Multiple Regression Modelling With Excess Zeros in the Dependent Variable

In many real-world datasets, especially in retail sales, dependent variables often contain a high proportion of zero values due to factors such as stockouts, seasonal effects, or customer inaction. Traditional regression techniques like Ordinary Least Squares (OLS) fail to adequately handle such excess zeros, potentially leading to biased estimates and flawed inferences. This study investigates the comparative effectiveness of the OLS and Tobit regression models in analysing retail sales data characterized by excess zeros. Using a secondary dataset of 1,000 customer transactions from a retail store, sourced from Kaggle, the analysis evaluates both models across varying levels of zero prevalence (0%–90%). Model performance is assessed using metrics including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and log-likelihood. Results reveal that as the proportion of zeros increases, the Tobit model consistently outperforms OLS, offering more accurate and interpretable estimates. Key predictors such as unit price, quantity purchased, and customer rating were identified as significant drivers of sales under the Tobit framework. The findings underscore the importance of selecting appropriate regression models for censored or excess zero datasets and provide practical insights for analysts and decision makers in retail and related sector.