How to calculate theoretically Output Impedance of a Linear Voltage Regulator
You'll need to know the characteristics of the semiconductors, too.

The basic idea is straightforward. You calculate the voltages and currents throughout the circuit for one operating point. Call the nominal load I0, giving an output voltage of V0.

Then you draw an additional load, say I0 + &Delta;I, and recalculate the numbers, which will yield a different output voltage of V0 - &Delta;V.

The ratio &Delta;V/&Delta;I is your output impedance.

In rough terms, the change in output current will cause a change in Q1's base current. That in turn will require a change in Q2's collector current, which will affect both the current through the zener diode and Q2's base current. The former will affect the zener voltage slightly, and the latter will affect the voltage drop through the feedback divider. Some of these effects cancel out and some don't.

The easiest way to do this is with a circuit simulator.