# TIBCO Statistica® Fixed Nonlinear Regression

The benefit of Fixed Nonlinear Regression is to specify nonlinear transformations, and then use these transformed variables in your regression analysis to build the model. The available transformations and their valid ranges are listed below. More than one transformation can be selected.

- X2 (X-squared) with valid range of -5.0E+08 to 5.0E+08
- X3 (X-cubed) with valid range of -5.0E+05 to 5.0E+05
- X4 (X to the fourth power) with valid range of -5.0E+04 to 5.0E+04
- X5 (X to the fifth power) with valid range of -5.0E+03 to 5.0E+03
- Sqrt(X) (Square root of X) with valid range of X³0
- LN(X) (Natural log of X) with valid range of X>0
- LOG(X) (Log base 10 of X) with valid range of X>0
- ex (Euler [e] = 2.71...) with valid range of -40 to +40
- 10x (10 to the power X) with valid range of -18 to +18
- 1/X (Inverse of X) with valid range of x not equal to 0

The default missing data code is assigned to the new (transformed) variables for a case if:

- original variable contains a missing value for the same case
- value for the case does not fall within the valid range

The fitting of higher-order polynomials of an independent variable with a mean not equal to zero can create difficult numerical problems. Specifically, the polynomials will be highly correlated due to the mean of the primary independent variable. With large numbers (e.g., Julian dates), this problem is very serious, and if proper protections are not put in place, can cause wrong results. The solution is to "center" the independent variable (sometimes, this procedures is referred to as "centered polynomials"), i.e., to subtract the mean, and then to compute the polynomials.

See the classic text by Neter, Wasserman, & Kutner (1985, Chapter 9), for a detailed discussion of this issue and analyses with polynomial models in general. Note that Statistica automatically checks for very large numbers created in the process of computing the polynomials and issues a warning message to alert you of potential multicollinearity problems.