust RobustEstimator.TheilSen) // fits a straight line that is insensitive to outliers

// f(x) = -0.167 + -0.096x + -0.001x^2 + 0.005x^3
let functionStringPoly3 = coefPoly_3.ToString()

let regressionComparison =
    [
        Chart.Point(testDataX,testDataY,Name="data")
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefSimpL   ) x)  |> Chart.Line |> Chart.withTraceInfo "SimpL"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefSimpLRTO) x)  |> Chart.Line |> Chart.withTraceInfo "SimpL Origin"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefSimpLXY ) x)  |> Chart.Line |> Chart.withTraceInfo "SimpL 9,1"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefPoly_1  ) x)  |> Chart.Line |> Chart.withTraceInfo "Poly 1"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefPoly_2  ) x)  |> Chart.Line |> Chart.withTraceInfo "Poly 2"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefPoly_3  ) x)  |> Chart.Line |> Chart.withTraceInfo "Poly 3"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefPoly_3w ) x)  |> Chart.Line |> Chart.withTraceInfo "Poly 3 weight"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefRobTh   ) x)  |> Chart.Line |> Chart.withTraceInfo "Robust Theil"
        [1. .. 0.01 .. 10.] |> List.map (fun x -> x,LinearRegression.predict(coefRobThSen) x)  |> Chart.Line |> Chart.withTraceInfo "Robust TheilSen"
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored
    |> Chart.withAnnotation(LayoutObjects.Annotation.init(X = 9.5,Y = 3.1,XAnchor = StyleParam.XAnchorPosition.Right,Text = functionStringPoly3))  
    |> Chart.withXAxisStyle("x data")
    |> Chart.withYAxisStyle("y data")
    |> Chart.withSize(800.,600.)

Simple Linear Regression

Simple linear regression aims to fit a straight regression line to the data. While the least squares approach efficiently minimizes the sum of squared residuals it is prone to outliers. An alternative is a robust simple linear regression like Theil's incomplete method or the Theil-Sen estimator, that are outlier resistant.

Univariable

open Plotly.NET
open FSharp.Stats
open FSharp.Stats.Fitting.LinearRegression

let xData = vector [|1. .. 10.|]
let yData = vector [|4.;7.;9.;12.;15.;17.;16.;23.;5.;30.|]

//Least squares simple linear regression
let coefficientsLinearLS = 
    OLS.Linear.Univariable.fit xData yData
let predictionFunctionLinearLS x = 
    OLS.Linear.Univariable.predict coefficientsLinearLS x

//Robust simple linear regression
let coefficientsLinearRobust = 
    RobustRegression.Linear.theilSenEstimator xData yData 
let predictionFunctionLinearRobust x = 
    RobustRegression.Linear.predict coefficientsLinearRobust x

//least squares simple linear regression through the origin
let coefficientsLinearRTO = 
    OLS.Linear.RTO.fitOfVector xData yData 
let predictionFunctionLinearRTO x = 
    OLS.Linear.RTO.predict coefficientsLinearRTO x



let rawChart = 
    Chart.Point(xData,yData)
    |> Chart.withTraceInfo "raw data"
    
let predictionLS = 
    let fit = 
        [|0. .. 11.|] 
        |> Array.map (fun x -> x,predictionFunctionLinearLS x)
    Chart.Line(fit)
    |> Chart.withTraceInfo "least squares (LS)"

let predictionRobust = 
    let fit = 
        [|0. .. 11.|] 
        |> Array.map (fun x -> x,predictionFunctionLinearRobust x)
    Chart.Line(fit)
    |> Chart.withTraceInfo "TheilSen estimator"

let predictionRTO = 
    let fit = 
        [|0. .. 11.|] 
        |> Array.map (fun x -> x,predictionFunctionLinearRTO x)
    Chart.Line(fit)
    |> Chart.withTraceInfo "LS through origin"

let simpleLinearChart =
    [rawChart;predictionLS;predictionRTO;predictionRobust;] 
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored

Multivariable

//Multivariate simple linear regression
let xVectorMulti =
    [
    [1.; 1. ;2.  ]
    [2.; 0.5;6.  ]
    [3.; 0.8;10. ]
    [4.; 2. ;14. ]
    [5.; 4. ;18. ]
    [6.; 3. ;22. ]
    ]
    |> matrix

let yVectorMulti = 
    let transformX (x:Matrix<float>) =
        x
        |> Matrix.getRows
        |> Array.map (fun v -> 100. + (v.[0] * 2.5) + (v.[1] * 4.) + (v.[2] * 0.5))
    xVectorMulti
    |> transformX
    |> vector

let coefficientsMV = 
    OLS.Linear.Multivariable.fit xVectorMulti yVectorMulti
let predictionFunctionMV x = 
    OLS.Linear.Multivariable.predict coefficientsMV x

Polynomial Regression

In polynomial regression a higher degree (d > 1) polynomial is fitted to the data. The coefficients are chosen that the sum of squared residuals is minimized.

open FSharp.Stats
open FSharp.Stats.Fitting.LinearRegression

let xDataP = vector [|1. .. 10.|]
let yDataP = vector [|4.;7.;9.;8.;6.;3.;2.;5.;6.;8.;|]

//Least squares polynomial regression

//define the order the polynomial should have (order 3: f(x) = ax^3 + bx^2 + cx + d)
let order = 3
let coefficientsPol = 
    OLS.Polynomial.fit order xDataP yDataP 
let predictionFunctionPol x = 
    OLS.Polynomial.predict coefficientsPol x

//weighted least squares polynomial regression
//If heteroscedasticity is assumed or the impact of single datapoints should be 
//increased/decreased you can use a weighted version of the polynomial regression.

//define the order the polynomial should have (order 3: f(x) = ax^3 + bx^2 + cx + d)
let orderP = 3

//define the weighting vector
let weights = yDataP |> Array.map (fun y -> 1. / y)
let coefficientsPolW = 
    OLS.Polynomial.fitWithWeighting orderP weights xDataP yDataP 
let predictionFunctionPolW x = 
    OLS.Polynomial.predict coefficientsPolW x

let rawChartP = 
    Chart.Point(xDataP,yDataP)
    |> Chart.withTraceInfo "raw data"
    
let fittingPol = 
    let fit = 
        [|1. .. 0.1 .. 10.|] 
        |> Array.map (fun x -> x,predictionFunctionPol x)
    Chart.Line(fit)
    |> Chart.withTraceInfo "order = 3"

let fittingPolW = 
    let fit = 
        [|1. .. 0.1 .. 10.|] 
        |> Array.map (fun x -> x,predictionFunctionPolW x)
    Chart.Line(fit)
    |> Chart.withTraceInfo "order = 3 weigthed"

let polRegressionChart =
    [rawChartP;fittingPol;fittingPolW] 
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored

Nonlinear Regression

Nonlinear Regression is used if a known model should be fitted to the data that cannot be represented in a linear system of equations. Common examples are:

gaussian functions
log functions
exponential functions

To fit such models to your data the NonLinearRegression module can be used. Three solver-methods are available to iteratively converge to a minimal least squares value.

