Class PolynomialModel
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Model evaluator for best fit polynomial p(x) = y.
Stored properties:
DoF = len(y)-len(x) = degrees of freedom
rnorm = 2-norm of the residuals y-Ax
coeff = coefficients
degree = polynomial degree
Computed properties:
cov = covariance matrix [ inv(A'A); O(n^3) ]
var = coefficient variance [ diag(cov); O(n^2)]
std = standard deviation of coefficients [ sqrt(var); O(n^2) ]
p = test statistic for chisquare goodness of fit [ chi2.sf; O(1) ]
Methods:
__call__(x): return the polynomial evaluated at x
ci(x,sigma=1): return confidence interval evaluated at x
pi(x,alpha=0.05): return prediction interval evaluated at x
Note that the covariance matrix will not include the ones column if
the polynomial goes through the origin.
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__init__(self,
s,
origin=False)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature |
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__call__(self,
x)
Evaluate the polynomial at x. |
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ci(self,
x,
sigma=1)
Evaluate the polynomial and the confidence intervals at x. |
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pi(self,
x,
p=0.05)
Evaluate the polynomial and the prediction intervals at x. |
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Inherited from object:
__delattr__,
__getattribute__,
__hash__,
__new__,
__reduce__,
__reduce_ex__,
__repr__,
__setattr__
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cov
covariance matrix
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var
result variance
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std
result standard deviation
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p
probability of rejection
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Inherited from object:
__class__
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__init__(self,
s,
origin=False)
(Constructor)
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x.__init__(...) initializes x; see x.__class__.__doc__ for signature
- Overrides:
object.__init__
- (inherited documentation)
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Evaluate the polynomial and the confidence intervals at x.
sigma=1 corresponds to a 1-sigma confidence interval
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Evaluate the polynomial and the prediction intervals at x.
p = 1-alpha = 0.05 corresponds to 95% prediction interval
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__str__(self)
(Informal representation operator)
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str(x)
- Overrides:
object.__str__
- (inherited documentation)
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cov
covariance matrix
- Get Method:
- _cov(self)
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var
result variance
- Get Method:
- _var(self)
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std
result standard deviation
- Get Method:
- _std(self)
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p
probability of rejection
- Get Method:
- _p(self)
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