Comparing Linear and Nonlinear Models for Load Profile Data Using ANOVA, AIC, and BIC

Ilir Keka and Betim Çiço

SAGE Open, 2025, vol. 15, issue 1, 21582440251326389

Abstract: To select the best model for the relationship between the response variable and predictor variables different approaches can be used. In this paper the aim is to find the best model that gives the best forecast of the values for the line of best fit, or to find the model, which is mostly approximated to the real model. This study aims to compare linear and nonlinear models for analyzing electric data, addressing the research gap in identifying the most effective modeling approach. The research methods involved the application of Analysis of Variance (ANOVA), Akaike’s Information Criterion (AIC), and Bayesian Information Criterion (BIC) to evaluate six models, including polynomial regressions of degrees 2, 3, and 4, linear regression, multiple linear regression, and models based on interaction terms. The results revealed that nonlinear models, particularly the polynomial regression with a degree of 4 model, demonstrated superior performance in terms of goodness of fit and predictive accuracy. This model has the lowest AIC and BIC values and an adjusted R -squared of .07619 or 0.76%. The F -statistic for this model is high, at 279, which is greater than 1. The study’s main focus is on data transformation and visualization, which were essential for using the R tool to find patterns and relationships in the data. This study has a lot of potential because it provides useful information for decision-making in the energy sector.

Keywords: Analysis of the Variance (ANOVA); Akaike’s Information Criterion (AIC); Bayesian Information Criterion (BIC); multiple linear model; non-linear model; regression; polynomial regression; load profile; visualization; R tool (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:sae:sagope:v:15:y:2025:i:1:p:21582440251326389

DOI: 10.1177/21582440251326389

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