# Influence of Atmospheric Pollutants and Weather Conditions on Agricultural Productivity in Italy
## 2 Materials and Methods
### Analysis  
For the data fitting (pollutant concentration, millimeters of rain, and annual crop production considered in the crop life cycle period), a linear regression model was used in the first analysis. Using the relationship found, the effective crops production affected by the pollutants was calculated. The linear regression model showed very weak values of the Pearson coefficient, calculated for each pollutant, indicating poor data linearity. Therefore, a quadratic regression of the type was used to fit the data which gave the best results. The coefficients of the quadratic curve are reported in Table 10. Since the R\({}^{2}\) values are in some cases very low, they are better than the linear ones found in the first analysis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **a** & **b** & **c** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{Padua} & \multirow{4}{*}{Corn} & PM10 & \(-265.1\) & \(16\),\(072\) & \(-2.0\times 10^{6}\) & \(0.28\) \\  & & O\({}_{3}\) & \(-151.13\) & \(12\),\(627\) & \(2.0\times 10^{5}\) & \(0.16\) \\  & & NO\({}_{2}\) & \(163.94\) & \(-3658.3\) & \(3.0\times 10^{5}\) & \(0.10\) \\  & & SO\({}_{2}\) & \(143,438\) & \(-1.0\times 10^{6}\) & \(3.0\times 10^{6}\) & \(0.17\) \\ \cline{2-6}  & \multirow{4}{*}{Durum} & PM10 & \(-466.77\) & \(28\),\(497\) & \(-3.0\times 10^{5}\) & \(0.27\) \\  & & O\({}_{3}\) & \(-37.943\) & \(3605.2\) & \(5.3\times 10^{3}\) & \(0.44\) \\  & & NO\({}_{2}\) & \(487.44\) & \(-32\),\(116\) & \(6.4\times 10^{5}\) & \(0.36\) \\  & & SO\({}_{2}\) & \(-61,445\) & \(453,088\) & \(-7.0\times 10^{5}\) & \(0.07\) \\ \hline \multirow{4}{*}{Venice} & \multirow{4}{*}{Corn} & PM10 & \(-3623.8\) & \(221\),\(392\) & \(-3.0\times 10^{6}\) & \(0.50\) \\  & & O\({}_{3}\) & \(6991.5\) & \(-652,581\) & \(2.0\times 10^{7}\) & \(0.12\) \\  & & NO\({}_{2}\) & \(-3509.8\) & \(215,512\) & \(-3.0\times 10^{6}\) & \(0.17\) \\  & & SO\({}_{2}\) & \(-629,932\) & \(4.0\times 10^{6}\) & \(-7.0\times 10^{6}\) & \(0.13\) \\ \hline \multirow{4}{*}{Ferrara} & Common & PM10 & \(1372.9\) & \(-88\),\(888\) & \(2.0\times 10^{6}\) & \(0.50\) \\  & wheat & O\({}_{3}\) & \(-2488.7\) & \(237,538\) & \(-5.0\times 10^{6}\) & \(0.20\) \\  & & NO\({}_{2}\) & \(423.13\) & \(-33,148\) & \(8.3\times 10^{5}\) & \(0.35\) \\ \hline \multirow{4}{*}{Palermo} & Durum & PM10 & \(-384.63\) & \(19\),\(788\) & \(-3.5\times 10^{4}\) & \(0.14\) \\  & wheat & O\({}_{3}\) & \(-30.273\) & \(3706.7\) & \(1.0\times 10^{5}\) & \(0.10\) \\  & & SO\({}_{2}\) & \(-489.76\) & \(5.15\times 10^{3}\) & \(2.0\times 10^{5}\) & \(0.17\) \\ \hline \multirow{4}{*}{Bari} & Durum & PM10 & \(-5015.7\) & \(229\),\(396\) & \(-3.0\times 10^{6}\) & \(0.68\) \\  & & O\({}_{3}\) & \(-570.38\) & \(59\),\(382\) & \(-1.0\times 10^{6}\) & \(0.80\) \\  & wheat & NO\({}_{2}\) & \(23.684\) & \(-1390.1\) & \(9.8\times 10^{4}\) & \(0.10\) \\ \hline \end{tabular}
\end{table} 
Table 10: Quadratic correlation coefficients. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Rain, mm** & \\ \cline{2-4}  & **Padua** & **Venice** \\ \hline
2012 & 851.6 & 748.4 \\
2013 & 800.0 & 790.8 \\
2014 & 849.7 & 858.2 \\
2015 & 536.5 & 577.9 \\
2016 & 767.5 & 783.6 \\
2017 & 707.3 & 739.1 \\
2018 & 671.8 & 736.0 \\
2019 & 1045.3 & 982.8 \\
2020 & 647.0 & 702.9 \\
2021 & 713.6 & 621.8 \\
2022 & 523.5 & 603.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Millimeters of rain measured in the considered Italian cities in the period April–November 2012–2022. For subsequent analysis of significance between crops and air quality, a one-way analysis of variance (ANOVA) was performed. The ANOVA was necessary to verify if any variations or different levels of the independent variable (concentration of pollutants and millimeters of rain) affect the dependent variable (production) through a measurable effect and if at least one pair of means has significant differences.