## 3 Results
### Estimation Based on Linear Regression  
In this subsection, we scrutinize the possibilities of a statistical learning technique, namely linear regression, to estimate the company EV, and for this aim several experiments are carried out. The real company EVs are identified as the desired output \(\mathbf{y}\), and the estimated values are represented by \(\widehat{\mathbf{y}}\) in vector form. Different input variables \(\mathbf{x}_{l}\) are explored to analyze the performance of the estimation models. We followed three steps. Firstly, we proposed a model that considered exclusively endogenous variables obtained directly or indirectly from the balance sheet and the income statement. For better performance of ML, specific variables developed in previous sections, such as previous years FCFs and the net debt, were also incorporated as entries for the model. The underling rationale was that these variables are constitutive elements of DCF, they are a-priori knowledgeable, and their incorporation could drive increased accuracy toward the solution. Secondly, we extended the experiments by incorporating exogenous variables, namely, GDP, CPI, and RIR from markets where companies operated. Although these variables were not directly linked with the business relation at the current day, they were well related to business perspectives, and so to certainly stain what companies could do in the future, with compliance with the past, hence improving or worsening the FCF. Thirdly, we analyzed endogenous and exogenous variables combined, and how this blended set of information could improve the effectiveness in fitting market valuations. Particularly in our analysis, we considered the variables previously selected and calculated for the DCF model i.e., the four designated exogenous variables from previous experiments. The training phase of the company-valuation model was done with 70% of the total sample data (677 samples), whereas the model was tested using the remaining 30% [65; 66]. The dataset was normalized in two different ways to better adjust the company-valuation model, namely, statistically and operationally. The first normalization attended to standard re-scaling for application of this set of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Sector**} & \multicolumn{4}{c}{**Technology**} & \multicolumn{4}{c}{**Utilities**} \\ \hline \multicolumn{2}{c}{**For. Est. **} & \multicolumn{2}{c}{**M11**} & \multicolumn{2}{c}{**M2**} & \multicolumn{2}{c}{**M3**} & \multicolumn{2}{c}{**M4**} & \multicolumn{2}{c}{**M5**} & \multicolumn{2}{c}{**M1**} & \multicolumn{2}{c}{**M2**} & \multicolumn{2}{c}{**M3**} & \multicolumn{2}{c}{**M4**} & \multicolumn{2}{c}{**M5**} \\ \hline \multirow{3}{*}{**Brazil**} & Mean & 8.49 \(\times\) 10\({}^{3}\) & 2.46 \(\times\) 10\({}^{3}\) & -4.83 \(\times\) 10\({}^{3}\)  
techniques, while the second one was strictly attached to the normalization against a key operational variable, namely the Earnings before Interest, Taxes, Depreciation, and Amortization (EBITDA). Figure 6 shows the real normalized EV values (in red) and the estimated ones (in blue). Panel (a) presents the results when incorporating as entry just the endogenous variables of the DCF valuation method. In Panel (b), the results for just the exogenous variables were considered, while Panel (c) incorporated both endogenous and exogenous as input variables for the analysis. Visual inspection of these three figures shows that estimates on Panel (c) better tacked the real valuations. In a second level, estimates on Panel (a) also followed up the real values to a certain extent, while the estimated EV only based on exogenous variables on Panel (b) resulted in the worst model, as expected. These visual results are consistent with expectations in all settings as the incorporation of exogenous information was supplying the model with additional prediction capabilities.