Say we are regressing wages on education and race. We have 3 possible values for race: black, white and hispanic. So, I include the binary variables black and white in my regression.
After running my regression, I see that white has a positive coefficient and black has a negative one. How do I know what sign the coeficcient for hispanic is? (in other words, how do I know how being hispanic affects wages?)
This would be the constant in your regression.
Not dealing with race, for item $i$ and a category with 3 levels W, B and H,
$x_{i1}=1$ if W, $x_{i1}=0$ if not W
$x_{i2}=1$ if B, $x_{i2}=0$ if not B
and model $$ y_i=\beta_0+\beta_1 x_{i1}+\beta_2 x_{i2}+\epsilon_i $$
$\beta_0$ is the coefficient for the baseline ( the final level, H)