Specify the parameters for Nonlinear Regression

Stat > Regression > Nonlinear Regression > Parameters

Minitab estimates parameters by using an iterative algorithm to minimize the sum of squares of the residual error (SSE). You must supply the algorithm's starting values for each parameter. In addition, you can put constraints on the estimated parameter values in the fitted model.

For some models and data sets, the starting values can significantly affect the results. Certain starting values may lead to a failure to converge, or convergence to a local, not global, SSE minimum. Sometimes, it may be difficult to develop good starting values. For practical suggestions, see Bates and Watts (1988)¹.

Tip

For the single predictor expectation functions that Minitab supplies, view the function sketches in the catalog to help generate starting values. These sketches illustrate how the parameters are connected to portions of the response curve.

Required starting values

Values: Enter one or more starting values for each parameter. If you enter multiple values for a parameter, separate the values with a space or use shorthand notation. For example, 10:40/5 specifies starting values from 10 to 40 in increments of 5.
Locked: Force a parameter in the fitted model to equal your starting value. At least one parameter must be unlocked.

Optional constraints

You can constrain the estimated parameter value to a range you specify.

Lower Bound: Enter a value that the estimated parameter should be greater than or equal to.
Upper Bound: Enter a value that the estimated parameter should be less than or equal to.

Note

If you enter multiple starting values for at least one parameter, Minitab determines which starting value combination produces the smallest initial SSE and uses that combination to perform the nonlinear regression analysis. To view this combination, select Information for each iteration in the Results dialog box. Or, select Grid of starting values and SSE values in the Storage dialog box and examine the worksheet for the combination that produces the smallest initial SSE.

¹ D.M. Bates and D.G. Watts (1988). "A Relative Offset Orthogonality Convergence Criterion for Nonlinear Least Squares", Technometrics, 23, 179-183.