Packages

c

scalation.analytics

ResponseSurface

class ResponseSurface extends Predictor with Error

The ResponseSurface class uses multiple regression to fit a quadratic/cubic surface to the data. For example in 2D, the quadratic regression equation is

y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_0*x_1, x_12] + e

See also

scalation.metamodel.QuadraticFit

Linear Supertypes
Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new ResponseSurface(x_: MatrixD, y: VectorD, cubic: Boolean = false, technique: RegTechnique = QR)

    x_

    the input vectors/points

    y

    the response vector

    cubic

    the order of the surface (defaults to quadratic, else cubic)

    technique

    the technique used to solve for b in x.t*x*b = x.t*y

Value Members

  1. def allForms(): MatrixD

    Create all forms/terms for each point placing them in a new matrix.

  2. def backElim(): (Int, VectoD, VectorD)

    Perform backward elimination to remove the least predictive variable from the model, returning the variable to eliminate, the new parameter vector, the new R-squared value and the new F statistic.

  3. def cForms(p: VectorD): VectorD

    Given a vector/point 'p', compute the values for all of its cubic, quadratic, linear and constant forms/terms, returning them as a vector.

    Given a vector/point 'p', compute the values for all of its cubic, quadratic, linear and constant forms/terms, returning them as a vector. for 1D: p = (x_0) => 'VectorD (1, x_0, x_02, x_03)' for 2D: p = (x_0, x_1) => 'VectorD (1, x_0, x_02, x_03, x_0*x_1, x_02*x_1, x_0*x_12, x_1, x_12, x_13)'

    p

    the source vector/point for creating forms/terms

  4. def coefficient: VectoD

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    ResponseSurfacePredictor
  5. def diagnose(yy: VectoD): Unit

    Compute diagostics for the predictor.

    Compute diagostics for the predictor. Override to add more diagostics. Note, for 'rmse', 'sse' is divided by the number of instances 'm' rather than degrees of freedom.

    yy

    the response vector

    Definition Classes
    Predictor
    See also

    en.wikipedia.org/wiki/Mean_squared_error

  6. def fit: VectorD

    Return the quality of fit.

    Return the quality of fit.

    Definition Classes
    ResponseSurfacePredictor
  7. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    ResponseSurfacePredictor
  8. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  9. def predict(z: VectoD): Double

    Given a point 'z', use the quadratic 'rsm' regression equation to predict a value for the function at 'z'.

    Given a point 'z', use the quadratic 'rsm' regression equation to predict a value for the function at 'z'. for 1D: b_0 + b_1*z_0 + b_2*z_02 for 2D: b_0 + b_1*z_0 + b_2*z_02 + b_3*z_1 + b_4*z_1*z_0 + b_5*z_1^2

    z

    the point/vector whose functional value is to be predicted

    Definition Classes
    ResponseSurfacePredictor
  10. def predict(z: VectoI): Double

    Given a new discrete data vector z, predict the y-value of f(z).

    Given a new discrete data vector z, predict the y-value of f(z).

    z

    the vector to use for prediction

    Definition Classes
    Predictor
  11. def qForms(p: VectorD): VectorD

    Given a vector/point 'p', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector.

    Given a vector/point 'p', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector. for 1D: p = (x_0) => 'VectorD (1, x_0, x_02)' for 2D: p = (x_0, x_1) => 'VectorD (1, x_0, x_02, x_0*x_1, x_1, x_1^2)'

    p

    the source vector/point for creating forms/terms

  12. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    ResponseSurfacePredictor
  13. def train(): Unit

    Train the predictor by fitting the parameter vector ('b'-vector) in the quadratic 'rsm' regression equation, e.g., for 2D using the least squares method on 'y'.

    Train the predictor by fitting the parameter vector ('b'-vector) in the quadratic 'rsm' regression equation, e.g., for 2D using the least squares method on 'y'.

    Definition Classes
    ResponseSurfacePredictor
  14. def train(yy: VectoD): Unit

    Train the predictor by fitting the parameter vector ('b'-vector) in the quadratic 'rsm' regression equation, e.g., for 2D

    Train the predictor by fitting the parameter vector ('b'-vector) in the quadratic 'rsm' regression equation, e.g., for 2D

    yy = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_1*x_0, x_12] + e

    using the least squares method.

    yy

    the new response vector

    Definition Classes
    ResponseSurfacePredictor
  15. def vif: VectorD

    Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing 'xj' against the rest of the variables.

    Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing 'xj' against the rest of the variables. A VIF over 10 indicates that over 90% of the variance of 'xj' can be predicted from the other variables, so 'xj' is a candidate for removal from the model.