Packages

c

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 = 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

Linear Supertypes
Error, Predictor, AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. PolyRegression
  2. Error
  3. Predictor
  4. AnyRef
  5. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

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

    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, 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.

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

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    PolyRegression → Predictor
  9. 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

  10. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  11. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. 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

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

    Return the quality of fit including 'rSquared'.

    Return the quality of fit including 'rSquared'.

    Definition Classes
    PolyRegression → Predictor
  16. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    PolyRegression → Predictor
  17. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  18. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  19. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. val mae: Double
    Attributes
    protected
    Definition Classes
    Predictor
  22. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. final def notify(): Unit
    Definition Classes
    AnyRef
  24. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  25. 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
  26. 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

  27. 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
  28. val rSq: Double
    Attributes
    protected
    Definition Classes
    Predictor
  29. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    PolyRegression → Predictor
  30. val rg: Regression[MatrixD, VectorD]
  31. val rmse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  32. val sse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  33. val ssr: Double
    Attributes
    protected
    Definition Classes
    Predictor
  34. val sst: Double
    Attributes
    protected
    Definition Classes
    Predictor
  35. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  36. def toString(): String
    Definition Classes
    AnyRef → Any
  37. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation using the least squares method on 'y'

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation using the least squares method on 'y'

    Definition Classes
    PolyRegression → Predictor
  38. def train(yy: VectoD): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation

    Train 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 response vector

    Definition Classes
    PolyRegression → Predictor
  39. 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.

  40. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  41. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  42. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  43. val x: MatrixD

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

Ungrouped