In this paper, we present a novel method forstatistical inductance extraction and modeling for interconnects considering process variations. The new method, called statHenry, is based on the collocation-based spectrals tochastic method where orthogonal polynomials are used to represent the statistical processes. The coefficients of thepartial inductance orthogonal polynomial are computed viathe collocation method where a fast multi-dimensional Gaussian quadrature method is applied with sparse grids. To further improve the efficiency of the proposed method,a random variable reduction scheme is used. Given the interconnect wire variation parameters, the resulting method can derive the parameterized closed form of the inductance value. We show that both partial and loop inductance variations can be significant given the width and height variations. This new approach can work withany existing inductance extraction tool to extract the variational partial and loop inductance or impedance. Experimental results show that our method is orders of magnitude faster than the Monte Carlo method for several practical interconnect structures.