Summary table for Nonlinear Regression

Find definitions and interpretations for every statistic in the Summary table.

Iterations

This value indicates the number of iterations required to obtain the final sum of squared errors (Final SSE). Generally, you cannot ascribe meaning to this number. However, if the number of iterations equals the maximum number of iterations displayed in the Method table, this indicates that the algorithm did not converge on a solution. Instead, Minitab reached the maximum number of iterations and stopped. If this occurs, you can try changing the algorithm, the maximum number of iterations, the starting values, and the expectation function.

Final SSE

The final SSE is the sum of the squared residuals. It quantifies the variation in the data that the predictors do not explain. The displayed value represents the smallest SSE that the algorithm could obtain, given the starting conditions.

Interpretation

The lower the Final SSE value, the better the model describes the response. If you are comparing models or starting conditions, comparing multiple Final SSE values can be meaningful. However, a single Final SSE value may not be intuitively meaningful. Minitab uses the Final SSE to calculate S, which is usually more intuitive to interpret.

DFE

The error degrees of freedom (DFE) equals the sample size – the number of parameters. In general, the total degrees of freedom (DF) are the amount of information in your data and it is determined by the number of observations in your sample. The analysis uses that information to estimate the values of the parameters.

MSE

The mean square error (MSE) is the variance around the fitted values. MSE = Final SSE / DFE.

Interpretation

The square root of MSE is S. Usually, you interpret S instead of MSE.

S

S represents the standard deviation of the distance between the data values and the fitted values. S is measured in the units of the response. Because R2 is meaningless outside the linear model context, S is an important measure of the goodness-of-fit for a nonlinear model. Because S is expressed in the same units as the response variable, S is generally more intuitive to interpret than the Final SEE.

Interpretation

Use S to assess how well the model describes the response. S is measured in the units of the response variable and represents how far the data values fall from the fitted values. The lower the value of S, the better the model describes the response. However, a low S value by itself does not indicate that the model meets the model assumptions. You should check the residual plots to verify the assumptions.

For example, you work for a potato chip company that examines the factors that affect the percentage of crumbled potato chips per container. You reduce the model to the significant predictors, and S is calculated as 1.79. This result indicates that the standard deviation of the data points around the fitted values is 1.79. If you are comparing models, values that are lower than 1.79 indicate a better fit, and higher values indicate a worse fit.

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