Polynomial_regression

Polynomial_regression - Polynomial regression Daniel...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Polynomial regression Daniel Borcard, Département de sciences biologiques, Université de Montréal Reference: Legendre and Legendre (1998) p. 526 A variant form of multiple regression can be used to fit a nonlinear model of an explanatory variable x (or several explanatory variables x j ) to a response variable y . The method consists in using the explanatory variable x in different powers in the regression equation: power 1 (which is the original variable), power 2, power 3, etc. The equation becomes a polynomial function of order k of variable x : ˆ y = a 1 x + a 2 x 2 + a 3 x 3 + ... + a k x k + b Adding an order to the equation adds a segment with a different slope sign to the curve representing the fitted values. A first-order equation is a straight line; a second-order equation is a parabola; a third-order equation is represented by an S-shaped curve; and so on. R 2 = 0.0139 0 0.5 1 1.5 2 2.5 3 0 10 20 30 R 2 = 0.2566 0 0.5 1 1.5 2 2.5 3 0 10 20 30 R 2 = 0.0836 0 0.5 1 1.5 2 2.5 3 0 10 20 30 R 2 = 0.7519 0 0.5 1 1.5 2 2.5 3 0 10 20 30
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6.3.2 Trend surface analysis This technique is a particular case of multiple regression , where the explanatory variables are geographical (x-y) coordinates, sometimes completed by higher order polynomials. When applying this method, one generally supposes that the spatial
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/15/2012 for the course GEO 4167 taught by Professor Staff during the Spring '12 term at University of Florida.

Page1 / 5

Polynomial_regression - Polynomial regression Daniel...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online