a comparative analysis of univariate regression models using the simulated exponential dataset

In this study, we investigated the effectiveness of univariate regression models in evaluating asimulated exponential dataset. several univariate regression models were used, including simpleleast squares (sls), least median squares (lms), single median (sm), repeated median (rm),jacobian model (jm), alternating conditional expectation (ace), and additivity and variancestabilization (avas). the performance of these regression models was verified through statisticalparameters. the study involved simulating exponential data using eq (1). the variable xcontained data ranging from 1 to 100 with an interval of one.???? = 1 ∶ 100, ????1 =⁡√????⁡, ???? = ????????1 (1)the processing and regression of the exponential simulated dataset were carried out usingmatlab software (v-2009, mathworks, usa) with programs written by the correspondingauthor (m. khanmohammadi khorrami). an m-file/matlab algorithm was implemented,providing comprehensive details of the univariate regression models. the results obtained in thisstudy can also be useful for comparative analysis with different algorithms. the investigationfocused on utilizing non-linear data in univariate regression analysis, and it was found that theace and avas models provided valuable recommendations for future applications. the valuesobtained for the ace model, including sum of squares total (sst), sum of squared regression(ssr), sum of squares error (sse), r2, and adjusted r2, were 99, 99, 3.65*10-5, 1.00, and 1.00,respectively. for the avas model, the values were 100, 100, 8.81*10-3, 0.99, and 0.99,respectively. these results indicate that the ace and avas models successfully explained asignificant portion of the total variation in the data (sst) and the variation accounted for by themodel (ssr). additionally, the low sse value suggests minimal errors in the model s predictions.an r2 value of 1.000 implies that the model captures all the variability present in the data,indicating a strong fit. the ace and avas models offer several advantages over traditional linearregression models. they are flexible and powerful tools for modeling complex relationshipsbetween variables, including the ability to capture nonlinear relationships. this study demonstratesthe high potential of the ace model for regression of exponential simulated datasets, which holdsimportance in data analysis.