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Home Bivariate Data Regression Regression after Linearisation
See also: regression, linear/nonlinear, derivation of regression formulas 

Regression after Linearisation


The first two approaches require the type of functional relationship to be known. In many standard cases, the second approach may be appropriate:
 
  • Transform the curvilinear model to a linear model, by applying a proper transformation to both the independent and the dependent variable. For the univariate case, you may visually check the linearity after the transformation, by plotting the transformed variables against each other.
  • Calculate the regression parameters for the linearized model.
  • Transform the regression parameters of the linearized model back to the original (curvilinear) case.


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 = abx lg y = a* + b*x a = 10a* b = 10b*
y = axb lg y = a* + b* lg x a = 10a* b = 10b*
y = aebx ln y = a* + b*x a = ea* b = b*
y = ae(b / x) ln y = a* + b* (1/x) a = ea* 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 + bxn y = a* + b*xn a = a* b = b*

Last Update: 2009-Mär-29