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My question is about the difference (in general) between the interaction terms $x_1x_2$ and $x_1/x_2$ in multiple linear regression.

Suppose you are performing multiple linear regression and you have interactions present i.e. an independent variable has a different effect on the outcome depending on the values of another independent variable. Therefore you decide to model as follows:

$$ Y = \beta_0 + \beta_1x_1 + \beta_2 x_2 + \beta_3x_1x_2 $$

For example where $Y$could represent Impurity after a chemical reaction, $x_1$represents Reaction Temperature, $x_2$ represents Reaction Time.

Adding an interaction term between Reaction Temperature and Reaction Time $x_1x_2$ would effectively change the gradient for Reaction Time as we change the value of Reaction Temperature from low to high (and vice-versa for Reaction Temperature).

My questions are:

  1. What impact does the interaction term $x_1/x_2$ have when compared to $x_1x_2$ ?
  2. In what circumstances might you include an interaction term of $x_1/x_2$ as opposed to $x_1x_2$ ?
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