# Modeling Soil Temperature with Fuzzy Logic and Supervised Learning Methods
## 3 Results
### Statistical Outcomes Derived from MLR Analysis  
The MLR model demonstrated satisfactory performance in predicting soil temperature, exhibiting both statistical significance and adequate explanatory power. The detailed model parameters and results are presented in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Soil Depth (cm)**} & \multicolumn{4}{c}{**2016–2021 (Training)**} & \multicolumn{4}{c}{**2022–2024 (Testing)**} \\ \cline{3-6}  & & \multicolumn{4}{c}{**Temperature (\({}^{\circ}\)C)**} \\ \cline{3-6}  & & **Air** & **Soil** & **Air** & **Soil** \\ \hline \multirow{6}{*}{5} & Avg & \(13.74\) & \(14.54\) & \(13.78\) & \(15.85\) \\  & Min & \(1.15\) & \(-1.80\) & \(1.73\) & \(2.36\) \\  & Max & \(25.08\) & \(31.74\) & \(25.59\) & \(33.48\) \\  & SE & \(0.92\) & \(1.14\) & \(1.27\) & \(1.63\) \\  & SD & \(7.50\) & \(9.27\) & \(7.64\) & \(9.80\) \\  & Sk & \(-1.42\) & \(-1.38\) & \(-1.33\) & \(-1.25\) \\  & Kr & \(-0.03\) & \(0.15\) & \(-0.05\) & \(0.28\) \\ \hline \multirow{6}{*}{10} & Avg & \(13.74\) & \(14.99\) & \(13.78\) & \(15.93\) \\  & Min & \(1.15\) & \(0.97\) & \(1.73\) & \(2.89\) \\  & Max & \(25.08\) & \(30.99\) & \(25.59\) & \(31.92\) \\  & SE & \(0.87\) & \(1.03\) & \(1.27\) & \(1.58\) \\  & SD & \(7.40\) & \(8.77\) & \(7.64\) & \(9.47\) \\  & Sk & \(-1.39\) & \(-1.46\) & \(-1.33\) & \(-1.32\) \\  & Kr & \(-0.05\) & \(0.11\) & \(-0.05\) & \(0.24\) \\ \hline \multirow{6}{*}{20} & Avg & \(13.74\) & \(14.97\) & \(13.78\) & \(15.81\) \\  & Min & \(1.15\) & \(2.40\) & \(1.73\) & \(3.73\) \\  & Max & \(25.08\) & \(29.29\) & \(25.59\) & \(30.10\) \\  & SE & \(0.87\) & \(0.96\) & \(1.27\) & \(1.47\) \\  & SD & \(7.40\) & \(8.11\) & \(7.64\) & \(8.80\) \\  & Sk & \(-1.39\) & \(-1.50\) & \(-1.33\) & \(-1.37\) \\  & Kr & \(-0.05\) & \(0.09\) & \(-0.05\) & \(0.21\) \\ \hline \multirow{6}{*}{50} & Avg & \(13.74\) & \(14.98\) & \(13.78\) & \(15.73\) \\  & Min & \(1.15\) & \(4.78\) & \(1.73\) & \(5.32\) \\  & Max & \(25.08\) & \(26.43\) & \(25.59\) & \(27.73\) \\  & SE & \(0.87\) & \(0.78\) & \(1.27\) & \(1.23\) \\  & SD & \(7.40\) & \(6.60\) & \(7.64\) & \(7.37\) \\  & Sk & \(-1.39\) & \(-1.48\) & \(-1.33\) & \(-1.38\) \\  & Kr & \(-0.05\) & \(0.09\) & \(-0.05\) & \(0.17\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of input and output variables. All variables in the model are statistically significant (at the 1% significance level). With a coefficient value of 1.224 and a \(t\)-value of 57.597, the average air temperature is the most important determining variable in the model. While the variable depth contributes positively to soil temperature with a positive coefficient (0.097), the negative coefficient (\(-\)0.007) of the interaction term depth-temperature indicates that the temperature increase slows down with depth. This situation shows that the effect of air temperature decreases, especially in deep layers. The general significance of the model was confirmed with F = 1563.45 and \(p\) \(<\) 0.01. The explanatory power of the model is quite high with an R\({}^{2}\) value of 0.931 and an adjusted R\({}^{2}\) value (R\({}^{2}_{\text{adi}}\)) of 0.93. These results show that about 93% of the total change in soil temperature is explained by the model. The error measurements of the model for the training and test periods are shown in Table 3. In the training set, the MAE is 1.54 \({}^{\circ}\)C, the RMSE is 2.00 \({}^{\circ}\)C, and the R\({}^{2}\) value is 0.93. In the testing set, these values are 1.89 \({}^{\circ}\)C (MAE), 2.33 \({}^{\circ}\)C (RMSE), and 0.94 (R\({}^{2}\)), respectively. No significant loss of performance was observed between the training and testing periods, indicating that the generalization ability of the model is strong and that there is no overfitting problem. This MLR model, developed for the province of Tokat, is able to provide very accurate predictions of soil temperature, especially considering key variables such as air temperature and depth.