Packages

c

scalation.analytics

TrigRegression

class TrigRegression extends Predictor with Error

The TrigRegression class supports trigonometric regression. In this case, 't' is expanded to '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'. Fit the parameter vector 'b' in the regression equation

y = b dot x + e = b_0 + b_1 sin (wt) + b_2 cos (wt) + b_3 sin (2wt) + b_4 cos (2wt) + ... + 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

link.springer.com/article/10.1023%2FA%3A1022436007242#page-1

Linear Supertypes
Error, Predictor, AnyRef, Any
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  1. TrigRegression
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Instance Constructors

  1. new TrigRegression(t: VectorD, y: VectorD, k: Int, technique: RegTechnique = QR)

    t

    the input vector: t_i expands to x_i

    y

    the response vector

    k

    the maximum multiplier in the trig function (kwt)

    technique

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

Value Members

  1. 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.

  2. def coefficient: VectoD

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    TrigRegression → Predictor
  3. 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

  4. def expand(t: Double): VectorD

    Expand the scalar 't' into a vector of powers of 't': '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'.

    Expand the scalar 't' into a vector of powers of 't': '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'.

    t

    the scalar to expand into the vector

  5. def fit: VectorD

    Return the quality of fit.

    Return the quality of fit.

    Definition Classes
    TrigRegression → Predictor
  6. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    TrigRegression → Predictor
  7. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  8. 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
    TrigRegression → Predictor
  9. 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

  10. 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
  11. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    TrigRegression → Predictor
  12. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation using 'y'.

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation using 'y'.

    Definition Classes
    TrigRegression → Predictor
  13. 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 [expanded t] + e

    using the least squares method.

    yy

    the response vector

    Definition Classes
    TrigRegression → Predictor
  14. 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.