regression

README

regression v2

Multiple linear regression analysis library written in Go

NOTE: This project is originally based on https://github.com/sajari/regression

installation

$ go get github.com/anyappinc/regression/v2

example usage

Import the package, create a regression and add data to it. You can use as many variables as you like, in the below example there are 3 variables for each observation.

package main

import (
	"fmt"

	"github.com/anyappinc/regression/v2"
)

func main() {
	r := regression.NewRegression()
	r.SetObjectiveVariableLabel("Murders per annum per 1,000,000 inhabitants")
	r.SetExplanatoryVariableLabel(0, "Inhabitants")
	r.SetExplanatoryVariableLabel(1, "Percent with incomes below $5000")
	r.SetExplanatoryVariableLabel(2, "Percent unemployed")
	r.AddObservations(
		regression.NewObservation(11.2, []float64{587000, 16.5, 6.2}),
		regression.NewObservation(13.4, []float64{643000, 20.5, 6.4}),
		regression.NewObservation(40.7, []float64{635000, 26.3, 9.3}),
		regression.NewObservation(5.3, []float64{692000, 16.5, 5.3}),
		regression.NewObservation(24.8, []float64{1248000, 19.2, 7.3}),
		regression.NewObservation(12.7, []float64{643000, 16.5, 5.9}),
		regression.NewObservation(20.9, []float64{1964000, 20.2, 6.4}),
		regression.NewObservation(35.7, []float64{1531000, 21.3, 7.6}),
		regression.NewObservation(8.7, []float64{713000, 17.2, 4.9}),
		regression.NewObservation(9.6, []float64{749000, 14.3, 6.4}),
		regression.NewObservation(14.5, []float64{7895000, 18.1, 6}),
		regression.NewObservation(26.9, []float64{762000, 23.1, 7.4}),
		regression.NewObservation(15.7, []float64{2793000, 19.1, 5.8}),
		regression.NewObservation(36.2, []float64{741000, 24.7, 8.6}),
		regression.NewObservation(18.1, []float64{625000, 18.6, 6.5}),
		regression.NewObservation(28.9, []float64{854000, 24.9, 8.3}),
		regression.NewObservation(14.9, []float64{716000, 17.9, 6.7}),
		regression.NewObservation(25.8, []float64{921000, 22.4, 8.6}),
		regression.NewObservation(21.7, []float64{595000, 20.2, 8.4}),
		regression.NewObservation(25.7, []float64{3353000, 16.9, 6.7}),
	)
	model, err := r.Run()
	if err != nil {
		log.Fatalln(err)
	}

	fmt.Printf("Regression formula:\n%v\n", model.FormulaString())
}

Note: You can also add observations one by one.

Once calculated, you can look at the R^2, Standard Error, ANOVA, Coefficients, etc. e.g.

// Get the coefficient for the "Inhabitants" variable 0:
c := model.ExplanatoryVars[0].Coeff

You can also use the model to predict new observation

prediction, err := model.Predict([]float64{587000, 16.5, 6.2})

Documentation

Index

• Variables
• func NewObservation(o float64, es []float64) *observation
• type ANOVA
• type ConditionError
  • func (e ConditionError) Error() string
  • func (e ConditionError) Is(err error) bool
  • func (e ConditionError) Unwrap() error
• type ConditionErrorHint
• type ExplanatoryVarHint
• type ExplanatoryVarResult
• type InterceptResult
• type Model
  • func (m *Model) FormulaString() string
  • func (m *Model) GetObservationsAnalysis() *ObservationsAnalysis
  • func (m *Model) Predict(vars []float64) (float64, error)
• type ObservationsAnalysis
• type Regression
  • func NewRegression() *Regression
  • func (r *Regression) AddObservations(observations ...*observation) error
  • func (r *Regression) BackwardElimination(p float64, forcedExpVarsIndexesSet map[int]struct{}) ([]Model, error)
  • func (r *Regression) DisregardIndex(idx int)
  • func (r *Regression) GetExplanatoryVariableLabel(i int) string
  • func (r *Regression) GetObjectiveVariableLabel() string
  • func (r *Regression) ResetDisregarding()
  • func (r *Regression) Run() (*Model, error)
  • func (r *Regression) SetExplanatoryVariableLabel(i int, label string)
  • func (r *Regression) SetObjectiveVariableLabel(label string)
  • func (r *Regression) ValidateExplanatoryVars() []int