GaussNewton
LevenbergMarquardt
LevenbergMarquardtConstrained

For solving a nonlinear problem the model function has to be converted to a NonLinearRegression.Model type consisting of

parameter names,
the function itself, and
partial derivatives of all unknown parameters.

For clarification a exponential relationship in the form of y = a * exp(b * x) should be solved:

open System
open FSharp.Stats.Fitting
open FSharp.Stats.Fitting.LinearRegression
open FSharp.Stats.Fitting.NonLinearRegression

let xDataN = [|1.;2.; 3.; 4.|]
let yDataN = [|5.;14.;65.;100.|]

//search for:  y = a * exp(b * x)

// 1. create the model
// 1.1 define parameter names
let parameterNames = [|"a";"b"|]

// 1.2 define the exponential function that gets a parameter vector containing the 
//searched parameters and the x value and gives the corresponding y value
let getFunctionValue =                 
    fun (parameterVector: Vector<float>) x -> 
        parameterVector.[0] * Math.Exp(parameterVector.[1] * x)
      //a                   *      exp(b                   * x)

// 1.3 Define partial derivatives of the exponential function. 
//     Take partial derivatives for every unknown parameter and
//     insert it into the gradient vector sorted by parameterNames.
let getGradientValues =
    fun (parameterVector:Vector<float>) (gradientVector: Vector<float>) xValueN -> 
        // partial derivative of y=a*exp(b*x) in respect to the first parameter (a)   --> exp(b*x)
        gradientVector.[0] <- Math.Exp(parameterVector.[1] * xValueN)  
        // partial derivative of y=a*exp(b*x) in respect to the second parameter (b)  --> a*x*exp(b*x)
        gradientVector.[1] <- parameterVector.[0] * xValueN * Math.Exp(parameterVector.[1] * xValueN)  

        gradientVector

// 1.4 create the model
let model = createModel parameterNames getFunctionValue getGradientValues

// 2. define the solver options
// 2.1 define the stepwidth of the x value change
let deltaX = 0.0001

// 2.2 define the stepwidth of the parameter change
let deltaP = 0.0001

// 2.3 define the number of iterations
let k = 1000

// 2.4 define an initial guess
//     For many problems you can set a default value or let the user decide to choose an 
//     appropriate guess. In the case of an exponential or log model you can use the 
//     solution of the linearized problem as a first guess.
let initialParamGuess (xData:float []) (yData:float [])=
    //gets the linear representation of the problem and solves it by simple linear regression 
    //(prone to least-squares-deviations at high y_Values)
    let yLn = yData |> Array.map (fun x -> Math.Log(x)) |> vector
    let linearReg = 
        LinearRegression.OLS.Linear.Univariable.fit (vector xData) yLn
    //calculates the parameters back into the exponential representation
    let a = exp linearReg.[0]
    let b = linearReg.[1]
    [|a;b|]

// 2.5 create the solverOptions
let solverOptions = 
    let guess = initialParamGuess xDataN yDataN
    NonLinearRegression.createSolverOption 0.0001 0.0001 1000 guess

// 3. get coefficients
let coefficientsExp = GaussNewton.estimatedParams model solverOptions xDataN yDataN
//val coefficients = vector [|5.68867298; 0.7263428835|]

// 4. create fitting function
let fittingFunction x = coefficientsExp.[0] * Math.Exp(coefficientsExp.[1] * x)

let rawChartNLR = 
    Chart.Point(xDataN,yDataN)
    |> Chart.withTraceInfo "raw data"

let fittingNLR = 
    let fit = 
        [|1. .. 0.1 .. 10.|] 
        |> Array.map (fun x -> x,fittingFunction x)
    Chart.Line(fit)
    |> Chart.withTraceInfo "NLR"

let NLRChart =
    [rawChartNLR;fittingNLR] 
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored

LevenbergMarquardtConstrained

For nonlinear regression using the LevenbergMarquardtConstrained module, you have to follow similar steps as in the example shown above. In this example, a logistic function of the form y = L/(1+e^(-k(t-x))) should be fitted to count data:

open FSharp.Stats.Fitting.NonLinearRegression

let xHours = [|0.; 19.5; 25.5; 30.; 43.; 48.5; 67.75|]

let yCount = [|0.0; 2510000.0; 4926400.0; 9802600.0; 14949400.0; 15598800.0; 16382000.0|]

// 1. Choose a model
// The model we need already exists in FSharp.Stats and can be taken from the "Table" module.
let model' = Table.LogisticFunctionAscending

// 2. Define the solver options
// 2.1 Initial parameter guess
// The solver needs an initial parameter guess. This can be done by the user or with an estimator function.
// The cutoffPercentage says at which percentage of the y-Range the lower part of the slope is. 
// Manual curation of parameter guesses can be performed in this step by editing the param array.
let initialParamGuess' = LevenbergMarquardtConstrained.initialParam xHours yCount 0.1

// 2.2 Create the solver options
let solverOptions' = Table.lineSolverOptions initialParamGuess'

// 3. Estimate parameters for a possible solution based on residual sum of squares
// Besides the solverOptions, an upper and lower bound for the parameters are required.
// It is recommended to define them depending on the initial param guess
let lowerBound =
    initialParamGuess'
    |> Array.map (fun param ->
        // Initial paramters -20%
        param - (abs param) * 0.2
    )
    |> vector

let upperBound =
    initialParamGuess'
    |> Array.map (fun param ->
        param + (abs param) * 0.2
    )
    |> vector

let estParams =
    LevenbergMarquardtConstrained.estimatedParams model' solverOptions' 0.001 10. lowerBound upperBound xHours yCount

// 3.1 Estimate multiple parameters and pick the one with the least residual sum of squares (RSS)
// For a more "global" minimum. it is possible to estimate multiple possible parameters for different initial guesses.

//3.1.1 Generation of parameters with varying steepnesses
let multipleSolverOptions =
    LevenbergMarquardtConstrained.initialParamsOverRange xHours yCount [|0. .. 0.1 .. 2.|]
    |> Array.map Table.lineSolverOptions

let estParamsRSS =
    multipleSolverOptions
    |> Array.map (fun solvO ->
        let lowerBound =
            solvO.InitialParamGuess
            |> Array.map (fun param -> param - (abs param) * 0.2)
            |> vector
        let upperBound =
            solvO.InitialParamGuess
            |> Array.map (fun param -> param + (abs param) * 0.2)
            |> vector
        LevenbergMarquardtConstrained.estimatedParamsWithRSS 
            model' solvO 0.001 10. lowerBound upperBound xHours yCount
    )
    |> Array.minBy snd
    |> fst

// The result is the same as for 'estParams', but tupled with the corresponding RSS, which can be taken
// as a measure of quality for the estimate.

