Overview

Data science includes a set of statistical techniques that allow extracting the knowledge immersed in the data automatically. One of the fundamental techniques in data science is the treatment of regression models. Regression is the process of fitting models to data. The models must have numerical responses. The regression process depends on the model. If a model is parametric, regression estimates the parameters from the data. If a model is linear in the parameters, estimation is based on methods from linear algebra that minimize the norm of a residual vector. If a model is nonlinear in the parameters, estimation is based on search methods from optimization that minimize the norm of a residual vector.The most important topics to be discussed in this book are the following: - Parametric Regression Analysis - What Are Linear Regression Models? - Linear Regression - Linear Regression Workflow - Regression Using Dataset Arrays - Regression Using Tables - Linear Regression with Interaction Effects - Interpret Linear Regression Results - Cook's Distance - Coefficient Standard Errors and Confidence Intervals - Coefficient of Determination (R-Squared) - Delete-1 Statistics - Durbin-Watson Test - F-statistic and t-statistic - Hat Matrix and Leverage - Residuals - Summary of Output and Diagnostic Statistics - Wilkinson Notation - Stepwise Regression - Robust Regression - Reduce Outlier Effects - Ridge Regression - Lasso and Elastic Net - Wide Data via Lasso and Parallel Computing - Lasso Regularization - Lasso and Elastic Net with Cross Validation - Partial Least Squares - Linear Mixed-Effects Models - Prepare Data for Linear Mixed-Effects Models - Relationship Between Formula and Design Matrices - Estimating Parameters in Linear Mixed-Effects Models - Linear Mixed-Effects Model Workflow - Fit Mixed-Effects Spline Regression

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9781796508666

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