Packages

class Regression extends Predictor with Error

The Regression class supports multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equation

y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + 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 [ alternative: b = solve (y) ]

where 'x_pinv' is the pseudo-inverse. Three techniques are provided:

'Fac_QR' // QR Factorization: slower, more stable (default) 'Fac_Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

This version uses parallel processing to speed up execution.

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 Regression(x: MatrixD, y: VectorD, technique: RegTechnique = QR)

    x

    the input/design m-by-n matrix augmented with a first column of ones

    y

    the response vector

    technique

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

Type Members

  1. type Fac_QR = Fac_QR_H[MatrixD]

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 build(x: MatriD, y: VectoD): Predictor
    Definition Classes
    Predictor
  8. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  9. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  10. def diagnose(yy: VectoD): Unit

    Compute diagostics for the predictor.

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

    yy

    the response vector

    Attributes
    protected
    Definition Classes
    Predictor
    See also

    en.wikipedia.org/wiki/Mean_squared_error

  11. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  12. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  13. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  14. def eval(yy: VectoD = y): Unit

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    yy

    the response vector

    Definition Classes
    RegressionPredictor
  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 the fit, including 'rSquared'.

    Return the quality of the fit, including 'rSquared'.

    Definition Classes
    RegressionPredictor
  17. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit. Override when necessary.

    Definition Classes
    Predictor
  18. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  19. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  20. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  21. val index_rSq: Int
    Definition Classes
    Predictor
  22. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  23. val mae: Double
    Attributes
    protected
    Definition Classes
    Predictor
  24. def metrics: Map[String, Any]

    Build a map of selected quality of fit measures/metrics.

    Build a map of selected quality of fit measures/metrics.

    Definition Classes
    Predictor
  25. val mse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  26. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  27. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  28. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  29. 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
    RegressionPredictor
  30. 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
  31. val rSq: Double
    Attributes
    protected
    Definition Classes
    Predictor
  32. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  33. val rmse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  34. val sse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  35. val ssr: Double
    Attributes
    protected
    Definition Classes
    Predictor
  36. val sst: Double
    Attributes
    protected
    Definition Classes
    Predictor
  37. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  38. def toString(): String
    Definition Classes
    AnyRef → Any
  39. 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, x_1 , ... x_k] + e using the least squares method.

    yy

    the new response vector

    Definition Classes
    RegressionPredictor
  40. def train(): Regression

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

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation y = b dot x + e = [b_0, ... b_k] dot [1, x_1 , ... x_k] + e using the least squares method. FIX - needs to be updated

  41. 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.

  42. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  43. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  44. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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