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? (1) do older or younger people have more interest? older and younger people have the same interest (2) does advertising help or hurt? helps now suppose there is a statistically significant interaction between these two terms. in your own words, what does this mean about the conclusions above? see answer in comment field

Answer 1

A significant interaction between age and advertising in a multiple linear regression model indicates the effect of one factor depends on the level of the other, altering outcomes from when such interactions are not included.

Step-by-step explanation:

When considering a multiple linear regression model without interactions, a significant and positive predictor like age or amount of advertising would suggest that, individually, these factors increase a consumer's interest in a product—older consumers may have more interest, and more advertising would typically help to increase interest.

If there is a statistically significant interaction between age and advertising, this means that the effect of one predictive factor on the consumer's interest depends on the level of the other factor. For example, additional advertising might have a greater effect on consumer interest for one age group over another, rather than having a consistent effect across all age groups. This could lead to conclusions that differ from when interaction terms are not considered.