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Assume that
and
are two predictor variables. Minitab provides two measures of the strengths of
interactions. The measures come from the training data. The first measure
describes the strength of the interaction as a percentage of the total response
squared deviation:

The second measure describes the strength of the interaction as a percentage
of the response squared deviation from the variables in the interaction:

From the training data, the total squared deviation of the response surface
is as follows:

where is the fitted value from the TreeNet model and is the mean of the response variable.

The calculation for the deviation of the interaction requires the
calculation of the deviation for both variables jointly. The joint calculation
for the deviations has the following form:

where is the fitted value from a bivariate partial dependence surface. For the calculation of this fitted value, go to Partial dependence plots for Fit Model and Discover Key Predictors with TreeNet® Regression.

The calculation for the deviation of the interaction removes the main
effects from the joint calculation:

where and are fitted values from univariate partial dependence surfaces for and . For the calculation of these fitted values, go to Partial dependence plots for Fit Model and Discover Key Predictors with TreeNet® Regression.