Question on Interaction terms with a dummy variable I have the following model.
Sales = B0 + B1.Age + B2.Mobile

where Mobile is a dummy variable that has the value of 1 if mobile, and 0 otherwise. Age is a customers age in months.
I have been asked to add an interaction term to the model.
B3.Age*Mobile

however I feel this makes no sense as the result will be an additional Age variable, or 0. The Age variable will simply be included twice in the model and we do not gain any new information from this.
when Mobile = 1,  B3*(Age*1) = B3.Age

when Mobile = 0,  B3*(Age*0) = 0

Am I wrong in thinking this is incorrect? Or am I missing something here?
 A: The starting point of your thinking is correct but the conclusion is wrong. The new variable is indeed either Age or 0 but this does change the model: It leads to different age slopes for the two mobile groups. Simply make the distinction of case (Mobile = 0 vs. 1) for the entire equation.
Without interaction for Mobile = 0:
B0 + B1 * Age

and Mobile = 1:
B0 + B1 * Age + B2 = (B0 + B2) + B1 * Age

Thus you get two different regression lines with the same slope w.r.t. Age, namely B1. But you have different intercepts: B0 vs. B0 + B2. Thus, B2 can be interpreted as the difference in intercepts.
Now with interaction you still get for Mobile = 0:
B0 + B1 * Age

but for Mobile = 1:
B0 + B1 * Age + B2 + B3 * Age = (B0 + B2) + (B1 + B3) * Age

Thus, you have two regression lines with different intercepts and different Age slopes. B2 is again the difference in intercepts. B3 is the difference in slopes.
A: Let $s$ denote sales, $m$ be an indicator for mobile, and $a$ the age. Imagine you ran the regression:
$$ s_i = b_0 + b_1 a_i + b_2 m_i + b_3 m_i a_i + \epsilon_i $$
What's the expected sales for a 30 year old that doesn't use mobile?
$$ E[s \mid m = 0, a = 30] = b_0 + 30 b_1 $$
What's the expected sales for a 30 year old that does use mobile?
$$ E[s \mid m = 1, a = 30] = b_0 + b_2 + 30 (b_1 + b_3) $$
By including a mobile indicator $m_i$, you're estimating a constant difference in sales between mobile and non-mobile users. By including the interactive term $m_ia_i$, you're estimating a different effect for age depending on whether they use mobile or not! 
