多重线性回归
具有多个预测变量的线性回归
在一个多重线性回归模型中,响应变量取决于多个预测变量。您可以使用或不使用 LinearModel
对象来执行多重线性回归,也可以使用回归学习器来执行多重线性回归。
为了提高在中低维数据集上的准确度,可以使用 fitlm
拟合线性回归模型。
为了减少在高维数据集上的计算时间,可以使用 fitrlinear
拟合线性回归模型。
App
回归学习器 | 使用有监督机器学习训练回归模型来预测数据 |
模块
RegressionLinear Predict | 使用线性回归模型预测响应 (自 R2023a 起) |
函数
对象
LinearModel | Linear regression model |
CompactLinearModel | Compact linear regression model |
RegressionLinear | Linear regression model for high-dimensional data |
RegressionPartitionedLinear | Cross-validated linear regression model for high-dimensional data |
主题
线性回归简介
- What Is a Linear Regression Model?
Regression models describe the relationship between a dependent variable and one or more independent variables. - Linear Regression
Fit a linear regression model and examine the result. - Stepwise Regression
In stepwise regression, predictors are automatically added to or trimmed from a model. - Reduce Outlier Effects Using Robust Regression
Fit a robust model that is less sensitive than ordinary least squares to large changes in small parts of the data. - Choose a Regression Function
Choose a regression function depending on the type of regression problem, and update legacy code using new fitting functions. - Summary of Output and Diagnostic Statistics
Evaluate a fitted model by using model properties and object functions. - Wilkinson Notation
Wilkinson notation provides a way to describe regression and repeated measures models without specifying coefficient values.
线性回归工作流
- Linear Regression Workflow
Import and prepare data, fit a linear regression model, test and improve its quality, and share the model. - Interpret Linear Regression Results
Display and interpret linear regression output statistics. - Linear Regression with Interaction Effects
Construct and analyze a linear regression model with interaction effects and interpret the results. - Linear Regression Using Tables
This example shows how to perform linear and stepwise regression analyses using tables. - Linear Regression with Categorical Covariates
Perform a regression with categorical covariates using categorical arrays andfitlm
. - Analyze Time Series Data
This example shows how to visualize and analyze time series data using atimeseries
object and theregress
function. - Train Linear Regression Model
Train a linear regression model usingfitlm
to analyze in-memory data and out-of-memory data. - Predict Responses Using RegressionLinear Predict Block
This example shows how to use the RegressionLinear Predict block for response prediction in Simulink®. (自 R2023a 起) - Accelerate Linear Model Fitting on GPU
This example shows how you can accelerate regression model fitting by running functions on a graphical processing unit (GPU).
偏最小二乘回归
- Partial Least Squares
Partial least squares (PLS) constructs new predictor variables as linear combinations of the original predictor variables, while considering the observed response values, leading to a parsimonious model with reliable predictive power. - 偏最小二乘回归和主成分回归
应用偏最小二乘回归 (PLSR) 和主成分回归 (PCR),并研究这两种方法的有效性。