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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.

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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 $\Pr(Y=1) = \pi$.

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