Authors : Mritunjay Mukherjee

Volume/Issue : Volume 10 - 2025, Issue 9 - September

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Google Scholar : https://tinyurl.com/4z5uyuk3

Scribd : https://tinyurl.com/effr5cz4

DOI : https://doi.org/10.38124/ijisrt/25sep997

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Abstract : Regression modelsform the backbone of modern statistical inference and predictive analytics.This paper presents a rigorous mathematical examination of two fundamental approaches: linear regression and logistic regression. Beginning with the formulation of each model, we derive their objective functions—the least squares criterion for linear regression and the log-likelihood for logistic regression. Closed-form solutions for linear regression are contrasted with the iterative optimization required in logistic regression, highlighting the importance of gradient-based methods. Special emphasis is placed on demonstrating how these mathematical principles can be applied to real-life datasets.

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