Can I have multiple interactions with the same dummy? For example, $\newcommand{\dummy}{{\rm dummy}}\dummy =1$ if $x - {\rm mean}(x)$. Can I have:
$$\hat{y}=\dummy + x_2+ x_3 +\dummy\times x_2 +\dummy\times x_3\quad?$$
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$\begingroup$ I see no reason why not but could you expand a bit on what the dummy is? $\endgroup$– mdeweyCommented Dec 18, 2016 at 20:51
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I don't see why not from the information you gave. say that $y$ is wages is USD, $x_1$ is sex (1=female), $x_2$ is number of shoes and $x_3$ is height. say $\hat{y}= 1000 + 5x_1 + 100x_2 + 2x_3 + 10x_1x_2 - 15x_1x_3$ than $x_1$ means that females without shoes and with the height of 0 will earn 5 USD more than males. $x_1x_2$ means that each additional shoe, when height is 0, adds 10 USD more for females above the increase for men, per shoe. etc.
