Lack of fit table for Nonlinear Regression

Find definitions and interpretation guidance for every statistic in the Lack of Fit table. Minitab automatically displays the lack of fit table when your data contain replicates. Replicates are multiple observations with identical predictor values. If your data do not contain replicates, it is impossible to calculate the pure error that is required to perform this test.

DF

The total degrees of freedom (DF) are the amount of information in your data. The analysis uses that information to estimate the values of unknown population parameters. The total DF is determined by the number of observations in your sample. Increasing your sample size provides more information about the population, which increases the total DF.

The DF for each source of error show how much information that term uses. The degrees of freedom for the lack of fit test is the degrees of freedom for error minus the degrees of freedom for pure error.

SS

The different sums of squares (SS) for error measure the variance attributable to the total error, lack of fit error, and pure error. The SS that Minitab uses for the lack of fit test is the total sum of squares for error minus the sum of squares for pure error.

Interpretation

Minitab uses the sums of squares to calculate the p-value for the lack of fit test. Usually, you interpret the p-value instead of the sums of squares.

MS

The different mean squares (MS) for error measure how much variation is attributable to the total error, lack of fit error, and pure error. The mean squares equal the sums of squares divided by their degrees of freedom.

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

Interpretation

Minitab uses the means squares to calculate the p-value for the lack of fit test. Usually, you interpret the p-value instead of the mean squares.

F

An F-value appears for the Lack of Fit term in the Lack of Fit test table. The F-value is the test statistic used to determine whether the model is missing higher-order terms that include the predictors in the current model.

Interpretation

Minitab uses the F-value to calculate the p-value, which you use to make a decision about the statistical significance of the terms and model. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

A sufficiently large F-value indicates that the lack of fit is significant.

P-value – Lack-of-fit

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Minitab automatically performs the pure error lack-of-fit test when your data contain replicates, which are multiple observations with identical x-values. Replicates represent "pure error" because only random variation can cause differences between the observed response values.

Interpretation

To determine whether the model correctly specifies the relationship between the response and the predictors, compare the p-value for the lack-of-fit test to your significance level to assess the null hypothesis. The null hypothesis for the lack-of-fit test is that the model correctly specifies the relationship between the response and the predictors. Usually, a significance level (denoted as alpha or α) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the model does not correctly specify the relationship between the response and the predictors when the model does specify the correct relationship.
P-value ≤ α: The lack-of-fit is statistically significant
If the p-value is less than or equal to the significance level, you conclude that the model does not correctly specify the relationship. To improve the model, you may need to add terms or transform your data.
P-value > α: The lack-of-fit is not statistically significant

If the p-value is larger than the significance level, the test does not detect any lack-of-fit.

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