class TrigRegression extends PredictorVec
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 solve for the parameter vector 'b' using the Normal Equations:
x.t * x * b = x.t * y b = fac.solve (.)
- See also
link.springer.com/article/10.1023%2FA%3A1022436007242#page-1
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new
TrigRegression(t: VectoD, y: VectoD, ord: Int, technique: RegTechnique = QR)
- t
the input vector: t_i expands to x_i
- y
the response vector
- ord
the order (k), 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
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val
b: VectoD
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def
backwardElim(cols: Set[Int]): (Int, VectoD, VectoD)
Perform backward elimination to remove the least predictive variable from the existing 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 existing model, returning the variable to eliminate, the new parameter vector and the new quality of fit. May be called repeatedly.
- cols
the columns of matrix x included in the existing model
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- PredictorVec
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def
clone(): AnyRef
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def
crossVal(ord: Int, k: Int = 10, rando: Boolean = true): Unit
Perform 'k'-fold cross-validation.
Perform 'k'-fold cross-validation.
- ord
the maximum multiplier in the trig function (kwt)
- k
the number of folds
- rando
whether to use randomized cross-validation
- Definition Classes
- TrigRegression → PredictorVec
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def
crossValidate(algor: (VectoD, VectoD, Int) ⇒ PredictorVec, k: Int = 10, rando: Boolean = true): Array[Statistic]
- Definition Classes
- PredictorVec
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val
e: VectoD
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def
eval(tt: VectoD, yy: VectoD): Unit
Compute the error and useful diagnostics for the test dataset.
Compute the error and useful diagnostics for the test dataset.
- yy
the test response vector
- Definition Classes
- PredictorVec
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def
eval(): Unit
Compute the error and useful diagnostics for the entire dataset.
Compute the error and useful diagnostics for the entire dataset.
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- PredictorVec → Predictor
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def
eval(xx: MatriD, yy: VectoD): Unit
Compute the error and useful diagnostics for the test dataset.
Compute the error and useful diagnostics for the test dataset.
- xx
the test data matrix
- yy
the test response vector FIX - implement in classes
- Definition Classes
- Predictor
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def
expand(t: Double): VectoD
Expand the scalar 't' into a vector of powers of trig terms/columns: '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'.
Expand the scalar 't' into a vector of powers of trig terms/columns: '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'.
- t
the scalar to expand into the vector
- Definition Classes
- TrigRegression → PredictorVec
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def
expand(t: VectoD): MatriD
Expand the vector 't' into a matrix.
Expand the vector 't' into a matrix.
- t
the vector to expand into the matrix
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- PredictorVec
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def
finalize(): Unit
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def
fit: VectoD
Return the quality of fit measures including 'rSq'.
Return the quality of fit measures including 'rSq'.
- Definition Classes
- PredictorVec
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def
fitLabel: Seq[String]
Return the labels for the fit.
Return the labels for the fit.
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- PredictorVec
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def
fitMap: Map[String, String]
Build a map of quality of fit measures.
Build a map of quality of fit measures.
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- PredictorVec
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final
def
flaw(method: String, message: String): Unit
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- Error
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def
forwardSel(cols: Set[Int]): (Int, VectoD, VectoD)
Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit.
Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit. May be called repeatedly.
- cols
the columns of matrix x included in the existing model
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- PredictorVec
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def
parameter: VectoD
Return the vector of parameters/coefficients.
Return the vector of parameters/coefficients.
- Definition Classes
- PredictorVec → Predictor
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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
- Definition Classes
- TrigRegression → PredictorVec
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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 expanded/orhogonalized vector to predict
- Definition Classes
- PredictorVec → Predictor
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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
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def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
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- PredictorVec → Predictor
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var
rg: Regression
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synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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def
train(yy: VectoD = y): Regression
Train the predictor by fitting the parameter vector 'b' in the multiple regression equation using the least squares method.
Train the predictor by fitting the parameter vector 'b' in the multiple regression equation using the least squares method.
- yy
the response vector
- Definition Classes
- PredictorVec → Predictor
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def
vif: VectoD
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.
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