Log Normal Regression and its Application

Log Normal Regression and its Application Ni Luh Sri Diantini1, Calvin Riswandi1 1Statistics Department Matana University Email: [email protected], [email protected] Received: 19 December 2024, revised: 17 March 2025, accepted: 24 March 2025 Abstract The log-normal distribution represents a type of continuous probability distribution that is characterized by a positive skew, which signifies a long tail on the right. A log-normal distribution describes a statistical distribution of values that have been logarithmically transformed from a related normal distribution. In situations where predictor variables affect positive outcomes, log-normal regression becomes significant. This research will construct a regression model that utilizes a continuous response variable following a log-normal distribution, known as log-normal regression (LNR). The purpose of developing the LNR model is to overcome the assumptions in classical regression that are often unmet, such as normality, since not all data can full fill these assumptions. Therefore, need an alternative method that does not require the normality assumption. One method that can be employed is a regression with a specific distribution approach, such as the log-normal distribution, known as log-normal regression. The LNR model will be developed through the maximum likelihood estimation (MLE) approach to achieve parameter estimation using a numerical method based on the Newton-Raphson iteration. Following this, hypothesis testing will be performed using the maximum likelihood ratio test (MLRT) and a partial test that employs the Wald test. The ultimate objective of this research is to illustrate how to apply the proposed LNR model to real data. LNR model will be applied to analysis the number of poor people in Indonesia, examining the factors that contribute to this issue. The results obtained in this study that variables human development index, unemployment rate, percentage of gross regional domestic product, and minimum wage in provinces influencing significance the number of poor people in Indonesia.