Basics Of Implementations

All the Least Squares methods support basic Methods and Properties to provide uniform way to access and interpret the results; these basics are declared in the AbstractLS class.

A particular class can override and extend the basic interface according to the specific algorithm.

Basic Properties

These properties reflect computation status and the resulting coefficients of LS-fitting:

Property	Description
Status	Computation status: the returned value MethodSucceeded indicates that model fitting was successful, model parameters are found and available via the Parameters property and class instance is ready to use for analysis and prognoses.
Parameters	Model parameters (regression coefficients). If the Status does not indicate successful fitting then an attempt to access this property causes an Exception.

Property

Description

Property Status

Computation status:

the returned value MethodSucceeded indicates that model fitting was successful, model parameters are found and available via the Parameters property and class instance is ready to use for analysis and prognoses.

Property Parameters

Model parameters (regression coefficients).

If the Status does not indicate successful fitting then an attempt to access this property causes an Exception.

Basic Operations

The basic operations are realized with the methods to evaluate regression quality and to make predictions for single and series observations:

Operations	Description	Performance
Estimate	Methods for predictions given observations of regressors. Instance methods use the current regression model presented by the Parameters property, but static versions take regression coefficients as input parameter.	Single estimation: Instance methods: Static methods: Multiple estimation: Instance methods: Static methods:
EstimateResidual and EstimateResiduals	Methods to calculate model residuals given observations of regressors and regressand. Instance methods use the current regression model presented by the Parameters property, but static versions take additional input parameters, regression coefficients and model estimations.	Single estimation: Instance methods: Static methods: Multiple estimation: Instance methods: Static methods:
CalculateR2	Methods to compute the measure of model fitness quality, the R-squared value in the range 0 .. 1 which is the rate of variation explained by regression model relatively to regressand's variance. The instance method use the current regression model presented by the Parameters property, the static version requires additionally regression coefficients and model estimations as input parameters.	Instance method: Static method:

Operations

Description

Performance

method Estimate

Methods for predictions given observations of regressors.

Instance methods use the current regression model presented by the Parameters property, but static versions take regression coefficients as input parameter.

Single estimation:

Instance methods:
Static methods:

Multiple estimation:

Instance methods:
Static methods:

method EstimateResidual

and

method EstimateResiduals

Methods to calculate model residuals given observations of regressors and regressand.

Instance methods use the current regression model presented by the Parameters property, but static versions take additional input parameters, regression coefficients and model estimations.

Single estimation:

Instance methods:
Static methods:

Multiple estimation:

Instance methods:
Static methods:

method CalculateR2

Methods to compute the measure of model fitness quality, the R-squared value in the range 0 .. 1 which is the rate of variation explained by regression model relatively to regressand's variance.

The instance method use the current regression model presented by the Parameters property, the static version requires additionally regression coefficients and model estimations as input parameters.

Instance method:

Static method:

Note
For performance reason, static methods are not recommended for large number of repeated calculations.

Reference

FinMath.LeastSquares

AbstractLS