Publication date: 10/01/2019

Analysis of Variance

The Analysis of Variance report provides the calculations for comparing the fitted model to a model where all predicted values equal the response mean.

Note: If either a Frequency or a Weight variable is entered in the Fit Model launch window, the entries in the Analysis of Variance report are adjusted in keeping with the descriptions in Frequency and Weight.

The Analysis of Variance report contains the following columns:

Source

The three sources of variation: Model, Error, and C. Total (Corrected Total).

DF

The associated degrees of freedom (DF) for each source of variation. The C. Total DF is always one less than the number of observations, and it is partitioned into degrees of freedom for the Model and Error as follows:

The Model DF is the number of parameters (other than the intercept) used to fit the model.

The Error DF is the difference between the C. Total DF and the Model DF.

Sum of Squares

The associated Sum of Squares (SS) for each source of variation.

The total (C. Total) SS is the sum of the squared differences between the response values and the sample mean. It represents the total variation in the response values.

The Error SS is the sum of the squared differences between the fitted values and the actual values. It represents the variability that remains unexplained by the fitted model.

The Model SS is the difference between C. Total SS and Error SS. It represents the variability explained by the model.

Mean Square

The mean square statistics for the Model and Error sources of variation. Each Mean Square is the sum of squares divided by its corresponding DF.

Note: The square root of the Mean Square for Error is the same as RMSE in the Summary of Fit report.

MSE Used

(Appears only when the Error Specification is Pure Error or Specified.) The mean square error used when the default error specification is not selected. This value is used to calculate the F Ratio instead of the mean square error in the Mean Square column.

DFE Used

(Appears only when the Error Specification is Pure Error or Specified.) The error degrees of freedom used when the default error specification is not selected. This value is used to calculate the Prob > F value instead of the Error DF in the DF column.

F Ratio

The model mean square divided by the error mean square. The F Ratio is the test statistic for a test of whether the model differs significantly from a model where all predicted values are the response mean.

Prob > F

The p-value for the test. The Prob > F value measures the probability of obtaining an F Ratio as large as what is observed, given that all parameters except the intercept are zero. Small values of Prob > F indicate that the observed F Ratio is unlikely. Such values are considered evidence that there is at least one significant effect in the model.

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