The resistivity of the wire will not change: in fact, the resistivity is a property of the material used to build the wire, so it does not depend on its length.
Instead, the resistance of the wire depends on the length L:
[tex]R= \frac{\rho L}{A} [/tex]
where [tex]\rho[/tex] is the resistivity of the material and A is the cross-sectional area of the wire.
