Linear Regression With Matlab
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Linear Regression With Matlab
Linear regression is the first step, and often the only step, required to fit a simple model to data. Supported by a Glossary and tutorial appendices, this is an ideal introduction to regression analysis. Includes Matlab code.
Statistics With Matlab
Author: L. Marvin
language: en
Publisher: Createspace Independent Publishing Platform
Release Date: 2017-11-02
Regression models describe the relationship between a response (output) variable, and one or more predictor (input) variables. Statistics and Machine Learning Toolbox allows you to fit linear, generalized linear, and nonlinear regression models, including stepwise models and mixed-effects models. Once you fit a model, you can use it to predict or simulate responses, assess the model fit using hypothesis tests, or use plots to visualize diagnostics, residuals, and interaction effects. Statistics and Machine Learning Toolbox also provides nonparametric regression methods to accommodate more complex regression curves without specifying the relationship between the response and the predictors with a predetermined regression function. You can predict responses for new data using the trained model. Gaussian process regression models also enable you to compute prediction intervals This book develops the linear model of regression taking into account the stages of identification, estimation, diagnosis and prediction. The most important content is the following: - Parametric Regression Analysis - Choose a Regression Function - Linear Regression - Prepare Data - Choose a Fitting Method - Choose a Model or Range of Models - Fit Model to Data - Examine Quality and Adjust the Fitted Model - Predict or Simulate Responses to New Data - Share Fitted Models - Linear Regression Workflow - Linear Regression with Interaction Effects - Interpret Linear Regression Results - Cook's Distance - Coefficient Standard Errors and Confidence Intervals - Coefficient Covariance and Standard Errors - Coefficient Confidence Intervals - Coefficient of Determination (R-Squared) - Durbin-Watson Test - F-statistic - Assess Fit of Model Using F-statistic - t-statistic - Assess Significance of Regression Coefficients Using t-statistic - Hat Matrix and Leverage - Residuals - Assess Model Assumptions Using Residuals - Summary of Output and Diagnostic Statistics - Wilkinson Notation - Linear Mixed-Effects Model Examples - Generalized Linear Model Examples - Generalized Linear Mixed-Effects Model Examples - Repeated Measures Model Examples - Stepwise Regression - Stepwise Regression to Select Appropriate Models - Compare large and small stepwise models - Robust Regression - Reduce Outlier Effects - Robust Regression versus Standard Least-Squares Fit - Ridge Regression - Lasso and Elastic Net - Wide Data via Lasso and Parallel Computing - Partial Least Squares - Linear Mixed-Effects Models - Estimating Parameters in Linear Mixed-Effects Models - Fit Mixed-Effects Spline Regression
Linear Time Series with MATLAB and OCTAVE
This book presents an introduction to linear univariate and multivariate time series analysis, providing brief theoretical insights into each topic, and from the beginning illustrating the theory with software examples. As such, it quickly introduces readers to the peculiarities of each subject from both theoretical and the practical points of view. It also includes numerous examples and real-world applications that demonstrate how to handle different types of time series data. The associated software package, SSMMATLAB, is written in MATLAB and also runs on the free OCTAVE platform. The book focuses on linear time series models using a state space approach, with the Kalman filter and smoother as the main tools for model estimation, prediction and signal extraction. A chapter on state space models describes these tools and provides examples of their use with general state space models. Other topics discussed in the book include ARIMA; and transfer function and structural models; as well as signal extraction using the canonical decomposition in the univariate case, and VAR, VARMA, cointegrated VARMA, VARX, VARMAX, and multivariate structural models in the multivariate case. It also addresses spectral analysis, the use of fixed filters in a model-based approach, and automatic model identification procedures for ARIMA and transfer function models in the presence of outliers, interventions, complex seasonal patterns and other effects like Easter, trading day, etc. This book is intended for both students and researchers in various fields dealing with time series. The software provides numerous automatic procedures to handle common practical situations, but at the same time, readers with programming skills can write their own programs to deal with specific problems. Although the theoretical introduction to each topic is kept to a minimum, readers can consult the companion book ‘Multivariate Time Series With Linear State Space Structure’, by the same author, if they require more details.