How to determine regulator's components values?
I will get you started with a procedure but you will need to choose appropriate parts and do the calculations.


Choose a Zener


Perhaps we might like to use one of these parts. Applying my engineers eye, I would personally choose the 6.2V part (but that is simply because of the specifications - anything below your target output voltage would do).

The current through \$R_{REF}\$ must be sufficient to keep the zener in proper regulation + the current through P1. That current (for the zener) is specified in the datasheet.


Choose P1; 


A 10k trimpot would work nicely here (but as we are looking at an ideal amplifier it could easily be much larger).

As the datasheet linked shows the current for which Vz is specified, and the current through P1 will simply be Vz / P1, you can now calculate the maximum value of \$R_{REF}\$ if we know the minimum input voltage.

3 Find the minimum input voltage 

The minimum input voltage will be \$V_{out} + V_{BE[Q1]} + v_{RCC} + V_{CE(sat)} Q1\$. I would assume \$V_{CE(sat)}\$ to be 0.2V and V(RCC) will be a Vbe bias at current limit, so you can now find the minimum input voltage.

For the output voltage set, assuming that the value at the non-inverting input of the error amplifier is Vz when at the maximum output voltage, then you need to choose them such that the voltage across R4 is equal to Vz.

So from the voltage divider equation, \$ Vz = \frac {{V_o} \cdot {R4}} {R4 + R5}\$; note that the ratio of R4 and R5 is what is important.

From that, you should now be able to solve and keep in mind that there are multiple solutions given what you have shown us.