Linear Regression in the Spotlight: From Statistical Staple to Misused Tool

Abstract

This article explores the application, assumptions, and frequent misuses of linear regression
analysis in research, particularly within the business, social sciences and medical fields. While
linear regression remains one of the most widely used and accessible statistical tools due to its
simplicity and interpretability, it is often misapplied, especially when researchers overlook the
foundational assumptions required for valid inferences. The paper reviews the key assumptions of
linearity, normality, homoscedasticity, and independence of errors, and discusses the appropriate
use of linear regression in descriptive, predictive, and causal research. Through a critical review
of published studies and an empirical analysis of customer satisfaction data from Kaggle, the
article identifies common violations, including the inappropriate modelling of discrete and ordinal
dependent variables, unjustified covariate adjustments, and misinterpretation of regression
coefficients. Residual plots and diagnostic tests further reveal that linear regression is frequently
applied where it is not suitable, leading to misleading conclusions. The study concludes with
practical recommendations to improve statistical literacy and rigor among researchers,
emphasizing the importance of involving statisticians and aligning statistical instruction with
domain-specific research contexts.