In this study we investigated the relationship between nitrogen level application and the grain yield of sesame (Sesamum indicum L.) using a quadratic regression modelling. The response variable used was the sesame grain yield from a replicated field experimental data. Ordinary least squares estimation was used to fit a second-order polynomial model, then analysis of variance, residual diagnostics, and sensitivity analyses was used to access model adequacy.  A mixed-effects quadratic model with a random intercept for replication was used in order to account for replication, this was also evaluated and compared with the fixed-effects model using the likelihood-based criteria. The results of the quadratic regression model revealed a significant nonlinear relationship between the sesame grain yield and the nitrogen level, which was characterized with a positive linear and negative quadratic effects , demonstrating a diminishing marginal return as the nitrogen levels goes higher. The quadratic model explained a large proportion of yield variability (R² = 0.819) and allowed analytical estimation of the nitrogen level associated with maximum expected yield. Although heteroscedasticity was detected, inference based on heteroscedasticity-consistent standard errors remained unchanged. the AIC and the BIC showed that the fixed-effects quadratic model outperformed the mixed-effects quadratic model. We have found from the results of this study that the quadratic regression modeling provided a simple, efficient and robust methodological framework for modeling nonlinear relationships to figure out how higher levels of nitrogen application affects crop yield this helps pinpoint the optimal amount of nitrogen for best crop yields in experimental studies.