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Polynomial_regression

# Polynomial_regression - Polynomial regression Daniel...

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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

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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 structure of the observed variable is a result of one or two
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Polynomial_regression - Polynomial regression Daniel...

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