I find a lot of resources online which explains the dummy variable trap and that you should remove 1 category of your dummy variable before fitting it into a multilinear model to avoid multicollinearity.
While I understand what you should do I don't understand why you should do it in term of mathematical explanation.
I mean, let's take a concrete example: I have a variable
Gender with values
Female. If I take the multilinear model equation I get:
$$y = B_0 + x_1B_1 + x_2B_2$$
with $x_1 = 1$ and $x_2 = 0$. So I get: $y=0+1\times1 + 0\times1$ so how is it different from $y=0+1\times1$ (which the second dummy variable removed ? Could someone give me a concrete mathematical example of how this "trap" works? Thanks