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What is Non-Linear Regression?

Module by: Lekulana Kolobe

Summary: This module introduces non-linear regression, gives an example and an exercise in order to engage the reader.

In statistics, Nonlinear regression, is the problem of fitting a model y = f (x, t) + c to measured x, y data, where f is a nonlinear function of x with parameter t (often t = time).

Example 1

[Taken from Wikipedia2006NL] If we take a logarithm of y = Ae^Bx regression, it will be transformed to be log(y) = log(A) + Bx. Through the usual linear regression problem of optimizing the parameters —here logA and B— the exact solution can easily be found. However, the performing of such a linearization may bias some data towards being more "relevant" than others, which may not be a desirable effect.

Exercise 1

Give an example of a problem that can be modelled by non linear regression.

Solution

Consider a depreciation problem where the value of a used cellphone depreciates more over the first year than the second, and more over the second year than the third, etc. The non-linear function to accurately model this situation is:

Value = p0 + p1*exp(-p2*Age)

Here the ''exp'' function is the value of e (2.7182818...) raised to the power in brackets. This type of function is called a "negative exponential" and is appropriate for modelling a value whose rate of decrease is proportional to the difference between the value and some base value.

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