The Nonlinear Fit Report

The initial Nonlinear Fit report includes the following items, shown in Figure 13.5.

Control Panel

Provides options for controlling the fitting process.

Starts the fitting process.

Stop

Stops the fitting process.

Step

Proceeds through the fitting process one iteration at a time.

Reset

Resets the editable values into the formula, resets the iteration values, and calculates the SSE at these new values.

Criterion

Shows iteration measures from the fitting process.

Current

Shows the current value of each Criterion.

Stop Limit

Sets limits on the measures listed under Criterion.

Plot

Shows a plot of the X and Y variables for models with only one X variable. The model based on the current values is shown on the plot. To change the current values of the parameters, use the sliders or edit boxes beneath the plot.

Figure 13.5 Initial Nonlinear Fit Report

After you click Go to fit a model, the report includes the following additional items, shown in Figure 13.6.

Save Estimates

Saves the current parameter values to the parameters in the formula column.

Confidence Limits

Computes confidence intervals for all parameters. The intervals are profile likelihood confidence intervals, and are shown in the Solution report. The confidence limit computations involve a new set of iterations for each limit of each parameter, and the iterations often do not find the limits successfully. The Edit Alpha and Convergence Criterion options are for the confidence interval computations. For details about the Goal SSE for CL, see Profile Likelihood Confidence Limits.

Solution

Shows the parameters estimates and other statistics.

SSE

Shows the residual sum of squared errors. SSE is the objective that is to be minimized. If a custom loss function is specified, this is the sum of the loss function.

DFE

Shows the degrees of freedom for error, which is the number of observations used minus the number of parameters fitted.

MSE

Shows the mean squared error. It is the estimate of the variance of the residual error, which is the SSE divided by the DFE.

RMSE

Estimates the standard deviation of the residual error, which is square root of the MSE.

Parameter

Lists the names that you gave the parameters in the fitting formula.

Estimate

Lists the parameter estimates produced. Keep in mind that with nonlinear regression, there might be problems with this estimate even if everything seems to work.

ApproxStdErr

Lists the approximate standard error, which is computed analogously to linear regression. It is formed by the product of the RMSE and the square root of the diagonals of the derivative cross-products matrix inverse.

Lower CL and Upper CL

Shows the confidence limits for the parameters. They are missing until you click the Confidence Limits on the Control Panel. For more details about the confidence intervals, see Profile Likelihood Confidence Limits.

Excluded Data

Shows a report showing fit statistics for excluded rows. This is useful for validating the model on observations not used to fit the model. You can use this feature in conjunction with the Remember Solution option to change the exclusions, and get a new report reflecting the different exclusions

Correlation of Estimates

Displays the correlations between the parameter estimates.

Figure 13.6 Fitted Model Report