// 4. Create fitting function
let fittingFunction' = Table.LogisticFunctionAscending.GetFunctionValue estParamsRSS

let fittedY = Array.zip [|1. .. 68.|] ([|1. .. 68.|] |> Array.map fittingFunction')

let fittedLogisticFunc =
    [
    Chart.Point (Array.zip xHours yCount)
    |> Chart.withTraceInfo"Data Points"
    Chart.Line fittedY
    |> Chart.withTraceInfo "Fit"
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored    
    |> Chart.withXAxisStyle "Time"
    |> Chart.withYAxisStyle "Count"

Smoothing spline

A smoothing spline aims to minimize a function consisting of two error terms:

error1: sum of squared residuals
- Similar to the OrdinaryLeastSquares regression this error term ensures the fidelity to the data.
error2: integral of the second derivative of the fitting function
- This error term ensures the smoothness of the resulting curve.

A smoothing parameter (lambda) mediates between the two error terms.

E = error1 + (lambda * error2)
- If lambda = 0, the resulting curve minimizes the sum of squared residuals and results in an interpolating curve.
- If lambda = infinity, the resulting curve is punished by the smoothness measurement and results in a straight regression line.

The spline is constructed out of piecewise cubic polynomials that meet at knots. In the defined knots the function is continuous. Depending on the used smoothing factor and the defined knots the smoothing spline has a unique solution. The resulting curve is just defined within the interval defined in the x values of the data.

The right amount of smoothing can be determined by cross validation or generalized cross validation.

open FSharp.Stats.Fitting

let xDataS = [|1.;2.; 3.; 4.|]
let yDataS = [|5.;14.;65.;75.|]

let data = Array.zip xDataS yDataS

//in every x position a knot should be located
let knots = xDataS

let spline lambda x = (Spline.smoothingSpline data knots) lambda x

let fit lambda = 
    [|1. .. 0.1 .. 4.|]
    |> Array.map (fun x -> x,spline lambda x)
    |> Chart.Line
    |> Chart.withTraceInfo (sprintf "lambda: %.3f" lambda)

let rawChartS = Chart.Point(data)

let smoothingSplines =
    [
    rawChartS
    fit 0.001
    fit 0.02
    fit 1.
    ]
    |> Chart.combine
    |> Chart.withTemplate ChartTemplates.lightMirrored

namespace FsMath

namespace Plotly

namespace Plotly.NET

module Defaults from Plotly.NET
<summary> Contains mutable global default values. Changing these values will apply the default values to all consecutive Chart generations. </summary>

val mutable DefaultDisplayOptions: Plotly.NET.DisplayOptions

Multiple items
type DisplayOptions = inherit DynamicObj new: unit -> DisplayOptions static member addAdditionalHeadTags: additionalHeadTags: XmlNode list -> (DisplayOptions -> DisplayOptions) static member addDescription: description: XmlNode list -> (DisplayOptions -> DisplayOptions) static member combine: first: DisplayOptions -> second: DisplayOptions -> DisplayOptions static member getAdditionalHeadTags: displayOpts: DisplayOptions -> XmlNode list static member getDescription: displayOpts: DisplayOptions -> XmlNode list static member getPlotlyReference: displayOpts: DisplayOptions -> PlotlyJSReference static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?AdditionalHeadTags: XmlNode list * [<Optional; DefaultParameterValue ((null :> obj))>] ?Description: XmlNode list * [<Optional; DefaultParameterValue ((null :> obj))>] ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions static member initCDNOnly: unit -> DisplayOptions ...

--------------------
new: unit -> Plotly.NET.DisplayOptions

static member Plotly.NET.DisplayOptions.init: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AdditionalHeadTags: Giraffe.ViewEngine.HtmlElements.XmlNode list * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Description: Giraffe.ViewEngine.HtmlElements.XmlNode list * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?PlotlyJSReference: Plotly.NET.PlotlyJSReference -> Plotly.NET.DisplayOptions

type PlotlyJSReference = | CDN of string | Full | Require of string | NoReference
<summary> Sets how plotly is referenced in the head of html docs. </summary>

union case Plotly.NET.PlotlyJSReference.NoReference: Plotly.NET.PlotlyJSReference

Multiple items
namespace FSharp

--------------------
namespace Microsoft.FSharp

namespace FSharp.Stats

namespace FSharp.Stats.Fitting

val testDataX: Vector<float>

val vector: l: 'a seq -> Vector<'a> (requires 'a :> System.Numerics.INumber<'a>)

val testDataY: Vector<float>

val coefSimpL: LinearRegression.Coefficients

Multiple items
module LinearRegression from FSharp.Stats.Fitting
<summary> Linear regression is used to estimate the relationship of one variable (y) with another (x) by expressing y in terms of a linear function of x. </summary>

--------------------
type LinearRegression = new: unit -> LinearRegression static member fit: xData: Vector<float> * yData: Vector<float> * ?FittingMethod: Method * ?Constraint: Constraint<float * float> * ?Weighting: Vector<float> -> Coefficients + 1 overload static member predict: coeff: Coefficients -> xValue: float -> float static member predictMultivariate: coeff: Coefficients -> xVector: Vector<float> -> float
<summary> This LinearRegression type summarized the most common fitting procedures. </summary>
<returns>Either linear regression coefficients or a prediction function to map x values/vectors to its corresponding y value.</returns>
<example><code> // e.g. days since experiment start let xData = vector [|1. .. 100.|] // e.g. plant size in cm let yData = vector [|4.;7.;8.;9.;7.;11.; ...|] // Estimate the intercept and slope of a line, that fits the data. let coefficientsSimpleLinear = LinearRegression.fit(xData,yData,FittingMethod=Fitting.Method.SimpleLinear,Constraint=Fitting.Constraint.RegressionThroughOrigin) // Predict the size on day 10.5 LinearRegression.predict(coefficientsSimpleLinear) 10.5 </code></example>

