Statistical Analysis of Log Transformation Effectiveness in Air Traffic Movement Forecasting During COVID-19 in South Africa

This study evaluates the effectiveness of log transformation in enhancing multiple regression models used to forecast air traffic movements (ATMs) in South Africa during the COVID-19 pandemic. Using 60 monthly observations from October 2016 to September 2021, the analysis incorporates variables such as revenue, lockdown levels, COVID-19 metrics, exchange rates, gross domestic product, and population. Two models are compared: one using raw ATMs and another with log-transformed ATMs as the dependent variable. While the untransformed model shows stronger explanatory power (R² = 0.904, adjusted R² = 0.891) compared to the log-transformed model (R² = 0.772, adjusted R² = 0.741), the latter demonstrates improved residual normality (Shapiro-Wilk p < 0.001) and homoscedasticity (Breusch-Pagan p = 0.852). Both models suffer from high multicollinearity with maximum variance inflation factors of 57.3, necessitating cautious interpretation of coefficients. The Durbin-Watson statistic indicates potential positive serial correlation in the untransformed model (1.235), while the log-transformed model shows a more acceptable value (1.842). Given the atypical and volatile nature of the pandemic data, along with limited sample size, results are restricted to in-sample fit. The study finds that log transformation can improve adherence to statistical assumptions but does not universally enhance model fit or forecasting accuracy in complex economic contexts. The study also highlights the trade-offs between interpretability, explanatory power, and statistical rigor. Recommendations for future work include exploring advanced time series and nonlinear modeling techniques.