Segmented regression models are generalization of linear and generalized linear models that replace a linear predictor with a piecewise linear predictor. Breakpoints where the piecewise linear predictor changes slope are unknown and estimated from data. We use segmented regression to model the relationship between the number of plant leaves and thermal time for hundreds of maize genotypes. Slope estimates from fitted segmented regression models provide estimates of leaf appearance rate (LAR) for each genotype. Estimates of breakpoints provide insight into developmental time points when changes in LAR occur for each genotype. We compare inferences about slopes and breakpoints obtained from the segmented R package with inferences obtained by bootstrap techniques. Furthermore, we use the estimated difference between slopes in two segments for each genotype and the estimated single breakpoint for each genotype as LAR characteristics of interest. We then use each of these characteristics as a response variable in a linear model to test for genotype effects.