Here's an example of a formula: Intelligence ~ SEX + AGE + SCHOOLING
How would I write out the regression equation for the above if for example schooling had 3 categories? E.g. High School, Undergraduate, Postgraduate, as well as SEX with 2 categories? E.g. Male, Female.
Because you said logistic regression, assume intelligence has two level: high and low.
Define: $Y = 1$ if intelligence is high, = 0 otherwise
$X_1 = 1$ for male, = 0 for female
$X_2 = \text{age}$
$X_3 = 1$ for High school, = 0 for other school
$X_4 = 1$ for Undergraduate, = 0 for other school
The model is: $$\log\left(\frac {\pi}{1-\pi}\right) = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 +\beta_4X_4,$$ where $\Pr(Y=1) = \pi$.
