## 3 Results
### Class IV NYHA HF-MPV Relationship  
Based on the logistic regression model, the estimated coefficients for which are presented in Table 1, we can predict the probability of a patient having class IV NYHA HF given the MPV value. This model aims to show how MPV predicts class IV NYHA HF in terms of the probability or chance that this event would happen. The pseudo R-square (in this case 0.054), adapted from the classic R-square from linear regression, refers to how much of the variability of an event, represented in this case by class IV NYHA HF, is explained by the independent variable--MPV, here indicating that 5.4% of the event variability represented by NYHA class IV HF was influenced by MPV variability. The model is: score (of class IV NYHA HF happening) = \(-7.1912\) + \(0.779\)\(\times\) MPV. Starting from this model, let us assume that we have a patient 1 who has an MPV of 7 fl and a patient 2 who has an MPV of 9 fl. By applying the above-mentioned mathematical formula, the results are: the score for patient \(1\) = \(-7.1912\) + \(0.779\)\(\times\) 7 = \(-1.73\), and the score for patient \(2\) = \(-7.1912\) + \(0.779\)\(\times\) 9 = \(-0.1802\)  
Because the values of \(-1.73\) and \(-0.1802\) do not give us much information in terms of interpretability, we can convert the score into probabilities, applying the following equation: \(\mathbf{p}=\frac{\mathbf{1}}{1+\mathbf{e}^{\kappa\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\bmbm{ }}}}}}}}}}}}}}}}\). So, the probability for patient 1 is 0.15, which means a 15% chance of having class IV NYHA HF, versus patient 2 whose probability is 0.45, which means a 45% chance of having class IV NYHA HF. The coefficient for MPV is 0.779 and reflects how much or to what extent it affects patients with class IV NYHA HF. The \(p\)-value associated with this coefficient is 0.000; therefore, it can be deduced that the mathematical model described and applied above is significant because it is below the 0.05 \(p\)-value threshold. Thus, we have evidence to believe that the impact of MPV is only true for our sample data, but applies to all the population. Starting from the arguments above, it can be said that, depending on the MPV value, we can predict the probability of having class IV NYHA HF, and that a patient with a higher MPV value has a higher probability of having class IV NYHA HF. These data are shown more clearly in Figure 1, in which three graphs are shown, as well as in Figure 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dep.** & **NYHA_IV_HF** &
\begin{tabular}{c} **No.** \\ **Observations:** \\ \end{tabular} & **260** & \\ \hline Model: & Logit & Df Residuals: & 258 & \\ Method: & MLE & Df Model: & 1 & \\  & & Pseudo R-squ.: & 0.05471 & \\ Converged: & TRUE & LL-Null: & \(-178.71\) & \\ \hline  & coef & std err & z & \(p>1\,\mathrm{z}\,\mathrm{i}\) & [0.025 & 0.975] \\ \hline Intercept & \(-7.1912\) & \(1.67\) & \(-4.307\) & \(0\) & \(-10.464\) & \(-3.919\) \\ MPV & \(0.779\) & \(0.186\) & \(4.196\) & \(0\) & \(0.415\) & \(1.143\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Logistic regression applied to patients with class IV NYHA HF based on MPV value. In all three graphic representations of Figure 1, it can be observed that patients with class IV NYHA HF (1) tended to have a higher MPV value (over 9 fl) compared to those without class IV NYHA HF (0) who had MPV values below 9 fl. Figure 2, which represents the probability of having class IV NYHA HF based on the MPV value by applying the logistic regression model, shows that as the MPV value increased, the probability of patients having class IV NYHA HF also increased. For instance, patients with an MPV of 9 fl had a 45% probability of having class IV NYHA HF, whereas patients with an MPV of 7 fl had a 15% probability of having class IV NYHA HF. Figure 1: MPV value in patients with class IV NYHA HF (1) versus patients without class IV NYHA HF (0).