We suggest the use of Poisson regression for time inference and hypothesis testing on a bifurcating Phylogenetic tree with known topology. This method is computationally simple and naturally accommodates variable substitution rates across different sites, without requiring the estimation of these rates. We identify the assumptions under which this is a maximum-likelihood inference approach and show that in some realistic situations--in particular, when the probability of repeated mutation within each branch of the tree is small--these assumptions hold with high probability.