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R3 is connected to the output as it's a stabilised voltage, so makes the design more accurate - essentially providing a constant current to the zener. Connecting R3 to the input means that it's voltage input, and thus current, will vary - this causes variations in the zener voltage, and thus variations in the output voltage.
Here is s simplified way to analyze this circuit. Think of TR2 (Q2) as an opamp. The emitter is the non-inverting input, the base is the inverting input, and the emitter of TR1 (Q1) is the output.
With no feedback, the transition voltage at the base is (Vz + Vbe, or 6.2 V with idealized components. This is the same as an opamp with a 6.2 V voltage reference connected to the non-inverting input. With no feedback, the "opamp" acts as an inverting comparator: as the voltage at the base goes above and below this voltage level, the output goes from saturated-low to saturated-high
RV1 and R4 form a negative-feedback voltage divider, just like the feedback resistors around a non-inverting opamp. The gain equation is the same. For example, if R4 and the adjusted value of VR1 both are 1K, the output will be 12.4 V.
Because a real opamp has way more forward gain than one transistor (Q2 is an emitter follower, and provides no voltage gain), the overall voltage regulation will not be as good. Also, because Q1's base current will be greater than a real opamp's input bias current, the calculated output voltage will be slightly off because this bias current is being drawn through one of the gain-setting resistors (VR1).