--------------------
new: unit -> LinearRegression

static member LinearRegression.fit: xData: Matrix<float> * yData: Vector<float> * ?FittingMethod: Method -> LinearRegression.Coefficients
static member LinearRegression.fit: xData: Vector<float> * yData: Vector<float> * ?FittingMethod: Method * ?Constraint: Constraint<float * float> * ?Weighting: Vector<float> -> LinearRegression.Coefficients

type Method = | SimpleLinear | Polynomial of int | Robust of RobustEstimator member Equals: Method * IEqualityComparer -> bool
<summary> Defines regression method. </summary>

union case Method.SimpleLinear: Method
<summary>Fits a straight line through two-, or multidimensional data (OLS).</summary>

val coefSimpLRTO: LinearRegression.Coefficients

type Constraint<'a> = | Unconstrained | RegressionThroughOrigin | RegressionThroughXY of 'a member Equals: Constraint<'a> * IEqualityComparer -> bool
<summary> Defines if regression function should pass any specific point. </summary>

union case Constraint.RegressionThroughOrigin: Constraint<'a>
<summary>The regression line must go through the origin (0,0)</summary>

val coefSimpLXY: LinearRegression.Coefficients

union case Constraint.RegressionThroughXY: 'a -> Constraint<'a>
<summary>The regression line must go through a specified point, defined as float*float tuple ('xCorrdinate*'yCoordinate)</summary>

val coefPoly_1: LinearRegression.Coefficients

union case Method.Polynomial: int -> Method
<summary>Fits a polynomial of the specified order (degree) to twodimensional data (OLS).</summary>

val coefPoly_2: LinearRegression.Coefficients

val coefPoly_3: LinearRegression.Coefficients

val coefPoly_3w: LinearRegression.Coefficients

val coefRobTh: LinearRegression.Coefficients

union case Method.Robust: RobustEstimator -> Method
<summary>Fits an outlier-insensitive straight line through twodimensional data (NOT OLS).</summary>

type RobustEstimator = | Theil | TheilSen member Equals: RobustEstimator * IEqualityComparer -> bool
<summary> Defines method of slope estimation for robust line regression. </summary>

union case RobustEstimator.Theil: RobustEstimator
<summary>Theils incomplete method</summary>

val coefRobThSen: LinearRegression.Coefficients

union case RobustEstimator.TheilSen: RobustEstimator
<summary>Theil Sen estimator</summary>

val functionStringPoly3: string

override LinearRegression.Coefficients.ToString: unit -> string

val regressionComparison: GenericChart.GenericChart

type Chart = static member AnnotatedHeatmap: zData: #('a1 seq) seq * annotationText: #(string seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a4 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible and 'a5 :> IConvertible) + 1 overload static member Area: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillPattern: Pattern * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Bar: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiKeys: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member BoxPlot: [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a0 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a0 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxPoints: BoxPoints * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxMean: BoxMean * [<Optional; DefaultParameterValue ((null :> obj))>] ?Jitter: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?PointPos: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Outline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Notched: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?NotchWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?QuartileMethod: QuartileMethod * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a0 :> IConvertible and 'a1 :> IConvertible and 'a2 :> IConvertible) + 2 overloads static member Bubble: x: #IConvertible seq * y: #IConvertible seq * sizes: int seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Candlestick: ``open`` : #IConvertible seq * high: #IConvertible seq * low: #IConvertible seq * close: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a4 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?IncreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Increasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?DecreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Decreasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((true :> obj))>] ?ShowXAxisRangeSlider: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a4 :> IConvertible and 'a5 :> IConvertible) + 2 overloads static member Column: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiKeys: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member Contour: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a2 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineSmoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursColoring: ContourColoring * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursOperation: ConstraintOperation * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursType: ContourType * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowContourLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLabelFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?Contours: Contours * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?NContours: int * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) static member Funnel: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Offset: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextInfo: TextInfo * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineStyle: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorFillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Connector: FunnelConnector * [<Optional; DefaultParameterValue ((null :> obj))>] ?InsideTextFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutsideTextFont: Font * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) static member Heatmap: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a2 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) + 1 overload ...

static member Chart.Point: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Point: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)

Multiple items
module List from FSharp.Stats
<summary> Module to compute common statistical measure on list </summary>

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module List from Microsoft.FSharp.Collections

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type List = new: unit -> List static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float list static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float list

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type List<'T> = | op_Nil | op_ColonColon of Head: 'T * Tail: 'T list interface IReadOnlyList<'T> interface IReadOnlyCollection<'T> interface IEnumerable interface IEnumerable<'T> member GetReverseIndex: rank: int * offset: int -> int member GetSlice: startIndex: int option * endIndex: int option -> 'T list static member Cons: head: 'T * tail: 'T list -> 'T list member Head: 'T member IsEmpty: bool member Item: index: int -> 'T with get ...

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new: unit -> List

val map: mapping: ('T -> 'U) -> list: 'T list -> 'U list

val x: float

static member LinearRegression.predict: coeff: LinearRegression.Coefficients -> xValue: float -> float

static member Chart.Line: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Line: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)

static member Chart.withTraceInfo: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: StyleParam.Visible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendRank: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroupTitle: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.combine: gCharts: GenericChart.GenericChart seq -> GenericChart.GenericChart

static member Chart.withTemplate: template: Template -> (GenericChart.GenericChart -> GenericChart.GenericChart)

module ChartTemplates from Plotly.NET

val lightMirrored: Template

static member Chart.withAnnotation: annotation: LayoutObjects.Annotation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?Append: bool -> (GenericChart.GenericChart -> GenericChart.GenericChart)

namespace Plotly.NET.LayoutObjects

Multiple items
type Annotation = inherit DynamicObj new: unit -> Annotation static member init: [<Optional; DefaultParameterValue ((null :> obj))>] ?X: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Align: AnnotationAlignment * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowHead: ArrowHead * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowSide: ArrowSide * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowSize: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?AX: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?AXRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?AY: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?AYRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?BGColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?BorderColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?BorderPad: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?BorderWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?CaptureEvents: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ClickToShow: ClickToShow * [<Optional; DefaultParameterValue ((null :> obj))>] ?Font: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?Height: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverLabel: Hoverlabel * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverText: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowArrow: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?StandOff: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartArrowHead: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartArrowSize: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartStandOff: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TemplateItemName: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextAngle: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?VAlign: VerticalAlign * [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?XAnchor: XAnchorPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?XClick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?XRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?XShift: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?YAnchor: YAnchorPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?YClick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?YRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?YShift: int -> Annotation static member style: [<Optional; DefaultParameterValue ((null :> obj))>] ?X: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Align: AnnotationAlignment * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowHead: ArrowHead * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowSide: ArrowSide * [<Optional; DefaultParameterValue ((null :> obj))>] ?ArrowSize: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?AX: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?AXRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?AY: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?AYRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?BGColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?BorderColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?BorderPad: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?BorderWidth: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?CaptureEvents: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ClickToShow: ClickToShow * [<Optional; DefaultParameterValue ((null :> obj))>] ?Font: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?Height: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverLabel: Hoverlabel * [<Optional; DefaultParameterValue ((null :> obj))>] ?HoverText: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowArrow: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?StandOff: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartArrowHead: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartArrowSize: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?StartStandOff: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?TemplateItemName: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextAngle: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?VAlign: VerticalAlign * [<Optional; DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?XAnchor: XAnchorPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?XClick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?XRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?XShift: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?YAnchor: YAnchorPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?YClick: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?YRef: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?YShift: int -> (Annotation -> Annotation)
<summary> Text annotations inside a plot </summary>

