Packages

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

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faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

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: MatT, y: VecT, 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[MatT]

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

    Coefficient/parameter vector [b_0, b_1, ...

    Coefficient/parameter vector [b_0, b_1, ... b_k]

    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 and the new quality of fit.

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

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  9. def diagnose(yy: VectoD, e: VectoD): Unit

    Compute diagostics for the regression model.

    Compute diagostics for the regression model.

    yy

    the response vector

    e

    the residual/error vector

  10. val e: VectoD

    Residual/error vector [e_0, e_1, ...

    Residual/error vector [e_0, e_1, ... e_m-1]

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

    Return the quality of fit including 'rSquared'.

    Return the quality of fit including 'rSquared'.

    Definition Classes
    RegressionPredictor
  15. def fitLabels: Array[String]

    Return the labels for the fit.

    Return the labels for the fit. Override when necessary.

    Definition Classes
    Predictor
  16. final 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
  17. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  19. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  20. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. final def notify(): Unit
    Definition Classes
    AnyRef
  22. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  23. def predict(z: MatT): 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

  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
    RegressionPredictor
  25. 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
  26. def report(): Unit

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

  27. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

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

    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 ordinary least squares 'OLS' method.

    yy

    the new response vector

  31. def train(): Unit

    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 ordinary least squares 'OLS' method.

    Definition Classes
    RegressionPredictor
  32. 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.

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

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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