It might be helpful to elaborate a bit more about radiation resistance.

Consider an antenna that has no loss. If we apply 100 watts, say, to
this antenna, the radiation resistance "consumes" that 100 watts. That
is to say, all 100 watts is radiated.

In the case of a resonant lossless quarter wave vertical, for example,
the current at the base will be about 1.67 amps if 100 watts is being
radiated. We can solve for Rr at the base from P = I^2 * Rr, where I is
the base current, to get Rr = P / I^2, with the result that Rr is about
36 ohms. This is the radiation resistance referred to the base -- it
"consumes" the 100 watts. (We could have calculated Rr at some other
point along the antenna, where I is different, and gotten a different
value. But P still has to equal I^2 * Rr, where I is the current at the
point to which Rr is being referred.)

Now, what determines the current we get at the base, for a given applied
power and radiator length? The answer is the current distribution --
that is, the way the current varies along the length of the conductor.
(I'm only considering a simple single wire antenna here. When other
conductors are involved, mutual coupling between conductors also plays a
role.) Putting a loading coil at the bottom of the antenna doesn't
change the current distribution, it only changes the feedpoint
reactance. So it doesn't change the feedpoint current for a given power
input, so the radiation resistance doesn't change. But if you put a
loading coil part way up the antenna, the current distribution does
change. This alters the base current for the same power input and
therefore the radiation resistance changes. Remember that Rr = P / I^2,
where Rr and I are measured at the same point (in this case the base
feedpoint), so if I changes, Rr changes. Likewise, top loading alters
the current distribution and consequently the radiation resistance. For
people who would like to see this graphically, the demo version of EZNEC
is adequate. Just look at the View Antenna display after running a
pattern, source data, or current calculation, and you'll see how the
current varies along the antenna. If you set a fixed power level in the
Options menu (Power Level selection), you can also see, by clicking Src
Dat, exactly how the current at the source changes as the current
distribution does.

If you have a fixed amount of loss, say at the base of the antenna due
to ground system loss, the amount of power dissipated in that loss as
heat is Ploss = I^2 * Rloss, where I is the current flowing through that
loss, in this case the current at the antenna base. So for a given
amount of applied power, you minimize the power lost when you minimize
the base current. This is exactly equivalent to saying you're raising
the radiation resistance referred to the base. That's why mobile antenna
users consider higher radiation resistance a virtue -- it means lower
feedpoint current for a given power input, and therefore less power lost
in the necessarily imperfect ground system.

While the principles are all the same, wire loss has to be treated a bit
differently because altering the current distribution changes the amount
of wire loss (which is usually combined into a single loss resistance
referred to the feedpoint, or the same point where the radiation
resistance is referred). Also, changing the wire length alters the wire
loss, as does the total current in the wire which increases as the wire
is shortened for a given power input. All these can be dealt with
analytically or with a modeling program, but it's easy to lose track of
exactly what's happening when all these factors are present at the same
time. Fortunately, wire loss is insignificant for the vast majority of
typical amateur applications. With modeling, it's easy to determine when
it is and isn't significant, simply by turning wire loss on and off and
observing how much the results change.

Roy Lewallen, W7EL