scalation.analytics

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 = b0 + b1 * t + b1 * t2... bk * 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. By default QR Decomposition (more robust) is used to compute 'x_pinv', with Gaussian Elimination as an option (set useQR to false).

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

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Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new PolyRegression(t: VectorD, y: VectorD, order: Int, useQR: Boolean = true)

    t

    the input vector

    y

    the response vector

    order

    the order of the polynomial

    useQR

    use QR Decomposition for pseudo-inverse, else Gaussian Elimination

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. def backElim(): (Int, VectorD, Double, Double)

    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.

  6. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  7. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  8. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  9. def expand(x: Double): VectorD

    Expand the scalar 'x' into a vector of powers of 'x': [1, x, x2 ... xk].

    Expand the scalar 'x' into a vector of powers of 'x': [1, x, x2 ... xk].

    x

    the scalar to expand

  10. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  11. def fit: (VectorD, Double, Double, Double)

    Return the fit (parameter vector b, quality of fit rSquared).

  12. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  13. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  14. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  15. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  16. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  17. final def notify(): Unit

    Definition Classes
    AnyRef
  18. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  19. def predict(z: MatrixD): VectorD

    Predict the value of y = f(z) by evaluating the formula y = b dot zi for each row zi of matrix z.

    Predict the value of y = f(z) by evaluating the formula y = b dot zi for each row zi of matrix z.

    z

    the new matrix to predict

    Definition Classes
    PolyRegressionPredictor
  20. def predict(z: VectorD): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b0, b1, b2) dot (1, z1, z2).

    z

    the new vector to predict

    Definition Classes
    PolyRegressionPredictor
  21. def predict(z: Double): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot expand (z), e.

    Predict the value of y = f(z) by evaluating the formula y = b dot expand (z), e.g., (b0, b1, b2) dot (1, z, z^2).

    z

    the new scalar to predict

  22. def predict(z: VectorI): 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
  23. val rg: Regression

  24. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  25. def toString(): String

    Definition Classes
    AnyRef → Any
  26. def train(yy: VectorD): Unit

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b0, .

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b0, ... bk] dot [1, t, t2 ... tk] + e using the least squares method.

    yy

    the new response vector

  27. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b0, .

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b0, ... bk] dot [1, t, t2 ... tk] + e using the least squares method.

    Definition Classes
    PolyRegressionPredictor
  28. def vif: VectorD

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

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

  29. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  30. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. final def wait(arg0: Long): Unit

    Definition Classes
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    @throws( ... )
  32. val x: MatrixD

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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