Implementation of a MATLAB-Based Computational Framework for Multivariate Linear Regression: A Case Study on Economic Growth in Jayapura

Bobi Frans  Kuddi; Agung Dwi Saputro; Feby Seru; Caecilia Bintang Girik Allo

doi:10.36456/jstat.vol19.no1.a11451

Authors

Bobi Frans Kuddi Universitas Cenderawasih
Agung Dwi Saputro Universitas Cenderawasih
Feby Seru Universitas Cenderawasih
Caecilia Bintang Girik Allo Universitas Cenderawasih

DOI:

https://doi.org/10.36456/jstat.vol19.no1.a11451

Keywords:

Jayapura, MATLAB, Multiple Linear Regression, Nelder–Mead optimization, Ordinary Least Squares, GRDP

Abstract

Regional economic performance is an important indicator for evaluating development and public welfare. This study implemented and evaluated a MATLAB-based computational framework for parameter estimation in a multiple linear regression model of Gross Regional Domestic Product (GRDP) in Jayapura. The analysis used 15 annual observations covering the period from 2010 to 2024, with infrastructure investment, unemployment rate, and tourist arrivals as explanatory variables. The predictors were normalized using Min–Max scaling, after which the parameters were estimated using the Nelder–Mead algorithm through MATLAB’s fminsearch function and directly compared with the analytical Ordinary Least Squares (OLS) solution. Optimization stability was evaluated using six independent starting values, while model predictive performance was assessed using leave-one-out cross-validation. The results showed that OLS and Nelder–Mead produced practically identical coefficients, fitted values, and performance measures, with a maximum prediction difference of only 4.11×10^-5. All Nelder–Mead starting values converged to essentially the same minimum, with a Residual Sum of Squares range of only 8.94×10^-8. The model produced an (R^2) of 0.7705 and an adjusted (R^2) of 0.7079. Infrastructure investment had a positive and statistically significant association with GRDP, whereas unemployment and tourist arrivals had negative but statistically insignificant coefficients. The in-sample MAPE was 21.95%, while the cross-validation MAPE was 29.42%, indicating moderate predictive performance. A Durbin–Watson statistic of 0.5644 indicated positive residual autocorrelation; therefore, the inferential results should be interpreted cautiously. These findings demonstrate that Nelder–Mead does not outperform OLS for unconstrained linear regression, but it can accurately and consistently reproduce the OLS solution as a numerical validation within a MATLAB-based computational framework.

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