Diffusion tensor image (DTI) is a powerful tool for quantitatively assessing the integrity of anatomical connectivity in white matter in clinical populations. The prevalent methods for group-level analysis of DTI are statistical analyses of invariant measures (e.g., fractional anisotropy) and principal directions across groups. The invariant measures and principal directions, however, do not capture all information in full diffusion tensor, which can decrease the statistical power of DTI in detecting subtle changes of white matters. Thus, it is very desirable to develop new statistical methods for analyzing full diffusion tensors. In this paper, we develop a set of toolbox, called RADTI, for the analysis of the full diffusion tensors as responses and establish their association with a set of covariates. The key idea is to use the recent development of log-Euclidean metric and then transform diffusion tensors in a nonlinear space into their matrix logarithms in a Euclidean space. Our regression model is a semiparametric model, which avoids any specific parametric assumptions. We develop an estimation procedure and a test procedure based on score statistics and a resampling method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest. Monte Carlo simulations are used to examine the finite sample performance of the test procedure for controlling the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic and age effects on the integrity of white matter in a diffusion tensor study of human immunodeficiency virus.