Português Cost function in a public university: regression as a tool for estimation and management

Abstract

This study aimed to propose a model to identify cost drivers and estimate the cost function of a public university, whose costs were calculated for all its units in the year 2019. The theoretical framework addressed cost management in universities, cost behavior in estimation and cost functions, and regression analysis. Understanding cost behavior as fixed or variable supports managerial decision-making, planning, and control, both in predicting future costs for the expansion or reduction of activity levels and in managing these costs by identifying bottlenecks and modifying their behavior, thereby clarifying the cost structure. The cost data of the university analyzed were extracted from the study by Hoffmann (2020), which applied the Activity-Based Costing methodology to determine the costs of institutional activities and outputs across 19 academic units. Data collection was conducted using a cross-sectional approach, covering the 19 units of the university, with cost data referring to the year 2019. Linear regression tests were performed to address the proposed hypotheses, adopting a 95% confidence interval, in order to verify the adequacy of cost drivers based on hours worked. The results were positive when the selected driver was appropriate for the observed phenomenon. Subsequently, a multiple regression model was used to estimate the university’s teaching cost function, yielding a coefficient of determination (R²) of 0.941, indicating that 94.10% of the variation in teaching costs was explained by variations in teaching hours and the number of PhD faculty members within each unit. Finally, statistical tests were conducted to assess significance, residual normality, multicollinearity, and homoscedasticity.