## 4 Results and Discussion
### Level 3: Machine Learning
#### 4.3.2 Linear Regression and Univariate Polynomial Regression  
These methodologies have been applied to build models that predict total CO\({}_{2}\) emissions and fuel consumption of vehicles from a single input (engine size, or the number of cylinders, etc.), and the result is presented in Table 12 and Figure 18.  
The coefficient of determination is ranged from 1 to 10, from worst to perfect prediction. It can be seen from Table 12 that the Univariate Polynomial Regression Degree 5 model achieves the highest coefficient of determination (R squared) in 7 out of 10 scenarios. Being  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Predictor**} & \multirow{2}{*}{**Target**} & \multirow{2}{*}{**Linear Regression**} & \multicolumn{6}{c}{**Univariate Polynomial Regression**} \\ \cline{3-8}  & & & **Degree 1** & **Degree 2** & **Degree 3** & **Degree 4** & **Degree 5** \\ \hline Engine Size & Total & 0.67594 & 0.67570 & 0.68466 & 0.68611 & 0.69022 & **0.69038** \\ Cylinders & Fuel Con & **0.66161** & 0.64166 & 0.65108 & 0.65165 & 0.65595 & 0.6596 \\ Fuel Consumption in City & sumption & 0.98443 & 0.98606 & 0.98606 & 0.98624 & 0.98626 & **0.98626** \\ Fuel Consumption in Highway & (L/100 & 0.4780) & 0.94701 & 0.94778 & 0.94793 & 0.94790 & **0.94794** \\ CO\({}_{2}\) Emissions & km) & **0.89053** & 0.88828 & 0.88851 & 0.8889 & 0.8894 & 0.88894 \\ \hline Engine Size & CO\({}_{2}\) & **0.72950** & 0.70852 & 0.71446 & 0.72162 & 0.72480 & 0.72552 \\ Cylinders & Emise- & 0.67752 & 0.69280 & 0.69839 & 0.69926 & 0.70195 & **0.70195** \\ Fuel Consumption in City & sions & 0.88922 & 0.88654 & 0.89650 & 0.89724 & 0.90846 & **0.99886** \\ Fuel Consumption in Highway & (g/km) & 0.82471 & 0.82107 & 0.84835 & 0.84839 & 0.85369 & **0.85448** \\ Total Fuel Consumption & & 0.88753 & 0.88828 & 0.90243 & 0.90289 & 0.91193 & **0.91215** \\ \hline \hline \end{tabular}
\end{table}
Table 12: Coefficient of determination (R squared) values of Linear Regression and Univariate Polynomial Regression models.  
Figure 17: Prediction results of different regression models.  
insignificantly different from it, the Linear Regression almost attains the same R squared value and at the same time, obtains the highest in 3 out of 10 scenarios.  
3.3 Multiple Linear Regression, Logarithmic Regression, Multivariate Polynomial Regression, Transformation of Data, and Exponential Regression  
These models are selected to estimate total CO\({}_{2}\) emissions and fuel consumption of vehicles from multiple inputs, and the result is presented in Table 13.  
Table 13 shows that in 3 out of 5 cases, the Multiple Linear Regression model has the largest coefficient of decision (R squared). Despite being insignificantly different from it, the Linear Regression comes close to attaining the same R squared value and also achieves the best score in 2 out of 5 scenarios (at Degree 2 and 5). On the other hand, the Logarithmic Regression with Log Transformation model receives lower determination scores in all scenarios. Notably, the Logarithmic Regression with Exponential Transformation model generates negative R squared values in all cases, implying that the goodness of fit level is worse than fitting the curve of the model.  
Figure 18: Scatterplot of prediction outputs of Linear Regression model in different scenarios.  
In this subsection, different Machine Learning models are applied to use vehicle specifications data for fuel consumption and carbon dioxide emission estimation. It is recognized that Linear Regression, Multiple Linear Regression, Univariate Polynomial Regression, and Multivariate Polynomial Regression are very potential in this field, which answered the research question RQ3.2.