Methods and formulas for model fit in Nonlinear Regression

Select the method or formula of your choice.

Sum of squared errors

The SSE (sum of squared errors) is the sum of the squared residuals.

S

The estimate of σ is:

Notation

TermDescription
SSEsum of the squared residuals
Nnumber of observations
Pnumber of free parameters

Pure error lack-of-fit test

Minitab obtains the groups that are determined by distinct combinations of predictor values. Within each group with more than one observation, Minitab calculates the contribution to pure error:

Minitab then sums these contributions across groups.

The degrees of freedom for lack of fit is the degrees of freedom for error minus the degrees of freedom for pure error. The sum of squares for lack of fit is the sum of squares for error minus the sum of squares for pure error.

Minitab calculates the mean squares by dividing the sums of squares by their degrees of freedom.

The F statistic equals the mean square for lack of fit divided by the mean square for pure error.

Notation

TermDescription
nnth observation
dfdegrees of freedom = degrees of freedom for error minus degrees of freedom for pure error
wnweight for observation n
μwweighted mean within this group

Residuals

The residual is the difference between an observed value and the corresponding fitted value. This part of the observation is not explained by the model. The residual of an observation is:

Notation

TermDescription
yiith observed response value
ith fitted value for the response
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