--------------------
new: unit -> LayoutObjects.Annotation

static member LayoutObjects.Annotation.init: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?X: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Y: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Align: StyleParam.AnnotationAlignment * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ArrowColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ArrowHead: StyleParam.ArrowHead * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ArrowSide: StyleParam.ArrowSide * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ArrowSize: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AX: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AXRef: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AY: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AYRef: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BGColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BorderColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BorderPad: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BorderWidth: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CaptureEvents: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ClickToShow: StyleParam.ClickToShow * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Font: Font * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Height: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?HoverLabel: LayoutObjects.Hoverlabel * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?HoverText: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowArrow: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StandOff: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StartArrowHead: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StartArrowSize: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StartStandOff: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TemplateItemName: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextAngle: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?VAlign: StyleParam.VerticalAlign * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XAnchor: StyleParam.XAnchorPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XClick: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XRef: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XShift: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YAnchor: StyleParam.YAnchorPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YClick: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YRef: #System.IConvertible * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YShift: int -> LayoutObjects.Annotation

argument X: float option
<summary> Init Annotation type </summary>

argument Y: float option
<summary> Init Annotation type </summary>

module StyleParam from Plotly.NET

type XAnchorPosition = | Auto | Left | Center | Right member Convert: unit -> obj override ToString: unit -> string static member convert: (XAnchorPosition -> obj) static member toString: (XAnchorPosition -> string)

union case StyleParam.XAnchorPosition.Right: StyleParam.XAnchorPosition

static member Chart.withXAxisStyle: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleText: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleStandoff: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: StyleParam.AxisType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinMax: (#System.IConvertible * #System.IConvertible) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: StyleParam.Mirror * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: (float * float) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: StyleParam.CategoryOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryArray: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: LayoutObjects.RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.RangeSelector * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.withYAxisStyle: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleText: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleStandoff: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: StyleParam.AxisType * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinMax: (#System.IConvertible * #System.IConvertible) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: StyleParam.Mirror * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.LinearAxisId * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Shift: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: (float * float) * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: StyleParam.CategoryOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryArray: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: LayoutObjects.RangeSlider * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.RangeSelector * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.withSize: width: float * height: float -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withSize: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Height: int -> (GenericChart.GenericChart -> GenericChart.GenericChart)

module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>

val toChartHTML: gChart: GenericChart.GenericChart -> string

val xData: Vector<float>

val yData: Vector<float>

val coefficientsLinearLS: Coefficients

module OLS from FSharp.Stats.Fitting.LinearRegressionModule
<summary> Ordinary Least Squares (OLS) regression aims to minimise the sum of squared y intercepts between the original and predicted points at each x value. </summary>

module Linear from FSharp.Stats.Fitting.LinearRegressionModule.OLS
<summary> Simple linear regression using straight lines: f(x) = a + bx. </summary>

module Univariable from FSharp.Stats.Fitting.LinearRegressionModule.OLS.Linear
<summary> Univariable handles two dimensional x,y data. </summary>

val fit: xData: Vector<float> -> yData: Vector<float> -> Coefficients
<summary> Calculates the intercept and slope for a straight line fitting the data. Linear regression minimizes the sum of squared residuals. </summary>
<param name="xData">vector of x values</param>
<param name="yData">vector of y values</param>
<returns>vector of [intercept; slope]</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. some measured feature let yData = vector [|4.;7.;9.;10.;11.;15.|] // Estimate the coefficients of a straight line fitting the given data let coefficients = Univariable.fit xData yData </code></example>

val predictionFunctionLinearLS: x: float -> float

val predict: coef: Coefficients -> x: float -> float
<summary> Takes intercept and slope of simple linear regression to predict the corresponding y value. </summary>
<param name="coef">vector of [intercept;slope] (e.g. determined by Univariable.coefficient)</param>
<param name="x">x value of which the corresponding y value should be predicted</param>
<returns>predicted y value with given coefficients at X=x</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. some measured feature let yData = vector [|4.;7.;9.;10.;11.;15.|] // Estimate the coefficients of a straight line fitting the given data let coefficients = Univariable.fit xData yData // Predict the feature at midnight between day 1 and 2. Univariable.predict coefficients 1.5 </code></example>

val coefficientsLinearRobust: Coefficients

module RobustRegression from FSharp.Stats.Fitting.LinearRegressionModule
<summary> Robust regression does not necessarily minimize the distance of the fitting function to the input data points (least squares), but has alternative aims (non-parametric). </summary>

module Linear from FSharp.Stats.Fitting.LinearRegressionModule.RobustRegression
<summary> Simple linear regression using straight lines: f(x) = a + bx. </summary>

val theilSenEstimator: xData: Vector<float> -> yData: Vector<float> -> Coefficients
<summary> Calculates simple linear regression coefficients using the Theil-Sen estimator in the form of [|intercept; slope;|]. Performs well if outlier corrupt the regression line. </summary>
<param name="xData">vector of x values</param>
<param name="yData">vector of y values</param>
<returns>vector of polynomial coefficients sorted as [intercept;constant;quadratic;...]</returns>
<example><code> // e.g. days since experiment start let xData = vector [|1. .. 100.|] // e.g. plant size in cm let yData = vector [|4.;7.;8.;9.;7.;11.; ...|] // Estimate the intercept and slope of a line, that fits the data. let coefficients = LinearRegression.RobustRegression.Linear.theilSenEstimator xData yData </code></example>
<remarks>Not robust if data count is low!</remarks>

val predictionFunctionLinearRobust: x: float -> float

val predict: coef: Coefficients -> x: float -> float
<summary> Takes vector of [intercept; slope] and x value to predict the corresponding y value </summary>
<param name="coef">vector of coefficients, sorted as [intercept;slope]</param>
<param name="x">x value of which the corresponding y value should be predicted</param>
<returns>predicted y value with given coefficients at X=x</returns>
<example><code> // e.g. days since experiment start let xData = vector [|1. .. 100.|] // e.g. plant size in cm let yData = vector [|4.;7.;8.;9.;7.;11.; ...|] // Estimate the intercept and slope of a line, that fits the data. let coefficients = LinearRegression.RobustRegression.Linear.theilEstimator xData yData // Predict the size on day 10.5 LinearRegression.RobustRegression.Linear.predict coefficients 10.5 </code></example>
<remarks>Equal to OLS.Linear.Univariable.predict!</remarks>

val coefficientsLinearRTO: Coefficients

module RTO from FSharp.Stats.Fitting.LinearRegressionModule.OLS.Linear
<summary> Fits straight regression lines through the origin f(x) = bx. </summary>

