## 5 Results  
### Logistic Regression Model During Vehicle Start-Up  
The dependent variable adopted for the study is dichotomous in nature. To determine the threshold value for the \"ecological level of CO2 emissions\", a value of 200 g/km was accepted. A value of 0 was assigned when the emission standard was exceeded, and 1 in the opposite case. The adopted emission value of 200 g/km results from the analysis of the average age of vehicles in Poland, which is approximately 14.5 years. This means that a significant portion of the cars in use were manufactured in 2009. Therefore, the emission standards that were in force at that time are specified in Regulation (EC) No. 443/2009 of the European Parliament and of the Council of 23 April 2009, which specifies emission standards for new passenger cars as part of the European Union's integrated approach to reducing CO2 emissions from light-duty vehicles [49]. This regulation sets a mentioned CO2 emission limit of 200 g/km for manufacturers. The logistic regression model for CO2 emissions during vehicle start-up was developed first. A univariate analysis of the impact of selected quantitative variables on the modeled variable was conducted. The linearity test was utilized for this purpose. The results of the test are presented in Table 3.  
The test results indicate that, at the adopted significance level of \(\alpha=0.05\), all variables should be included in the model's construction. The estimated parameter values of the model, along with the results of the Wald test (the calculated Wald statistic and the corresponding \(p\)-value) for their significance, are presented in Table 4. \begin{table}
\begin{tabular}{c c} \hline
**AUC Value** & **Assessment** \\ \hline
0.9 \(<\) AUC \(<\) 1.0 & Excellent discrimination \\
0.8 \(<\) AUC \(<\) 0.9 & Good discrimination \\
0.7 \(<\) AUC \(<\) 0.8 & Sufficient discrimination \\
0.6 \(<\) AUC \(<\) 0.7 & Weak discrimination \\
0.5 \(<\) AUC \(<\) 0.6 & Insufficient discrimination \\ \hline \end{tabular}
\end{table} 
Table 2: AUC classification [48]. At the adopted significance level of \(\alpha=0.05\), the calculated \(p\)-values for the variables of engine power, torque, and engine speed were 0.70, 0.13, and 0.06, respectively. This indicates that there is no basis for rejecting the null hypothesis for these variables; therefore, they are not statistically significant in the model. For the remaining variables, the p-value was 0.00, which is why they were included in the model construction. The model equation takes the following forms (9) and (10):  
\[P(environmentally=1|X)=\frac{e^{a}}{1+e^{a}} \tag{9}\]  
where  
\[a=2.13+0.20\cdot V-0.11\cdot\mathrm{L}_{\%}-0.46\cdot\varphi_{\%} \tag{10}\]  
V represents vehicle velocity, \(\mathrm{L}_{\%}\) represents relative engine load, and \(\varphi_{\%}\) represents throttle position. In the next step, the goodness of fit of the model was tested based on a comparison of predicted and observed values. For this purpose, the Hosmer-Lemeshow (HS) test was used. The calculated p-value of the HS test is 0.17 and does not warrant rejection of the null hypothesis, indicating that the model is a good fit to the data. Next, the odds ratios were calculated to determine how driving with the assumed parameter values would affect eco-friendly driving (specifically, emissions of CO2 lower than 200 g/km). The sign next to the calculated parameter values indicates whether the analyzed factor is a stimulant or a destimulant of the odds of the phenomenon under study (Table 5). The calculated odds ratios indicate that during vehicle acceleration, an increase in driving velocity of 1 km/h results in a 23% increase in the probability that CO2 emissions will be below 200 g/km. In the case of relative engine load, a 1% increase leads to a 9%