A multiple linear regression model with multiplicative log-normal error term for atmospheric concentration data.

Area of Science:

• Environmental Science
• Atmospheric Chemistry
• Statistical Modeling

Background:

• Homoscedasticity is a critical assumption in Ordinary Linear Squares (OLS) regression.
• The OLS method was applied to model black carbon concentrations at 12 Chinese monitoring sites.
• Residual analysis revealed significant heteroscedasticity in 11 out of 12 datasets using the Breusch-Pagan test.

Purpose of the Study:

• To address heteroscedasticity in black carbon concentration modeling.
• To develop a more robust regression method for atmospheric data.
• To improve the accuracy of source contribution estimations.

Main Methods:

• A hybrid modeling approach was used for black carbon source attribution.
• A novel assumption of multiplicative, log-normally distributed error terms was introduced.
• Maximum Likelihood Estimation (MLE) was employed to determine regression coefficients.

Main Results:

• The revised MLE method showed good agreement with residual distribution in 8 out of 12 datasets.
• The MLE computation was mathematically simplified by minimizing a log-scale objective function.
• Numerical simulations demonstrated superior accuracy and coverage probability compared to OLS and Weighted Least Squares (WLS).

Conclusions:

• The novel MLE approach effectively handles heteroscedasticity in log-normally distributed atmospheric data.
• This method offers significant improvements in regression coefficient estimation accuracy.
• The findings have implications for accurate source apportionment of black carbon concentrations.