val fitOfVector: xData: Vector<float> -> yData: Vector<float> -> Coefficients
<summary> Calculates the slope of a regression line through the origin </summary>
<param name="xData">vector of x values</param>
<param name="yData">vector of y values</param>
<returns>Slope of the regression line through the origin</returns>
<example><code> // e.g. days since a certain event let xData = vector [|0.;1.;2.;3.;4.;5.;|] // some measured feature, that theoretically is zero at day 0 let yData = vector [|1.;5.;9.;13.;17.;18.;|] // Estimate the slope of the regression line. let coefficients = LinearRegression.OLS.Linear.fit xData yData </code></example>

val predictionFunctionLinearRTO: x: float -> float

val predict: coef: Coefficients -> x: float -> float
<summary> Predicts the y value for a given slope and x value (intercept=0) </summary>
<param name="coef">The functions slope</param>
<param name="x">x value of which the corresponding y value should be predicted</param>
<returns>predicted y value</returns>
<example><code> let mySlope = 17.8 // Returns predicted y value at x=6 using a line with intercept=0 and slope=17.8 LinearRegression.OLS.Linear.RTO.predict mySlope 6. </code></example>

val rawChart: GenericChart.GenericChart

val predictionLS: GenericChart.GenericChart

val fit: (float * float) array

Multiple items
module Array from FSharp.Stats
<summary> Module to compute common statistical measure on array </summary>

--------------------
module Array from Microsoft.FSharp.Collections

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type Array = new: unit -> Array static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array

--------------------
new: unit -> Array

val map: mapping: ('T -> 'U) -> array: 'T array -> 'U array

val predictionRobust: GenericChart.GenericChart

val predictionRTO: GenericChart.GenericChart

val simpleLinearChart: GenericChart.GenericChart

val xVectorMulti: Matrix<float>

val matrix: ll: #('b seq) seq -> Matrix<'b> (requires 'b :> System.Numerics.INumber<'b> and default constructor and value type and comparison and 'b :> System.ValueType)

val yVectorMulti: Vector<float>

val transformX: x: Matrix<float> -> float array

val x: Matrix<float>

Multiple items
module Matrix from FsMath

--------------------
type Matrix<'T (requires 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType)> = interface IEquatable<Matrix<'T>> new: rows: int * cols: int * data: Vector<'T> -> Matrix<'T> override Equals: obj: obj -> bool override GetHashCode: unit -> int member GetSlice: rowStart: int option * rowEnd: int option * colStart: int option * colEnd: int option -> Matrix<'T> + 1 overload member SetCol: j: int * colData: 'T array -> unit member SetRow: i: int * rowData: 'T array -> unit override ToString: unit -> string member Transpose: unit -> Matrix<'T> member toArray2D: unit -> 'T array2d ...
<summary> Matrix type to hold values of a matrix in a 1D Arrays (Flattened Representation) </summary>

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new: rows: int * cols: int * data: Vector<'T> -> Matrix<'T>

Multiple items
val float: value: 'T -> float (requires member op_Explicit)

--------------------
type float = System.Double

--------------------
type float<'Measure> = float

static member Matrix.getRows: m: Matrix<'T> -> Vector<'T> array

val v: Vector<float>

val coefficientsMV: Coefficients

module Multivariable from FSharp.Stats.Fitting.LinearRegressionModule.OLS.Linear
<summary> Multivariable handles multi dimensional data where a vector of independent x values should be used to predict a single y value. </summary>

val fit: xData: Matrix<float> -> yData: Vector<float> -> Coefficients
<summary> Calculates the coefficients for a straight line fitting the data. Linear regression minimizes the sum of squared residuals. </summary>
<param name="xData">matrix of x vectors</param>
<param name="yData">vector of y values</param>
<returns>vector of linear coefficients</returns>
<example><code> let xVectorMulti = [ [1.; 1. ;2. ] [2.; 0.5;6. ] [3.; 0.8;10. ] [4.; 2. ;14. ] [5.; 4. ;18. ] [6.; 3. ;22. ] ] |> Matrix.ofJaggedSeq // Here the x values are transformed. In most cases the y values are just provided. let yVectorMulti = let transformX (x) = x |> Matrix.mapiRows (fun _ v -> 100. + (v.[0] * 2.5) + (v.[1] * 4.) + (v.[2] * 0.5)) xVectorMulti |> transformX |> vector let coefficientsMV = Multivariable.fit xVectorMulti yVectorMulti </code></example>

val predictionFunctionMV: x: Vector<float> -> float

val x: Vector<float>

val predict: coef: Coefficients -> x: Vector<float> -> float
<summary> Takes linear coefficients and x vector to predict the corresponding y value. </summary>
<param name="coef">Coefficients from linear regression.</param>
<param name="x">x vector for which the y value should be predicted</param>
<returns>predicted y value with given coefficients at X=x</returns>
<example><code> let xVectorMulti = [ [1.; 1. ;2. ] [2.; 0.5;6. ] [3.; 0.8;10. ] [4.; 2. ;14. ] [5.; 4. ;18. ] [6.; 3. ;22. ] ] |> Matrix.ofJaggedSeq // Here the x values are transformed. In most cases the y values are just provided. let yVectorMulti = let transformX (x) = x |> Matrix.mapiRows (fun _ v -> 100. + (v.[0] * 2.5) + (v.[1] * 4.) + (v.[2] * 0.5)) xVectorMulti |> transformX |> vector let coefficientsMV = Multivariable.fit xVectorMulti yVectorMulti let fittingFunctionMV x = Multivariable.predict coefficientsMV x </code></example>

val xDataP: Vector<float>

val yDataP: Vector<float>

val order: int

val coefficientsPol: Coefficients

module Polynomial from FSharp.Stats.Fitting.LinearRegressionModule.OLS
<summary> Linear regression using polynomials as regression function: f(x) = a + bx + cx^2 + .... </summary>

val fit: order: int -> xData: Vector<float> -> yData: Vector<float> -> Coefficients
<summary> Calculates the polynomial coefficients for polynomial regression. </summary>
<param name="order">order of the polynomial (1 = linear, 2 = quadratic, ... )</param>
<param name="xData">vector of x values</param>
<param name="yData">vector of y values</param>
<returns>vector of polynomial coefficients sorted as [intercept;constant;quadratic;...]</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. temperature measured at noon of the days specified in xData let yData = vector [|4.;7.;9.;8.;7.;9.;|] // Estimate the three coefficients of a quadratic polynomial. let coefficients = LinearRegression.OLS.Polynomial.fit 2 xData yData </code></example>

