Nonlinear Regression - Parameters
main topic     see also 

Stat > Regression > Nonlinear Regression > Parameters

Minitab estimates parameters by using an iterative algorithm to minimize the sum of the squared residuals (SSE). You must supply the algorithm's starting values for each parameter. Optionally, you can impose 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 failure to converge or convergence to a local, rather than global, SSE minimum. In some cases, you may need to expend considerable effort to develop good starting values. See [4] for practical suggestions.

Tip

For the single predictor expectation functions that Minitab supplies, look at 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.

See Understanding Algorithms and Starting Values - Nonlinear Regression for more information.

Dialog box items

Required starting values: Enter at least one starting value for each parameter in the table. The number of parameters depends on the function that you specify.

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 means starting values from 10 to 40 in increments of 5.

Locked: Check to 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 lesser 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, check Information for each iteration in the Results dialog box and view the results in the Session window. Or, check Grid of starting values and SSE values in the Storage dialog box and look in the worksheet for the combination that produces the smallest initial SSE.