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: Vector<float>

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.OrdinaryLeastSquares.Polynomial.coefficients 2 xData yData

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: Vector<float>

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.OrdinaryLeastSquares.Polynomial.coefficients 2 xData yData

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

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.OrdinaryLeastSquares.Polynomial.cooksDistance 2 xData yData

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!

order : int

order of the polynomial (1 = linear, 2 = quadratic, ... )

coef : Vector<float>

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.OrdinaryLeastSquares.Polynomial.coefficients xData yData 
 
 // Predict the temperature value at midnight between day 1 and 2. 
 LinearRegression.OrdinaryLeastSquares.Polynomial.fit coefficients 1.5

calculates derivative values at X=x with given polynomial coefficients. Level 1 = fst derivative; Level2 = snd derivative ...

coef : Vector<float>

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.OrdinaryLeastSquares.Polynomial.coefficients xData yData 
 
 // Predict the curvature of the regression function at midnight between day 1 and 2. 
 LinearRegression.OrdinaryLeastSquares.Polynomial.getDerivative coefficients 2 1.5