Variables

var (
	ErrNearSingular    = &ConditionError{isExactlySingular: false}
	ErrExactlySingular = &ConditionError{isExactlySingular: true}
)

var (
	// ErrNotEnoughObservations signals that there weren't enough observations to train the model.
	ErrNotEnoughObservations = errors.New("not enough observations")
	// ErrTooManyExplanatoryVars signals that there are too many explanatory variables for the number of observations being made.
	ErrTooManyExplanatoryVars = errors.New("not enough observations to support this many explanatory variables")
	// ErrNoExplanatoryVars signals that there is no explanatory variables to train the model.
	ErrNoExplanatoryVars = errors.New("no explanatory variables to train the models")
	// ErrInvalidArgument signals that any of given arguments to call the function was invalid.
	ErrInvalidArgument = errors.New("invalid argument")
)

Functions

func NewObservation

func NewObservation(o float64, es []float64) *observation

NewObservation creates a well formed *observation used for training.

Types

type ANOVA

type ANOVA struct {
	RegressionSumOfSquares    float64 // 回帰の平方和
	RegressionDegreeOfFreedom int     // 回帰の自由度
	RegressionMeanOfSquares   float64 // 回帰の平均平方
	RegressionFstat           float64 // 回帰のF値
	RegressionProb            float64 // 回帰の有意確率
	ResidualSumOfSquares      float64 // 残差の平方和
	ResidualDegreeOfFreedom   int     // 残差の自由度
	ResidualMeanOfSquares     float64 // 残差の平均平方
	TotalSumOfSquares         float64 // 合計の平方和
	TotalDegreeOfFreedom      int     // 合計の自由度
}

ANOVA : 分散分析の結果

type ConditionError

type ConditionError struct {
	Hint *ConditionErrorHint
	// contains filtered or unexported fields
}

func (ConditionError) Error

func (e ConditionError) Error() string

func (ConditionError) Is

func (e ConditionError) Is(err error) bool

func (ConditionError) Unwrap

func (e ConditionError) Unwrap() error

type ConditionErrorHint

type ConditionErrorHint struct {
	ExplanatoryVars []ExplanatoryVarHint
}

type ExplanatoryVarHint

type ExplanatoryVarHint struct {
	OriginalIndex int     // 元々のインデックス
	Label         string  // 名称
	Coeff         float64 // 偏回帰係数 B
	VIF           float64 // 共線性の統計量 VIF
}

type ExplanatoryVarResult

type ExplanatoryVarResult struct {
	OriginalIndex      int     // 元々のインデックス
	Label              string  // 名称
	Coeff              float64 // 偏回帰係数 B
	StandardError      float64 // 偏回帰係数の標準誤差（非標準化係数 標準誤差）
	StandardizedCoeff  float64 // 標準化偏回帰係数 β
	TStat              float64 // t値
	Prob               float64 // 有意確率（p値）
	Correlation        float64 // ゼロ次相関（通常の相関係数）
	PartialCorrelation float64 // 偏相関
	PartCorrelation    float64 // 部分相関
	Tolerance          float64 // 共線性の統計量 許容度 TOL
	VIF                float64 // 共線性の統計量 VIF
}

ExplanatoryVarResult : 回帰分析により算出された説明変数の結果

type InterceptResult

type InterceptResult struct {
	Value         float64 // 定数（y切片）の値
	StandardError float64 // 標準誤差（非標準化係数 標準誤差）
	TStat         float64 // t値
}

