By Kardi Teknomo, PhD .

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There are several non-linear curves that that can be transformed into linear curves. Remember that linear curve has straight line relationship. Using non-linear transformation, you can easily solve non-linear problem as a linear (straight-line) problem. In this section, you will learn most commonly used non-linear regression and how to transform them into linear regression.

The following charts show some of the ideas of non-linear transformation.

Non linear transformation

The following table summarizes the non-linear transformation. The transformation works mostly by taking logarithm. You may want to review power rules and logarithm rules here .

Model

Model Transformation

Parameters Transformation

Power

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Exponential-1

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Exponential-2

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Logarithmic

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Reciprocal-1

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Reciprocal-2

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Reciprocal-3

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Square Root

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation

Non Linear Transformation Non Linear Transformation

Example:

We have the following data

Non Linear Transformation

The scattered and trend curve of the data is shown below. It is clearly non-linear.

Non Linear Transformation

Although we can use MS Excel trend to find the curve directly, for demonstration purposes, we will compute it manually. We will try to compute manually the power curve, logarithmic curve and square root curve.

Click the following links to go directly to the detail and example of each non-linear model:

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See Also : Regression tutorial , Power Rules , Logarithm Rules , Kernel Regression

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