class ResponseSurface extends Predictor with Error
The ResponseSurface
class uses multiple regression to fit a quadratic/cubic
surface to the data. For example in 2D, the quadratic regression equation is
y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_0*x_1, x_12] + e
- See also
scalation.metamodel.QuadraticFit
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Instance Constructors
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new
ResponseSurface(x_: MatrixD, y: VectorD, cubic: Boolean = false, technique: RegTechnique = QR)
- x_
the input vectors/points
- y
the response vector
- cubic
the order of the surface (defaults to quadratic, else cubic)
- technique
the technique used to solve for b in x.t*x*b = x.t*y
Value Members
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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final
def
==(arg0: Any): Boolean
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def
allForms(): MatrixD
Create all forms/terms for each point placing them in a new matrix.
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final
def
asInstanceOf[T0]: T0
- Definition Classes
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val
b: VectoD
Coefficient/parameter vector [b_0, b_1, ...
Coefficient/parameter vector [b_0, b_1, ... b_k]
- Attributes
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- Definition Classes
- Predictor
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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 quality of fit.
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def
cForms(p: VectorD): VectorD
Given a vector/point 'p', compute the values for all of its cubic, quadratic, linear and constant forms/terms, returning them as a vector.
Given a vector/point 'p', compute the values for all of its cubic, quadratic, linear and constant forms/terms, returning them as a vector. for 1D: p = (x_0) => VectorD (1, x_0, x_02, x_03) for 2D: p = (x_0, x_1) => VectorD (1, x_0, x_02, x_03, x_0*x_1, x_02*x_1, x_0*x_12, x_1, x_12, x_13)
- p
the source vector/point for creating forms/terms
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def
clone(): AnyRef
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def
coefficient: VectoD
Return the vector of coefficient/parameter values.
Return the vector of coefficient/parameter values.
- Definition Classes
- Predictor
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val
e: VectoD
Residual/error vector [e_0, e_1, ...
Residual/error vector [e_0, e_1, ... e_m-1]
- Attributes
- protected
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- Predictor
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
finalize(): Unit
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def
fit: VectorD
Return the quality of fit including 'rSquared'.
Return the quality of fit including 'rSquared'.
- Definition Classes
- ResponseSurface → Predictor
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def
fitLabels: Array[String]
Return the labels for the fit.
Return the labels for the fit. Override when necessary.
- Definition Classes
- Predictor
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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
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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final
def
isInstanceOf[T0]: Boolean
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final
def
ne(arg0: AnyRef): Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
predict(z: VectoD): Double
Given a point z, use the quadratic 'rsm' regression equation to predict a value for the function at z.
Given a point z, use the quadratic 'rsm' regression equation to predict a value for the function at z. for 1D: b_0 + b_1*z_0 + b_2*z_02 for 2D: b_0 + b_1*z_0 + b_2*z_02 + b_3*z_1 + b_4*z_1*z_0 + b_5*z_1^2
- z
the point/vector whose functional value is to be predicted
- Definition Classes
- ResponseSurface → Predictor
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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
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def
qForms(p: VectorD): VectorD
Given a vector/point 'p', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector.
Given a vector/point 'p', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector. for 1D: p = (x_0) => VectorD (1, x_0, x_02) for 2D: p = (x_0, x_1) => VectorD (1, x_0, x_02, x_0*x_1, x_1, x_1^2)
- p
the source vector/point for creating forms/terms
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def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- Predictor
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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def
train(yy: VectorD): Unit
Retrain the predictor by fitting the parameter vector (b-vector) in the quadratic 'rsm' regression equation, e.g., for 2D yy = b dot x + e = [b_0, ...
Retrain the predictor by fitting the parameter vector (b-vector) in the quadratic 'rsm' regression equation, e.g., for 2D yy = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_1*x_0, x_12] + e using the least squares method.
- yy
the new response vector
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def
train(): Unit
Train the predictor by fitting the parameter vector (b-vector) in the quadratic 'rsm' regression equation, e.g., for 2D y = b dot x + e = [b_0, ...
Train the predictor by fitting the parameter vector (b-vector) in the quadratic 'rsm' regression equation, e.g., for 2D y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_1*x_0, x_12] + e using the least squares method.
- Definition Classes
- ResponseSurface → Predictor
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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.
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
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