Are values of resistivity independent of the cross-section and length of the resistor?
Resistivity is a property of a material. Resistance is a property of an item that is made up of a material.


  All copper wires, irrespective of their shape and size, have approximately the same resistivity, but a long, thin copper wire has a much larger resistance than a thick, short copper wire.
  https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity


The basic formula for resistance of an object is as follows:

$$R=\frac{\rho\ l}{A}$$


\$R\$ is resistance
\$\rho\$ is the resistivivity of the material
\$l\$ is the length of the object
\$A\$ is the cross-sectional area of the object


The resistivity of annealed copper per ASTM B3 is 0.15328 Ω·g/m² at 20°C. This works out to a resistance of 0.15328 Ω for a wire of length 1 m and mass 1 g (diameter 378.45 µm). A wire of the same diameter of length 2 m will have a resistance of 0.30656 Ω.