How does a resistance of a wire depend on its radius?

Resistance is inversely-proportional to the cross-sectional area of a conductor. For example, doubling its cross-sectional area will halve its resistance, while halving its cross-sectional area will double its resistance.

Since the cross-sectional area of a circular-section conductor is proportional to the square of its radius, doubling that radius will reduce its resistance by one quarter, while halving its radius will quadruple its resistance.