# Nonlinear Regression

Nonlinear regression is a method of finding a nonlinear model of the relationship between the dependent variable and a set of independent variables. Unlike traditional linear regression, which is restricted to estimating linear models, nonlinear regression can estimate models with arbitrary relationships between independent and dependent variables. This is accomplished using iterative estimation algorithms. Note that this procedure is not necessary for simple polynomial models of the form Y = A + BX**2. By defining W = X**2, we get a simple linear model, Y = A + BW, which can be estimated using traditional methods such as the Linear Regression procedure.

**Example.** Can population be predicted based on time? A scatterplot
shows that there seems to be a strong relationship between population
and time, but the relationship is nonlinear, so it requires the special
estimation methods of the Nonlinear Regression procedure. By setting
up an appropriate equation, such as a logistic population growth model,
we can get a good estimate of the model, allowing us to make predictions
about population for times that were not actually measured.

**Statistics.** For each iteration: parameter estimates and
residual sum of squares. For each model: sum of squares for regression,
residual, uncorrected total and corrected total, parameter estimates,
asymptotic standard errors, and asymptotic correlation matrix of parameter
estimates.

## Nonlinear Regression data considerations

**Data.** The dependent and independent variables should be quantitative. Categorical variables,
such as religion, major, or region of residence, need to be recoded to binary (dummy) variables or
other types of contrast variables.

**Assumptions.** Results are valid only if you have specified a function that accurately
describes the relationship between dependent and independent variables. Additionally, the choice of
good starting values is very important. Even if you've specified the correct functional form of the
model, if you use poor starting values, your model may fail to converge or you may get a locally
optimal solution rather than one that is globally optimal.

**Related procedures.** Many models that appear nonlinear at first can be transformed to a linear
model, which can be analyzed using the Linear Regression procedure. If you are uncertain what the
proper model should be, the Curve Estimation procedure can help to identify useful functional
relations in your data.

## Obtaining a Nonlinear Regression Analysis

This feature requires Custom Tables and Advanced Statistics.

- From the menus choose:
- Select one numeric dependent variable from the list of variables in your active dataset.
- To build a model expression, enter the expression in the Model Expression field or paste components (variables, parameters, functions) into the field.
- Identify parameters in your model by clicking Parameters.

A segmented model (one that takes different forms in different parts of its domain) must be specified by using conditional logic within the single model statement.

This procedure pastes NLR command syntax.