Question

initially we only considered multiple linear models without interactions. however, it is often useful to consider the possibility that two different predictive factors will also have a significant interaction. consider a model which predicts a consumer's interest in a product based on the consumer's age and the amount of advertising they have observed. assuming both of these predictors are significant and positive in their effect, what would this mean?

Answer 1

A significant and positive interaction in a multiple linear regression model between age and advertising indicates that their combined effect on consumer interest is greater than the effect of each variable alone, possibly leading to amplified interest with increased advertising among consumers of certain ages.

Step-by-step explanation:

If we consider a multiple linear regression model that includes an interaction term between the consumer's age and the amount of advertising they have observed, the presence of a significant and positive interaction would mean that the combined effect of age and advertising exposure on a consumer's interest in a product is more than the sum of the individual effects.

In other words, not only do both age and advertising contribute positively to a consumer's interest separately, but when considered together, their impact is amplified.

For example, an increase in advertising might have a more pronounced effect on interest for older consumers compared to younger ones, indicating an interaction between the two variables. It's important to analyze such interactions because it provides a more nuanced understanding of how predictive factors work together to influence the dependent variable.

Models with interactions help in tailoring strategies such as marketing campaigns more effectively by targeting consumers who are most likely to respond positively to the product being advertised.