{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T10:01:31Z","timestamp":1782381691982,"version":"3.54.5"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T00:00:00Z","timestamp":1712880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We address the estimation of regression parameters for the ill-conditioned predictive linear model in this study. Traditional least squares methods often encounter challenges in yielding reliable results when there is multicollinearity. Therefore, we employ a better shrinkage method, average least squares-centered penalized regression (ALPR), as it offers a more efficient approach for handling multicollinearity than ridge regression. Additionally, we integrate ALPR with the principal component (PC) dimension reduction method for enhanced performance. We compared the proposed PCALPR estimation technique with existing ones for ill-conditioned problems through comprehensive simulations and real-life data analyses using the mean squared error. This integration results in superior model performance compared to other methods, highlighting the potential of combining dimensionality reduction techniques with penalized regression for enhanced model predictions.<\/jats:p>","DOI":"10.3390\/sym16040469","type":"journal-article","created":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T09:28:06Z","timestamp":1712914086000},"page":"469","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Enhanced Model Predictions through Principal Components and Average Least Squares-Centered Penalized Regression"],"prefix":"10.3390","volume":"16","author":[{"given":"Adewale F.","family":"Lukman","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of North Dakota, Grand Forks, ND 58202, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7920-6866","authenticated-orcid":false,"given":"Emmanuel T.","family":"Adewuyi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-4020-6647","authenticated-orcid":false,"given":"Ohud A.","family":"Alqasem","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5881-9241","authenticated-orcid":false,"given":"Mohammad","family":"Arashi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6194-6199","authenticated-orcid":false,"given":"Kayode","family":"Ayinde","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Northwest Missouri State University, Maryville, MO 64468, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2217","DOI":"10.1080\/03610928308828603","article-title":"Regression analysis with multicollinear predictor variables: Definition, detection, and effects","volume":"12","author":"Gunst","year":"1983","journal-title":"Commun. 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