In linear regression, the dependent variable depression is affected by the independent variable "living in the countryside", B is a positive number, indicating that people living in the countryside are more depressed than those who do not live in the countryside. Meanwhile, there is another independent variable "residence duration", whose interaction term with "living in the countryside" has an effect on depression, and B is still a positive number. At this time, can it be stated that "people who live in the country are more depressed than those who don't live in the country, and the gap in depression will be further widened when they live in the country for a long time" (in other words, from the perspective of depression degree, non-rural < rural < long-term living in the country)?
Nope.
1. You never get a prove from a statistical model.
2. You never get information about causality from observational data.
The correlation between depression and area of residence can be (and likely is) spurious, and the same applies to any interaction. The variable "living in the countryside" is way too imprecise (it includes too many different factors that all are more or less directly associated with the mental state). Imo the value of finding such associations is really limited, as it does not help understanding the connections nor deriving guidance to improve whatever.
Also be aware that any conclusion applies only to the samples population, which may be restricted to a narrow patch of a country, a political system, a social/religious environment, and possibly even to a just a particular, possibly special subgroup of people living there that happened to take part in this study.
Hi, besides the confounding issues raised by Jochen Wilhelm (although I did not interpret your post as making any such statements), you should plot the interaction to see the interactional pattern.
Jerermy Dawson offers some excel-file in which you type in the regression coefficients from the model to show the pattern: http://www.jeremydawson.co.uk/slopes.htm
And, yes having some controls for potential confounders would strengthen the interpretation. Lack of exogeneity in observational data is no study-killer but should at least lead to some modesty and considerations of the limitations :)
Good luck
Holger
AS per @Holger Steinmetz, plotting the interaction graphically is critical to interpretation, even be it less than totally conclusive,
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