## 4 Results of the Measurements and Analyses
### Regression Analysis  
The regression equation allows you to verify one of the hypotheses: the zero hypothesis (H0), which assumes no influence of the explanatory variable (x) on the dependent variable (y), and the alternative hypothesis (H1), formulated as \"it is not true that H0\" and saying that the variable (x) has an influence on the variable (y). The decision regarding whether one of the hypotheses is true is made on the basis of the parameter _p_-value. If _p_-value > 0.05 (5%) then the risk of making a rejection error H0 is too high and we assume that H0 is true. In the opposite case (_p_-value < 0.05), we obtain the statistical evidence of the dependence (H1).  
In the conducted tests, the linear regression equation [40], described in the Minitab program, was used in order to check and illustrate the existing relationships between the thermal parameters of the tested transistors and the size of the voids occurring while soldering these devices. In this equation, the regression line y = ax + b expresses the prediction of the dependent variable (y) for the given independent variables (x). In the conducted analyses, the value of the variable (y) corresponds to the changes in the Rth value, while the value of the variable (x) corresponds to the measured void sizes in the soldering area of the TR_A and TR_B transistors' source in all their positions on the PCB laminate. In this way, predictions were made about how the discussed parameters will behave in relation to each other. The results of such analyses are shown in Figure 5.  
Figure 5a shows a graph of the linear regression analysis, revealing the dependence of the determined resistance Rth obtained from the measurements of the temperature measured through the cross-section of the TR_A transistor case [24] on the sum of the voids in the soldering area of its source \"S\" at the dissipated power P = 21.5 W. The obtained points in the area of the designated straight line are scattered randomly. The value of parameter _p_-value = 0.696, i.e., at the level of 70% (> 5%), does not allow for the rejection of the H0 hypothesis and confirms that the changes in the size of the void do not affect the values of the thermal resistance Rth.  
Similarly, for the same transistor TR_A, the regression analysis was performed by checking the influence of the size of individual voids on the value of thermal resistance Rth, which is presented in Figure 5b. Here, too, no relationships were found between the studied quantities to write down the essence of the function Rth = f(Individual Voids). In this case, the _p_-value was 0.64.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Module**} & **Transistor** & **Total** & **Max Individual** & **T\({}_{\text{emp1}}\)** & **T\({}_{\text{emp2}}\)** & **T\({}_{\text{emp min}}\)** & **R\({}_{\text{th T1}}\)** & **R\({}_{\text{th min}}\)** & **R\({}_{\text{th T2}}\)** & **R\({}_{\text{th T2}}\)** \\  & **Position** & **Voids** [\%] & **Soldering Area** [\%] & [\({}^{\circ}\)C] & [\({}^{\circ}\)C] & [\({}^{\circ}\)C] & [K/W] & [K/W] & [K/W] & [K/W] \\ \hline PCB1 & 1 & 18 & 12.7 & 83.5 & 78 & 78 & 2.509 & 2.256 & 2.256 & 2.383 \\  
The same conclusions can be made by analyzing the relationship of the void sizes for the TR_B transistor [23], which are respectively shown in Figure 5c,d. The analyses carried out with the use of the regression function show that the value of the total area of the void spaces and the individual area of each of the voids in the soldering area of the transistor source does not translate into the results of the determined thermal resistance Rth.