Packages

class Regression_WLS[MatT <: MatriD, VecT <: VectoD] extends Regression[MatriD, VectoD]

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

yy = b dot xx + e = b_0 + b_1 * xx_1 + ... b_k * xx_k + e

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

b = fac.solve (.)

The data matrix 'xx' is reweighted 'x = rootW * xx' and the response vector 'yy' is reweighted 'y = rootW * yy' where 'rootW' is the square root of the weights.

See also

www.markirwin.net/stat149/Lecture/Lecture3.pdf

en.wikipedia.org/wiki/Least_squares#Weighted_least_squares These are then pass to OLS Regression. Four factorization techniques are provided: 'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'SVD' // Singular Value Decomposition: slowest, most robust 'LU' // LU Factorization: better than Inverse 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique

Linear Supertypes
Regression[MatriD, VectoD], Error, Predictor, AnyRef, Any
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  1. Regression_WLS
  2. Regression
  3. Error
  4. Predictor
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Instance Constructors

  1. new Regression_WLS(xx: MatT, yy: VecT, technique: RegTechnique = QR, w: VectoD = null)

    xx

    the input/data m-by-n matrix (augment with a first column of ones to include intercept in model)

    yy

    the response vector

    technique

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

    w

    the weight vector (if null, computed in companion object)

Type Members

  1. type Fac_QR = Fac_QR_H[MatriD]
    Definition Classes
    Regression

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. var aic: Double
    Attributes
    protected
    Definition Classes
    Regression
  5. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  6. val b: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  7. 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 and the new quality of fit.

    Perform backward elimination to remove the least predictive variable from the model, returning the variable to eliminate, the new parameter vector and the new quality of fit.

    Definition Classes
    Regression
  8. var bic: Double
    Attributes
    protected
    Definition Classes
    Regression
  9. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  11. val df: Int
    Attributes
    protected
    Definition Classes
    Regression
  12. def diagnose(yy: VectoD): Unit

    Compute diagostics for the regression model.

    Compute diagostics for the regression model.

    yy

    the response vector

    Definition Classes
    Regression_WLS → Regression → Predictor
  13. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  16. var fStat: Double
    Attributes
    protected
    Definition Classes
    Regression
  17. val fac: Factorization
    Attributes
    protected
    Definition Classes
    Regression
  18. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  19. def fit: VectorD

    Return the quality of fit.

    Return the quality of fit.

    Definition Classes
    Regression → Predictor
  20. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    Regression → Predictor
  21. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  22. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  23. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  24. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  25. val k: Int
    Attributes
    protected
    Definition Classes
    Regression
  26. val m: Double
    Attributes
    protected
    Definition Classes
    Regression
  27. val mae: Double
    Attributes
    protected
    Definition Classes
    Predictor
  28. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  29. final def notify(): Unit
    Definition Classes
    AnyRef
  30. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  31. var p: VectoD
    Attributes
    protected
    Definition Classes
    Regression
  32. def predict(z: MatriD): VectoD

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

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

    z

    the new matrix to predict

    Definition Classes
    Regression
  33. 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
    Regression → Predictor
  34. 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
  35. var rBarSq: Double
    Attributes
    protected
    Definition Classes
    Regression
  36. val rSq: Double
    Attributes
    protected
    Definition Classes
    Predictor
  37. val r_df: Double
    Attributes
    protected
    Definition Classes
    Regression
  38. def report(): Unit

    Print results and diagnostics for each predictor 'x_j' and the overall quality of fit.

    Print results and diagnostics for each predictor 'x_j' and the overall quality of fit.

    Definition Classes
    Regression
  39. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  40. val rmse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  41. val sse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  42. val ssr: Double
    Attributes
    protected
    Definition Classes
    Predictor
  43. val sst: Double
    Attributes
    protected
    Definition Classes
    Predictor
  44. var stdErr: VectoD
    Attributes
    protected
    Definition Classes
    Regression
  45. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  46. var t: VectoD
    Attributes
    protected
    Definition Classes
    Regression
  47. def toString(): String
    Definition Classes
    AnyRef → Any
  48. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation for the response passed into the class 'y'.

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation for the response passed into the class 'y'.

    Definition Classes
    Regression → Predictor
  49. 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, x_1 , ... x_k] + e

    using the ordinary least squares 'OLS' method.

    yy

    the response vector

    Definition Classes
    Regression → Predictor
  50. 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.

    Definition Classes
    Regression
  51. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  52. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  53. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  54. def weights: VectoD

    Return the weight vector

  55. val x: MatriD
    Attributes
    protected
    Definition Classes
    Regression
  56. val y: VectoD
    Attributes
    protected
    Definition Classes
    Regression

Inherited from Regression[MatriD, VectoD]

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

Ungrouped