InterceptResult : 回帰分析により算出された定数（y切片）の結果

type Model

type Model struct {
	NumOfObservations             int                    // 分析に用いた観測値の数
	NumOfExplanatoryVars          int                    // 分析に用いた説明変数の数
	DisregardedExplanatoryVarsSet map[int]struct{}       // 分析に使用されなかったインデックスのセット
	UnexplainedVariation          float64                // 残差変動
	ExplainedVariation            float64                // 回帰変動
	TotalVariation                float64                // 全変動
	R                             float64                // 重相関係数
	R2                            float64                // 決定係数
	AdjustedR2                    float64                // 自由度調整済み決定係数
	StandardError                 float64                // 回帰の標準誤差（推定値の標準偏差）
	ANOVA                         *ANOVA                 // 分散分析
	ObjectiveVarLabel             string                 // 目的変数の名称
	Intercept                     *InterceptResult       // 定数（y切片）の分析結果
	ExplanatoryVars               []ExplanatoryVarResult // 各説明変数の分析結果
	// contains filtered or unexported fields
}

Model : 回帰モデル

func (*Model) FormulaString

func (m *Model) FormulaString() string

FormulaString : 回帰モデル式を文字列で取得する

func (*Model) GetObservationsAnalysis

func (m *Model) GetObservationsAnalysis() *ObservationsAnalysis

GetObservationsAnalysis : 観測値に関する分析結果を取得する

func (*Model) Predict

func (m *Model) Predict(vars []float64) (float64, error)

Predict calculates the predicted value

type ObservationsAnalysis

type ObservationsAnalysis struct {
	ObjectiveVarsDense                 *mat.Dense // 目的変数の観測値の行列
	ExplanatoryVarsDense               *mat.Dense // 説明変数の観測値の行列
	MeanOfObjectiveVars                float64    // 目的変数の観測値の平均
	StandardDeviationOfObjectiveVars   float64    // 目的変数の観測値の標準偏差
	MeansOfExplanatoryVars             []float64  // 各説明変数の観測値の平均
	StandardDeviationOfExplanatoryVars []float64  // 各説明変数の観測値の標準偏差
	PredictedVals                      []float64  // 予測値
	Residuals                          []float64  // 残差
}

ObservationsAnalysis : 観測値に関する分析結果

type Regression

type Regression struct {
	// contains filtered or unexported fields
}

Regression is the exposed data structure for interacting with the API.

func NewRegression

func NewRegression() *Regression

NewRegression initializes the structure and returns it for interacting with regression APIs.

func (*Regression) AddObservations

func (r *Regression) AddObservations(observations ...*observation) error

AddObservations adds observations.

func (*Regression) BackwardElimination

func (r *Regression) BackwardElimination(p float64, forcedExpVarsIndexesSet map[int]struct{}) ([]Model, error)

BackwardElimination : 変数減少法で解析する

`forcedExpVarsIndexesSet`に指定したインデックスの説明変数は強制投入（必ず使用）される

func (*Regression) DisregardIndex

func (r *Regression) DisregardIndex(idx int)

DisregardIndex adds given index to the disregarding set

func (*Regression) GetExplanatoryVariableLabel

func (r *Regression) GetExplanatoryVariableLabel(i int) string

GetExplanatoryVariableLabel gets the label of i-th explanatory variable.

func (*Regression) GetObjectiveVariableLabel

func (r *Regression) GetObjectiveVariableLabel() string

GetObjectiveVariableLabel gets the label of the objective variable.

func (*Regression) ResetDisregarding

func (r *Regression) ResetDisregarding()

ResetDisregarding : 無視する説明変数の設定をリセットする

func (*Regression) Run

func (r *Regression) Run() (*Model, error)

Run calculates a model using QR decomposition.

func (*Regression) SetExplanatoryVariableLabel

func (r *Regression) SetExplanatoryVariableLabel(i int, label string)

SetExplanatoryVariableLabel sets the label of i-th explanatory variable.

func (*Regression) SetObjectiveVariableLabel

func (r *Regression) SetObjectiveVariableLabel(label string)

SetObjectiveVariableLabel sets the label of the objective variable.

func (*Regression) ValidateExplanatoryVars

func (r *Regression) ValidateExplanatoryVars() []int

ValidateExplanatoryVars returns indexes of invalid explanatory variables. It considers an explanatory variable is not valid if is has all same observed values.