Generates summary statistics using user-supplied functions in a nonlinear regression model.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
[SerializableAttribute] public class UserBasisRegression

Visual Basic (Declaration)
<SerializableAttribute> _ Public Class UserBasisRegression

Visual C++
[SerializableAttribute] public ref class UserBasisRegression

Remarks

Fits a linear function of the form

$y = c_0 + c_1 f_1 (x) + c_2 f_2 (x) + \cdots + c_k f_k (x) + \varepsilon$

, where $f_1 (x),f_2 (x), \cdots ,f_k (x)$ are the user basis functions

evaluated at index values $i = 1,2, \ldots ,k,c_0$ is the intercept, $c_1 ,c_2 , \cdots ,c_k$ are the coefficients associated with the basis functions, and is the random error associated with y. The coefficients $c_0 ,c_1 , \cdots ,c_k$ are determined by least squares.

Description

UserBasisRegression generalizes the concept of linear regression to user defined basis functions. The linear regression model is

$y = c_0 + c_1 x_1 + \cdots + c_k x_k + \varepsilon$

, where are the k independent variables. UserBasisRegression generalizes this concept by setting

, where

is any user defined function of

This makes it easier for users to fit complex univariate models. For example, the LinearRegression class can be used to fit polynomials such as

$y = c_0 + c_1 x + c_2 x^2 \cdots + c_k x^k + \varepsilon$

, but this requires an input matrix where the ith column of that array contains the values of

With UserBasisRegression, these columns can be automatically generated. For this polynomial model, the user would define a user basis function $f_i (x) = x^{i + 1}$ . The UserBasisRegression class automatically inserts the necessary values into the regression equation and then calculates the coefficients and analysis of variance statistics.

Since the user provides a method for calculating the basis function, other more complex user basis functions are possible such as

$y = c_1 Sin(x) + c_2 Cos(x) + \varepsilon$

. In this case, nBasis=2,

, and

Inheritance Hierarchy

System..::.Object
Imsl.Stat..::.UserBasisRegression

Syntax

Remarks

Inheritance Hierarchy

See Also