val predictionFunctionPol: x: float -> float

val predict: coef: Coefficients -> x: float -> float
<summary> Takes polynomial coefficients and x value to predict the corresponding y value. </summary>
<param name="coef">vector of polynomial coefficients (e.g. determined by Polynomial.coefficients), sorted as [intercept;constant;quadratic;...]</param>
<param name="x">x value of which the corresponding y value should be predicted</param>
<returns>predicted y value with given polynomial coefficients at X=x</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. temperature measured at noon of the days specified in xData let yData = vector [|4.;7.;9.;8.;7.;9.;|] // Define the polynomial coefficients. let coefficients = LinearRegression.OLS.Polynomial.fit xData yData // Predict the temperature value at midnight between day 1 and 2. LinearRegression.OLS.Polynomial.predict coefficients 1.5 </code></example>
<remarks>If all coefficients are nonzero, the order is equal to the length of the coefficient vector!</remarks>

val orderP: int

val weights: float array

val y: float

val coefficientsPolW: Coefficients

val fitWithWeighting: order: int -> weighting: Vector<float> -> xData: Vector<float> -> yData: Vector<float> -> Coefficients
<summary> Calculates the polynomial coefficients for polynomial regression with a given point weighting. </summary>
<param name="order">order of the polynomial (1 = linear, 2 = quadratic, ... )</param>
<param name="weighting">Vector of weightings that define the releveance of each point for fitting.</param>
<param name="xData">vector of x values</param>
<param name="yData">vector of y values</param>
<returns>vector of polynomial coefficients sorted as [intercept;constant;quadratic;...]</returns>
<example><code> // e.g. days since a certain event let xData = vector [|1.;2.;3.;4.;5.;6.|] // e.g. temperature measured at noon of the days specified in xData let yData = vector [|4.;7.;9.;8.;7.;9.;|] // Estimate the three coefficients of a quadratic polynomial. let coefficients = LinearRegression.OLS.Polynomial.fit 2 xData yData </code></example>

val predictionFunctionPolW: x: float -> float

val rawChartP: GenericChart.GenericChart

val fittingPol: GenericChart.GenericChart

val fittingPolW: GenericChart.GenericChart

val polRegressionChart: GenericChart.GenericChart

namespace System

module NonLinearRegression from FSharp.Stats.Fitting

val xDataN: float array

val yDataN: float array

val parameterNames: string array

val getFunctionValue: parameterVector: Vector<float> -> x: float -> float

val parameterVector: Vector<float>

Multiple items
module Vector from FSharp.Stats

--------------------
module Vector from FsMath

--------------------
type Vector = static member add: v1: Vector<'T> -> v2: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member addScalar: scalar: 'T -> v: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member divide: v1: Vector<'T> -> v2: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member divideScalar: scalar: 'T -> v: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member dot: v1: Vector<'T> -> v2: Vector<'T> -> 'T (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member max: v: Vector<'T> -> 'T (requires 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType) static member mean: v: Vector<'T> -> 'T (requires 'T :> INumber<'T> and member DivideByInt and default constructor and value type and 'T :> ValueType) static member min: v: Vector<'T> -> 'T (requires 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType) static member multiply: v1: Vector<'T> -> v2: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) static member multiplyScalar: scalar: 'T -> v: Vector<'T> -> Vector<'T> (requires 'T :> INumber<'T> and value type and default constructor and 'T :> ValueType) ...

--------------------
type Vector<'T (requires 'T :> INumber<'T>)> = 'T array
<summary> Vector as a Array type alias </summary>

Multiple items
val float: value: 'T -> float (requires member op_Explicit)

--------------------
type float = Double

--------------------
type float<'Measure> = float

type Math = static member Abs: value: decimal -> decimal + 7 overloads static member Acos: d: float -> float static member Acosh: d: float -> float static member Asin: d: float -> float static member Asinh: d: float -> float static member Atan: d: float -> float static member Atan2: y: float * x: float -> float static member Atanh: d: float -> float static member BigMul: a: int * b: int -> int64 + 2 overloads static member BitDecrement: x: float -> float ...
<summary>Provides constants and static methods for trigonometric, logarithmic, and other common mathematical functions.</summary>

Math.Exp(d: float) : float

val getGradientValues: parameterVector: Vector<float> -> gradientVector: Vector<float> -> xValueN: float -> Vector<float>

val gradientVector: Vector<float>

val xValueN: float

val model: Model

val createModel: parameterNames: string array -> getFunctionValue: (Vector<float> -> float -> float) -> getGradientValue: (Vector<float> -> Vector<float> -> float -> Vector<float>) -> Model

val deltaX: float

val deltaP: float

val k: int

val initialParamGuess: xData: float array -> yData: float array -> float array

val xData: float array

val yData: float array

val yLn: Vector<float>

type Array = interface ICollection interface IEnumerable interface IList interface IStructuralComparable interface IStructuralEquatable interface ICloneable member Clone: unit -> obj member CopyTo: array: Array * index: int -> unit + 1 overload member GetEnumerator: unit -> IEnumerator member GetLength: dimension: int -> int ...
<summary>Provides methods for creating, manipulating, searching, and sorting arrays, thereby serving as the base class for all arrays in the common language runtime.</summary>

Math.Log(d: float) : float
Math.Log(a: float, newBase: float) : float

val vector: l: 'a seq -> Vector<'a> (requires 'a :> Numerics.INumber<'a>)

val linearReg: Coefficients

val a: float

val exp: value: 'T -> 'T (requires member Exp)

val b: float

val solverOptions: SolverOptions

val guess: float array

val createSolverOption: minimumDeltaValue: float -> minimumDeltaParameters: float -> maximumIterations: int -> initialParamGuess: float array -> SolverOptions

val coefficientsExp: Vector<float>

module GaussNewton from FSharp.Stats.Fitting.NonLinearRegression

val estimatedParams: model: Model -> solverOptions: SolverOptions -> xData: float array -> yData: float array -> Vector<float>
<summary>Returns a parameter vector as a possible solution for linear least square based nonlinear fitting of a given dataset (xData, yData) with a given model function. </summary>
<remarks></remarks>
<param name="model"></param>
<param name="solverOptions"></param>
<param name="xData"></param>
<param name="yData"></param>
<returns></returns>
<example><code></code></example>

val fittingFunction: x: float -> float

val rawChartNLR: GenericChart.GenericChart

static member Chart.Point: xy: (#IConvertible * #IConvertible) seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> IConvertible)
static member Chart.Point: x: #IConvertible seq * y: #IConvertible seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> IConvertible)

static member Chart.withTraceInfo: [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: StyleParam.Visible * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendRank: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroupTitle: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)

val fittingNLR: GenericChart.GenericChart

static member Chart.Line: xy: (#IConvertible * #IConvertible) seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> IConvertible)
static member Chart.Line: x: #IConvertible seq * y: #IConvertible seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> IConvertible)

val NLRChart: GenericChart.GenericChart

val xHours: float array

val yCount: float array

val model': Model

Multiple items
module Table from FSharp.Stats.Fitting.NonLinearRegression

--------------------
type Table<'R,'C,'T (requires comparison and comparison and 'T :> INumber<'T> and default constructor and value type and comparison and 'T :> ValueType)> = new: rowKeys: 'R array * colKeys: 'C array * dataMatrix: Matrix<'T> -> Table<'R,'C,'T> member GetColumn: c: 'C -> ('R * 'T) array member GetRow: r: 'R -> ('C * 'T) array override ToString: unit -> string member ColKeys: 'C array member Data: Vector<'T> member DataMatrix: Matrix<'T> member Item: r: 'R * c: 'C -> 'T with get member Item: r: 'R * c: 'C -> 'T with set member Item: i: int * j: int -> 'T with get ...
<summary> A 2D table with generic row‐labels and column‐labels, backed by a flattened Matrix<'T> </summary>

