LinearFittingAlgorithm

Full name Microsoft.VisualBasic.Data.Bootstrapping.Multivariate.LinearFittingAlgorithm Assembly Microsoft.VisualBasic.Data.Bootstrapping.Fittings Members 6

多元线性回归拟合算法模块，提供拟合入口、特征曲线升维以及回归系数置信区间的计算。 (Multiple linear regression fitting algorithms: fit entry points, feature curve scaling, and confidence interval computation.)

01 Syntax

Microsoft.VisualBasic.Data.Bootstrapping.Multivariate.LinearFittingAlgorithm

02 Methods

Name	Overloads	Summary
LinearFitting	2	对给定的自变量矩阵与观测值向量执行多元线性回归(最小二乘)拟合，并返回拟合模型及其误差测试结果。 (Performs ordinary least squares multiple linear regression on the given feature matrix and observed values, returning the fitted…
CurveScale	1	将自变量序列升维为多项式特征向量，用于构造形如以下形式的非线性(多项式)拟合： (Scales the input sequence into a polynomial feature vector for building nonlinear/polynomial fits of the form:) h(X) = a + bx1 + cx2^2…
left	1	计算回归系数置信区间的左边界。(Computes the lower bound of the confidence interval for a regression coefficient.)
right	1	计算回归系数置信区间的右边界。(Computes the upper bound of the confidence interval for a regression coefficient.)
ConfidenceInterval	1	计算回归系数在给定置信水平下的置信区间 [beta - tS, beta + tS]。(Computes the confidence interval [beta - tS, beta + tS] for a regression coefficient at the given confidence level.)

03 Members

method LinearFitting overload 2 #

LinearFitting(Double[0:,0:], Double())

使用二维自变量数组 x 与观测值数组 y 执行多元线性回归拟合。(Performs multiple linear regression fitting using a 2D feature array and an observed value array.)

Parameters

Name	Type	Description
`x`	`Double[0:,0:]`	自变量二维数组，每一行代表一个样本点的特征向量。(The 2D feature array, each row is a sample's feature vector.)
`y`	`Double()`	与 x 各行对应的观测值数组。(The observed values corresponding to each row of x.)

Returns

拟合得到的 MLRFit 模型。(The fitted multiple linear regression model.)

method LinearFitting #

LinearFitting(NumericMatrix, Vector)

对给定的自变量矩阵与观测值向量执行多元线性回归(最小二乘)拟合，并返回拟合模型及其误差测试结果。 (Performs ordinary least squares multiple linear regression on the given feature matrix and observed values, returning the fitted model and its fit errors.)

Parameters

Name Type Description

Name	Type	Description
`x`	`NumericMatrix`	自变量矩阵，每一行是一个样本点，每一列是一个特征维度。例如： (The feature matrix, each row is a sample point and each column is a feature dimension. e.g.) `x1 x2 x3 x4 a b c d a b c d a b c d a b c d a b c d`
`f`	`Vector`	观测值向量，与矩阵 x 的每一行一一对应。例如： (The observed value vector, corresponding to each row of matrix x. e.g.) `y1 y2 y3 y4 y5`

x

NumericMatrix

自变量矩阵，每一行是一个样本点，每一列是一个特征维度。例如： (The feature matrix, each row is a sample point and each column is a feature dimension. e.g.)

 x1  x2  x3  x4
  a   b   c   d
  a   b   c   d
  a   b   c   d 
  a   b   c   d
  a   b   c   d

f

Vector

观测值向量，与矩阵 x 的每一行一一对应。例如： (The observed value vector, corresponding to each row of matrix x. e.g.)

 y1
 y2
 y3
 y4
 y5

Returns

包含回归系数、拟合优度及逐点误差的 MLRFit 实例。(An MLRFit instance with regression coefficients, goodness-of-fit and per-point errors.)

method CurveScale #

CurveScale(IEnumerable(Of Double))

将自变量序列升维为多项式特征向量，用于构造形如以下形式的非线性(多项式)拟合： (Scales the input sequence into a polynomial feature vector for building nonlinear/polynomial fits of the form:)

 h(X) = a + b*x1 + c*x2^2 + d*x3^3 + ...

Parameters

Name	Type	Description
`X`	`IEnumerable(Of Double)`	原始自变量序列。(The original independent variable sequence.)

Returns

升维后的特征向量，第 i 个元素为 x^(i+1)。(The scaled feature vector where the i-th element is x^(i+1).)

method left #

left(Double, Double, Double)

计算回归系数置信区间的左边界。(Computes the lower bound of the confidence interval for a regression coefficient.)

Parameters

Name	Type	Description
`beta`	`Double`	回归系数估计值。(The estimated regression coefficient.)
`t`	`Double`	t 分布临界值(对应给定置信水平与自由度)。(The t-distribution critical value for the given confidence level and degrees of freedom.)
`S`	`Double`	回归系数的标准误。(The standard error of the regression coefficient.)

Returns

置信区间下界 beta - tS。(The lower bound beta - tS.)

method right #

right(Double, Double, Double)

计算回归系数置信区间的右边界。(Computes the upper bound of the confidence interval for a regression coefficient.)

Parameters

Name	Type	Description
`beta`	`Double`	回归系数估计值。(The estimated regression coefficient.)
`t`	`Double`	t 分布临界值(对应给定置信水平与自由度)。(The t-distribution critical value for the given confidence level and degrees of freedom.)
`S`	`Double`	回归系数的标准误。(The standard error of the regression coefficient.)

Returns

置信区间上界 beta + tS。(The upper bound beta + tS.)

method ConfidenceInterval #

ConfidenceInterval(Double, Double, Double)

计算回归系数在给定置信水平下的置信区间 [beta - tS, beta + tS]。(Computes the confidence interval [beta - tS, beta + tS] for a regression coefficient at the given confidence level.)

Parameters

Name	Type	Description
`beta`	`Double`	回归系数估计值。(The estimated regression coefficient.)
`t`	`Double`	t 分布临界值(对应给定置信水平与自由度)。(The t-distribution critical value for the given confidence level and degrees of freedom.)
`S`	`Double`	回归系数的标准误。(The standard error of the regression coefficient.)

Returns

由下界与上界组成的 DoubleRange 置信区间。(A DoubleRange confidence interval consisting of the lower and upper bounds.)