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.