Summary: The joint-regression model for two-way data assumes a linear relation between a continuous response and column effects. Standard methods for fitting the model condition on estimates of the column effects, but including column effects as covariates in the model results in a nonlinear estimation problem. We use methods from nonlinear regression to give estimation and inference for joint regression. The method is iterative but computationally requires only multiple regression software. Inference based on asymptotic results from nonlinear regression is conceptually clear and statistically valid. We show how to carry out estimation and inference and illustrate with a real example.