Step 1: Resistivity $\rho$ is the resistance offered by a conductor of unit length and unit cross-sectional area; it is a property of the material (independent of its dimensions).

Step 2: Since conductivity $\sigma = \dfrac{ne^2\tau}{m}$, and $\rho = 1/\sigma$: $\rho = \dfrac{m}{ne^2\tau}$.

Step 3: (a) $\rho \propto 1/n$ — resistivity DECREASES as free electron density $n$ increases.

Step 4: (b) $\rho \propto 1/\tau$ — resistivity DECREASES as relaxation time $\tau$ increases (fewer collisions means less resistance).