Polynomial (FSharp.Stats) | FSharp.Stats

FSharp.Stats

Polynomial Module

Namespace: FSharp.Stats.Fitting
Assembly: FSharp.Stats.dll
Parent Module: OLS

Linear regression using polynomials as regression function: f(x) = a + bx + cx^2 + ....

Functions and values

Function or value	Description
`cooksDistance order xData yData` Full Usage: `cooksDistance order xData yData` Parameters: order : `int` - order of the polynomial (1 = linear, 2 = quadratic, ... ) xData : `Vector<float>` - vector of x values yData : `Vector<float>` - vector of y values Returns: `Vector<float>` returns collection of cooks distances for each data point	Fits a polynomial model of user defined order to the data and returns the cooks distance for every data pair present in the input collections as an estimator for the influence of each data point in coefficient estimation. order : `int` order of the polynomial (1 = linear, 2 = quadratic, ... ) xData : `Vector<float>` vector of x values yData : `Vector<float>` vector of y values Returns: `Vector<float>` returns collection of cooks distances for each data point Example `// 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.;\|] // Returns distances for a quadratic polynomial let distances = LinearRegression.OLS.Polynomial.cooksDistance 2 xData yData` val xData: obj val yData: obj val distances: obj
`fit order xData yData` Full Usage: `fit order xData yData` Parameters: order : `int` - order of the polynomial (1 = linear, 2 = quadratic, ... ) xData : `Vector<float>` - vector of x values yData : `Vector<float>` - vector of y values Returns: `Coefficients` vector of polynomial coefficients sorted as [intercept;constant;quadratic;...]	Calculates the polynomial coefficients for polynomial regression. order : `int` order of the polynomial (1 = linear, 2 = quadratic, ... ) xData : `Vector<float>` vector of x values yData : `Vector<float>` vector of y values Returns: `Coefficients` vector of polynomial coefficients sorted as [intercept;constant;quadratic;...] Example `// 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` val xData: obj val yData: obj val coefficients: obj
`fitWithWeighting order weighting xData yData` Full Usage: `fitWithWeighting order weighting xData yData` Parameters: order : `int` - order of the polynomial (1 = linear, 2 = quadratic, ... ) weighting : `Vector<float>` - Vector of weightings that define the releveance of each point for fitting. xData : `Vector<float>` - vector of x values yData : `Vector<float>` - vector of y values Returns: `Coefficients` vector of polynomial coefficients sorted as [intercept;constant;quadratic;...]	Calculates the polynomial coefficients for polynomial regression with a given point weighting. order : `int` order of the polynomial (1 = linear, 2 = quadratic, ... ) weighting : `Vector<float>` Vector of weightings that define the releveance of each point for fitting. xData : `Vector<float>` vector of x values yData : `Vector<float>` vector of y values Returns: `Coefficients` vector of polynomial coefficients sorted as [intercept;constant;quadratic;...] Example `// 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` val xData: obj val yData: obj val coefficients: obj
`getDerivative coef level x` Full Usage: `getDerivative coef level x` Parameters: coef : `Coefficients` - vector of polynomial coefficients (e.g. determined by Polynomial.coefficients), sorted as [intercept;constant;quadratic;...] level : `int` - depth of derivative: 1 = slope, 2 = curvature, ... x : `float` - x value of which the corresponding y value should be predicted Returns: `float` predicted derivative with given polynomial coefficients at X=x	calculates derivative values at X=x with given polynomial coefficients. Level 1 = fst derivative; Level2 = snd derivative ... coef : `Coefficients` vector of polynomial coefficients (e.g. determined by Polynomial.coefficients), sorted as [intercept;constant;quadratic;...] level : `int` depth of derivative: 1 = slope, 2 = curvature, ... x : `float` x value of which the corresponding y value should be predicted Returns: `float` predicted derivative with given polynomial coefficients at X=x Example `// 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 polynomial coefficients let coefficients = LinearRegression.OLS.Polynomial.fit xData yData // Predict the curvature of the regression function at midnight between day 1 and 2. LinearRegression.OLS.Polynomial.getDerivative coefficients 2 1.5` val xData: obj val yData: obj val coefficients: obj
`predict coef x` Full Usage: `predict coef x` Parameters: coef : `Coefficients` - vector of polynomial coefficients (e.g. determined by Polynomial.coefficients), sorted as [intercept;constant;quadratic;...] x : `float` - x value of which the corresponding y value should be predicted Returns: `float` predicted y value with given polynomial coefficients at X=x	Takes polynomial coefficients and x value to predict the corresponding y value. If all coefficients are nonzero, the order is equal to the length of the coefficient vector! coef : `Coefficients` vector of polynomial coefficients (e.g. determined by Polynomial.coefficients), sorted as [intercept;constant;quadratic;...] x : `float` x value of which the corresponding y value should be predicted Returns: `float` predicted y value with given polynomial coefficients at X=x Example `// 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` val xData: obj val yData: obj val coefficients: obj