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Statistics, Data Mining, and Machine Learning in AstronomyA Practical Python Guide for the Analysis of Survey Data$
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Željko Ivezic, Andrew J. Connolly, Jacob T VanderPlas, and Alexander Gray

Print publication date: 2014

Print ISBN-13: 9780691151687

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691151687.001.0001

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Regression and Model Fitting

Regression and Model Fitting

Chapter:
(p.321) 8 Regression and Model Fitting
Source:
Statistics, Data Mining, and Machine Learning in Astronomy
Author(s):

Andrew J. Connolly

Jacob T. VanderPlas

Alexander Gray

Andrew J. Connolly

Jacob T. VanderPlas

Alexander Gray

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691151687.003.0008

Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, y, and a set of independent variables, x, that describes the expectation value of y given x: E [y¦x]. The purpose of obtaining a “best-fit” model ranges from scientific interest in the values of model parameters (e.g., the properties of dark energy, or of a newly discovered planet) to the predictive power of the resulting model (e.g., predicting solar activity). This chapter starts with a general formulation for regression, list various simplified cases, and then discusses methods that can be used to address them, such as regression for linear models, kernel regression, robust regression and nonlinear regression.

Keywords:   regression methods, linear models, principal component regression, kernel regression, linear regression, nonlinear regression, model fitting

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