Linear Regression Analysis

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.

Linear regression fits a linear relationship between dependent variable $y$ and one or more independent variable $X$.

\[y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 +... + \beta_m x_m +\epsilon\]

Compared to LinearRegression, we use ordinary least square method for model fitting instead of stochastic gradient descent. Thanks to the statistical explanatory property of OSL, we provide statistical inference and result for the linear model,like which in R.

Import

import * as Datacook from 'datacook';
const { LinearRegressionAnalysis } = DataCook.Model;

Constructor

lm = new LinearRegressionAnalysis();

Option Parameters

parameter	type	description
fitIntercept `optional`	boolean	Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations
normalize `optional`	boolean	This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm.

Methods

fit

Fit linear regression model according to X, y.

async fit(xData: Tensor | RecursiveArray<number>,
    yData: Tensor | RecursiveArray<number>,
    featureNames?: string[]): void

Parameters

Parameter	type	description
xData	Tensor \| RecursiveArray	input data of shape (nSamples,nFeatures) in type of array or tensor
yData	Tensor \| RecursiveArray	Tensor like of shape (n_sample, ), input target values
featureNames `optional`	string[]	features names of shape (nFeatures, )

printSummary

Print summary of model, the result will be output in console, like following.

Syntax

printSummary(): void 

Summary

Get summary of linear regression results.

Syntax

summary(): {
    coefficients: Array<CoefficientSummary>,
    rSquare: number,
    adjustedRSquare: number,
    residualStandardError: number,
    residualDegreeOfFreedom: number,
    aic: number,
}

Returns

{
    coefficients: Array<CoefficientSummary>,
    rSquare: number,
    adjustedRSquare: number,
    residualStandardError: number,
    residualDegreeOfFreedom: number,
    aic: number,
}

Examples

Bellow is an example of fitting trees grith data using height and volumn features.

import { Model } from '@pipcook/datacook'

const { LinearRegressionAnalysis } = Model;

const treesGrith = [ 8.3, 8.6, 8.8, 10.5, 10.7, 10.8, 11.0, 11.0, 11.1,
  11.2, 11.3, 11.4, 11.4, 11.7, 12.0, 12.9, 12.9, 13.3, 13.7, 13.8, 14.0, 14.2, 14.5,
  16.0, 16.3, 17.3, 17.5, 17.9, 18.0, 18.0, 20.6 ];
const treesHeight = [ 70, 65, 63, 72, 81, 83, 66, 75, 80, 75, 79, 76, 76,
  69, 75, 74, 85, 86, 71, 64, 78, 80, 74, 72, 77, 81, 82, 80, 80, 80, 87 ];
const treesVolumn = [ 10.3, 10.3, 10.2, 16.4, 18.8, 19.7, 15.6, 18.2, 22.6,
  19.9, 24.2, 21.0, 21.4, 21.3, 19.1, 22.2, 33.8, 27.4, 25.7, 24.9, 34.5, 31.7, 36.3,
  38.3, 42.6, 55.4, 55.7, 58.3, 51.5, 51.0, 77.0 ];

const lm = new LinearRegressionAnalysis({});
await lm.fit(cases, y);
lm.printSummary();