Data collected for a two-way analysis of variance contrasts the effects on the average of the response produced by varying the levels of two categorical variables. A factorial design specifies that the data will include every combination of the two variables. Parallel lines in the profile plot of the cell means defined by the two factors indicate an absence of interaction between the two factors. The model is estimated by a multiple regression with dummy variables. The partial F-test (or effect test) of the interaction components of the model indicates whether the presence of interaction is statistically significant.
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