Packages

c

scalation.analytics.par

PolyRegression

class PolyRegression extends Predictor with Error

The PolyRegression class supports polynomial regression. In this case, 't' is expanded to [1, t, t2 ... tk]. Fit the parameter vector 'b' in the regression equation

y = b dot x + e = b_0 + b_1 * t + b_2 * t2 ... b_k * tk + e

where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

b = x_pinv * y

where 'x_pinv' is the pseudo-inverse.

See also

www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx

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Error, Predictor, AnyRef, Any
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  1. PolyRegression
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Instance Constructors

  1. new PolyRegression(t: VectorD, y: VectorD, k: Int, technique: RegTechnique = QR)

    t

    the input vector: t_i expands to x_i = [1, t_i, t_i2, ... t_ik]

    y

    the response vector

    k

    the order of the polynomial

    technique

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

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. val b: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  6. def backElim(): (Int, VectoD, VectoD)

    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.

  7. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  8. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  9. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  10. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  11. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  12. def eval(): Unit

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    Definition Classes
    PolyRegression → Predictor
  13. def eval(xx: MatriD, yy: VectoD): Unit

    Compute the error and useful diagnostics for the test dataset.

    Compute the error and useful diagnostics for the test dataset.

    xx

    the test data matrix

    yy

    the test response vector FIX - implement in classes

    Definition Classes
    Predictor
  14. def expand(t: Double): VectorD

    Expand the scalar 't' into a vector of powers of 't': [1, t, t2 ... tk].

    Expand the scalar 't' into a vector of powers of 't': [1, t, t2 ... tk].

    t

    the scalar to expand into the vector

  15. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  16. def fit: VectoD

    Return the quality of fit including 'rSquared'.

  17. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  18. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  19. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  24. def predict(z: VectoD): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).

    z

    the new vector to predict

    Definition Classes
    PolyRegression → Predictor
  25. def predict(z: Double): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot expand (z), e.g., (b_0, b_1, b_2) dot (1, z, z^2).

    Predict the value of y = f(z) by evaluating the formula y = b dot expand (z), e.g., (b_0, b_1, b_2) dot (1, z, z^2).

    z

    the new scalar to predict

  26. 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
  27. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  28. val rg: Regression
  29. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  30. def toString(): String
    Definition Classes
    AnyRef → Any
  31. def train(yy: VectoD): Regression

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_0, ...

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_0, ... b_k] dot [1, t, t2 ... tk] + e using the least squares method.

    yy

    the new response vector

    Definition Classes
    PolyRegression → Predictor
  32. def train(): Regression

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b_0, ...

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b_0, ... b_k] dot [1, t, t2 ... tk] + e using the least squares method.

  33. 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.

  34. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  35. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  36. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  37. val x: MatrixD

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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