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whats the difference between additive relationships and interactive relationships in regards to statistics and research, I...

whats the difference between additive relationships and interactive relationships in regards to statistics and research, I need real world examples though because Im having a hard time understanding. thanks

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An additive model is a statistical regression model in which the systematic component is the arithmetic sum of the individual effects of the predictors. Consider the simple case of an experiment with 2 factors. If

Y is the response and

X1 and

X2 are the 2 predictors, then an additive linear model is given by Y=Bo+B1X1+B2X2+e

In contrast, an interaction model is a statistical regression model in which the systematic component is not the arithmetic sum of the individual effects of the predictors. Example is a 2-factor ANOVA model, which is an example of an interaction model. It can express as Y=Bo+B1X1+B2X2+B3X1X2+e

X1X2 is the interaction and B3 is the coefficient

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