I understand the logic behind using k - 1 dummy variables for K Categories (multi collinearilty etc) but trying to understand how the math behind it works.
Consider the following Example: We Code:
Female as 1 Male = 0
Regression Eqn: y = B0 + B1*Age + B2*Gender
y = B0 + B1Age + B2
For Male: y = B0 + B1*Age
Here it seems that we don't account for the effect of Gender when he is Male since the term becomes Zero.
Also If I Code categories other way round should I get the same regression Equation.