<![CDATA[The correct mathematical formulation and the determination of model that suit the characteristics of the data play crucial role in ensuring accurate modeling. Considering the various problems that exist today where complex mathematical formulations require advanced solutions, this study was conducted with the aim of testing the validity of analytical derivatives using relative differences and analysing the relationship between student academic achievement using the Generalized Linear Model (GLM). The initial stage of the study focused on testing the first derivative of the log-likelihood function for each estimated parameter. If the analytical derivative is correct, the next step is to analyse the regression relationship where the parameter estimation uses Maximum Likelihood Estimation (MLE). This study used secondary data from 40 students at University "X" in 2026, with final grades as the response variable; midterm and final exam, assignment, and self-study scores as predictor variables. The results showed that the relative differences for all parameters were equal to or close to zero, which means that the resulting analytical derivative was correct. Furthermore, analysis using GLM resulted in the conclusion that the estimated values were close to the actual values, so it can be said that the model has good accuracy and reliability.]]>
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