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Bayesian Analysis with Python

You're reading from   Bayesian Analysis with Python A practical guide to probabilistic modeling

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Product type Paperback
Published in Jan 2024
Publisher Packt
ISBN-13 9781805127161
Length 394 pages
Edition 3rd Edition
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Author (1):
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Osvaldo Martin Osvaldo Martin
Author Profile Icon Osvaldo Martin
Osvaldo Martin
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Table of Contents (15) Chapters Close

Preface
1. Chapter 1 Thinking Probabilistically FREE CHAPTER 2. Chapter 2 Programming Probabilistically 3. Chapter 3 Hierarchical Models 4. Chapter 4 Modeling with Lines 5. Chapter 5 Comparing Models 6. Chapter 6 Modeling with Bambi 7. Chapter 7 Mixture Models 8. Chapter 8 Gaussian Processes 9. Chapter 9 Bayesian Additive Regression Trees 10. Chapter 10 Inference Engines 11. Chapter 11 Where to Go Next 12. Bibliography
13. Other Books You May Enjoy
14. Index

6.3 Polynomial regression

One way to fit curves using a linear regression model is by building a polynomial, like this:

μ = 𝛽0 + 𝛽1x + 𝛽2x2 + 𝛽3x3 + 𝛽4x4...𝛽mxm

We call m the degree of the polynomial.

There are two important things to notice. First, polynomial regression is still linear regression; the linearity refers to the coefficients (the βs), not the variables (the xs). The second thing to note is that we are creating new variables out of thin air. The only observed variable is x, the rest are just powers of x. Creating new variables from observed ones is a perfectly valid ”trick” when doing regression; sometimes the transformation can be motivated or justified by theory (like taking the square root of the length of babies), but sometimes it is just a way to fit a curve. The intuition with polynomials is that for a given value of x, the higher the degree of the polynomial, the more flexible the curve can be. A polynomial of degree 1 is a line, a polynomial of degree 2 is a curve that can go up or...

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