# Statistics Dictionary

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### Nonlinear Transformation

Transforming a variable involves using a mathematical operation to change its measurement scale. Broadly speaking, there are two kinds of transformations.

• Linear transformation. A linear transformation preserves linear relationships between variables. Therefore, the correlation between x and y would be unchanged after a linear transformation. Examples of a linear transformation to variable x would be multiplying x by a constant, dividing x by a constant, or adding a constant to x.
• Nonlinear tranformation. A nonlinear transformation changes (increases or decreases) linear relationships between variables and, thus, changes the correlation between variables. Examples of nonlinear transformation of variable x would be taking the square root x or the reciprocal of x.

In regression analysis, when a residual plot reveals a data set to be nonlinear, analysts sometimes apply nonlinear transformations to the independent and/or dependent variables. If this transformation increases the linearity of the relationship between the variables, it allows the analyst to use linear regression techniques appropriately with nonlinear data.