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Table of Contents Bivariate Data Regression Curvilinear Regression | |
See also: regression, linear/nonlinear, derivation of regression formulas |
There are several ways to fit a curve other than a line (or, generally
speaking, an n-dimensional hyperplane) to the data:
The first two approaches require the type of functional relationship
to be known. In many standard cases, the second approach may be appropriate:
Below is a table of the transformations for linearizing some common
relationships.
Non-Linear Model | Step 1: Linearized Model | Step 2: Calculate Linear Model | Step 3: Back Transformation | |
y = ab^{x} | lg y = a^{*} + b^{*}x | a = 10^{a*} | b = 10^{b*} | |
y = ax^{b} | lg y = a^{*} + b^{*} lg x | a = 10^{a*} | b = 10^{b*} | |
y = ae^{bx} | ln y = a^{*} + b^{*}x | a = e^{a*} | b = b^{*} | |
y = ae^{(b / x)} | ln y = a^{*} + b^{*} (1/x) | a = e^{a*} | b = b^{*} | |
y = a + b/x | y = a^{*} + b^{*} (1/x) -- y is plotted against (1/x) | a = a^{*} | b = b^{*} | |
y = a / (b + x) | (1/y) = a^{*} + b^{*}x | a = b/a^{*} | a = 1/b^{*} | |
y = a + bx^{n} | y = a^{*} + b^{*}x^{n} | a = a^{*} | b = b^{*} |
Last Update: 2006-Jän-17