Fixed Nonlinear Regression Overview
You can use Fixed Nonlinear Regression to specify nonlinear transformations, and use these transformed variables in your regression analysis. You can use the following transformations with valid ranges. More than one transformation can be selected.
| Transformation | Valid range |
|---|---|
| X2 (X-squared) | -5.0E+08 to 5.0E+08 |
| X3 (X-cubed) | -5.0E+05 to 5.0E+05 |
| X4 (X to the fourth power) | -5.0E+04 to 5.0E+04 |
| X5 (X to the fifth power) | -5.0E+03 to 5.0E+03 |
| Sqrt(X) (Square root of X) | X³0 |
| LN(X) (Natural log of X) | X>0 |
| LOG(X) (Log base 10 of X) | X>0 |
| ex (Euler [e] = 2.71...) | -40 to +40 |
| 10x (10 to the power X) | -18 to +18 |
| 1/X (Inverse of X) | X ¹ 0 |
The default missing data code is assigned to the new (transformed) variables in the following cases:
- The original (un-transformed) variable contains a missing value for the same case
- The value for the case does not fall within the valid range
Fitting Centered Polynomial Models
The fitting of higher-order polynomials of an independent variable with a mean not equal to zero can create numerical problems. Specifically, the polynomials are highly correlated due to the mean of the primary independent variable. With large numbers, for example, Julian dates this problem is very serious. This can give wrong results if proper protections are not put in place. You must center the independent variable by subtracting the mean, and then computing the polynomials. For more information and analyses with polynomial models in general, see the classic text by Neter, Wasserman, & Kutner. Statistica automatically checks for very large numbers created in the process of computing the polynomials, and issues a warning message of potential multicollinearity problems.