--------------------
new: rowKeys: 'R array * colKeys: 'C array * dataMatrix: Matrix<'T> -> Table<'R,'C,'T>

val LogisticFunctionAscending: Model
<summary> Logistic function of the form "y = L/(1+e^(-k(t-x)))" </summary>

val initialParamGuess': float array

module LevenbergMarquardtConstrained from FSharp.Stats.Fitting.NonLinearRegression
<summary> This LevenbergMarquardt implementation supports the usage of box constrains. </summary>

val initialParam: xData: float array -> yData: float array -> cutoffPercentage: float -> float array
<summary>Returns an estimate for an initial parameter for the linear least square estimator for a given dataset (xData, yData). The initial estimation is intended for a logistic function. The returned parameters are the max y value, the steepness of the curve and the x value in the middle of the slope.</summary>
<remarks></remarks>
<param name="xData"></param>
<param name="yData"></param>
<param name="cutoffPercentage"></param>
<returns></returns>
<example><code></code></example>

val solverOptions': SolverOptions

val lineSolverOptions: initialParamGuess: float array -> SolverOptions

val lowerBound: Vector<float>

val param: float

val abs: value: 'T -> 'T (requires member Abs)

val upperBound: Vector<float>

val estParams: Vector<float>

val estimatedParams: model: Model -> solverOptions: SolverOptions -> lambdaInitial: float -> lambdaFactor: float -> lowerBound: Vector<float> -> upperBound: Vector<float> -> xData: float array -> yData: float array -> Vector<float>
<summary>Returns a parameter vector as a possible solution for linear least square based nonlinear fitting of a given dataset (xData, yData) with a given model function. </summary>
<remarks></remarks>
<param name="model"></param>
<param name="solverOptions"></param>
<param name="lambdaInitial"></param>
<param name="lambdaFactor"></param>
<param name="lowerBound"></param>
<param name="upperBound"></param>
<param name="xData"></param>
<param name="yData"></param>
<returns></returns>
<example><code></code></example>

val multipleSolverOptions: SolverOptions array

val initialParamsOverRange: xData: float array -> yData: float array -> steepnessRange: float array -> float array array
<summary>Returns an estimate for an initial parameter for the linear least square estimator for a given dataset (xData, yData). The steepness is given as an array and not estimated. An initial estimate is returned for every given steepness. The initial estimation is intended for a logistic function.</summary>
<remarks></remarks>
<param name="xData"></param>
<param name="yData"></param>
<param name="steepnessRange"></param>
<returns></returns>
<example><code></code></example>

val estParamsRSS: Vector<float>

val solvO: SolverOptions

SolverOptions.InitialParamGuess: float array

val estimatedParamsWithRSS: model: Model -> solverOptions: SolverOptions -> lambdaInitial: float -> lambdaFactor: float -> lowerBound: Vector<float> -> upperBound: Vector<float> -> xData: float array -> yData: float array -> Vector<float> * float
<summary>Returns a parameter vector tupled with its residual sum of squares (RSS) as a possible solution for linear least square based nonlinear fitting of a given dataset (xData, yData) with a given model function.</summary>
<remarks></remarks>
<param name="model"></param>
<param name="solverOptions"></param>
<param name="lambdaInitial"></param>
<param name="lambdaFactor"></param>
<param name="lowerBound"></param>
<param name="upperBound"></param>
<param name="xData"></param>
<param name="yData"></param>
<returns></returns>
<example><code></code></example>

val minBy: projection: ('T -> 'U) -> array: 'T array -> 'T (requires comparison)

val snd: tuple: ('T1 * 'T2) -> 'T2

val fst: tuple: ('T1 * 'T2) -> 'T1

val fittingFunction': (float -> float)

val fittedY: (float * float) array

val zip: array1: 'T1 array -> array2: 'T2 array -> ('T1 * 'T2) array

val fittedLogisticFunc: GenericChart.GenericChart

static member Chart.withXAxisStyle: [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleText: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleStandoff: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: StyleParam.AxisType * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinMax: (#IConvertible * #IConvertible) * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: StyleParam.Mirror * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridDash: StyleParam.DrawingStyle * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: StyleParam.LinearAxisId * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.LinearAxisId * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: (float * float) * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: StyleParam.CategoryOrder * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryArray: #IConvertible seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: LayoutObjects.RangeSlider * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.RangeSelector * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.withYAxisStyle: [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleText: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleStandoff: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Title: Title * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Color: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AxisType: StyleParam.AxisType * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MinMax: (#IConvertible * #IConvertible) * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Mirror: StyleParam.Mirror * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowSpikes: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SpikeThickness: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLine: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowGrid: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GridDash: StyleParam.DrawingStyle * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLine: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ZeroLineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Anchor: StyleParam.LinearAxisId * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Side: StyleParam.Side * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Overlaying: StyleParam.LinearAxisId * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AutoShift: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Shift: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: (float * float) * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Position: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryOrder: StyleParam.CategoryOrder * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?CategoryArray: #IConvertible seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSlider: LayoutObjects.RangeSlider * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RangeSelector: LayoutObjects.RangeSelector * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?BackgroundColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowBackground: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

val xDataS: float array

val yDataS: float array

val data: (float * float) array

val knots: float array

val spline: lambda: float -> x: float -> float

val lambda: float

module Spline from FSharp.Stats.Fitting

val smoothingSpline: data: (float * float) array -> basispts: float array -> (float -> float -> float)
<summary>Creates a smoothing spline through some data. Takes as spline points the x-values given by basispts. The resulting function takes lambda (regularization parameter) and a x_Value as input. </summary>
<remarks></remarks>
<param name="data"></param>
<param name="basispts"></param>
<returns></returns>
<example><code></code></example>

val fit: lambda: float -> GenericChart.GenericChart

val sprintf: format: Printf.StringFormat<'T> -> 'T

val rawChartS: GenericChart.GenericChart

val smoothingSplines: GenericChart.GenericChart