Interaction in explanatory variables occurs when the effect of one explanatory variable on the response variable depends on the value of another explanatory variable. In other words, the relationship between the response variable and one of the explanatory variables is different for different values of the other explanatory variable.

For example, let’s say we are studying the factors that affect the academic performance of students in a school. We have two explanatory variables: the amount of time spent studying each day (variable A) and the quality of the student’s home environment (variable B). We would expect that the more time a student spends studying, the better their academic performance will be. However, the relationship between study time and academic performance might be different for students with different home environments. For students with a high-quality home environment, the relationship between study time and academic performance might be relatively strong, while for students with a low-quality home environment, the relationship between the two variables might be weaker. This would be an example of interaction between the two explanatory variables.

Another example of interaction in explanatory variables could be seen in a study on the effectiveness of a certain medical treatment. The study could have two explanatory variables: the type of medical condition being treated (variable A) and the patient’s age (variable B). We would expect that the medical treatment would be more effective for some medical conditions than for others. However, the effectiveness of the treatment might also depend on the patient’s age. For example, the treatment might be more effective for younger patients with certain medical conditions, while it might be less effective for older patients with the same conditions. This would be an example of interaction between the two explanatory variables.

In both of these examples, the effect of one explanatory variable on the response variable depends on the value of the other explanatory variable. This is what is meant by interaction in explanatory variables. In order to properly analyze and interpret the data in such situations, statistical techniques that can account for interaction effects are often used. These techniques can help to determine whether the observed interaction is statistically significant and can provide insight into the nature of the relationship between the variables.