## 5 Results
### Regression Analysis Results
In the case of the multiple regression for amplitude level, it can be seen that the explanation strength of the model is very high; see Figure 6--top/right. On the contrary, \(\Delta\)t cannot be explained by the regression model at all. Meanwhile, the explanation strength of the regression model for \(\Delta\)t was equal to zero, and the _Pulse start_ variable might be completely described by the following regression model; see Figures 6-8 and 9A. Good explanation strength of the regression model was achieved for the _Amplitude Slope_; see Figures 6-8 and 9B. Both the _Amplitude Start_ and _UART Amplitude Start_ variables showed very high explanation strength in terms of multiple regression models; see Figures 6-8 and 9C,D. On the contrary, the offset value, typically 0.007 mV for most of the experimental conditions, revealed that there was no statistically significant relation between the offset value and the input variables (motor oil level and temperature). Detailed information about the measured values can be found in Table 4.  
Experimental data related to the \(\Delta\)t, amplitude starts from the level, slope of the level amplitude, and amplitude from the reference were selected according to the motor oil level in the level measurement device. Data were tested by one-way ANOVA (equal variances were not assumed). There are no statistically significant differences among the \(\Delta\)t groups. Amplitude start from the oil level revealed statistically significant differences for the two  
Figure 6: Relationships between X and Y variables. _Pulse_ (**A**), _Amplitude Slope_ (**B**), _Amplitude Start_ (**C**), _UART Amplitude Start_ (**D**). Figure 7: Results of multiple regression models with X variables. _Pulse_ (**A**), _Amplitude Slope_ (**B**), _Amplitude Start_ (**C**), _UART Amplitude Start_ (**D**). pairs 30-90 mm and 30-60 mm. Moreover, the slope exhibited a significantly different pair of variables (30-90 mm). Finally, amplitude from the reference did not show any statistically significant difference among all three groups. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Signal** & **Unit** & **Meaning** \\ \hline _Level_ & mm & This is the actual level of the measured oil. \\ _AmplitudeLev_ & mV & It is an echo echo amplitude of the ultrasonic signal reflected from the oil surface. It is the maximum measured value on the receiving piezo element. \\ _AmpStart_ (C) & us & This is the time delay calculated from the moment the ultrasonic signal is sent from the exciter to its return. It is the time of flight of the ultrasonic signal that is measured by the oscilloscope. \\ _Slope_ (B) & mV/ μs & This is the steepness of the front of the reflected ultrasonic signal. \\ _UARTAmpStart_ (D) & us & This is the time delay calculated from the moment the ultrasonic signal is sent from the exciter to its return. It is the time of flight of the ultrasonic signal, which is measured by the microprocessor from the discretized ultrasonic signal. \\ _Pulse_ (A) & us & This is the time length of the discretized received echo of the ultrasonic signal. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Description of measured parameters. Figure 8: Model building sequence—order of adding or removing terms. _Pulse_ (**A**), _Amplitude Slope_ (**B**), _Amplitude Start_ (**C**), _UART Amplitude Start_ (**D**). Figure 9: Model building sequence—bars represent contribution. _Pulse_ (**A**), _Amplitude Slope_ (**B**), _Amplitude Start_ (**C**), _UART Amplitude Start_ (**D**). Time of flight is a measured parameter that represents the time interval from the emission of the initial burst until the reception of the leading edge of the corresponding echo signal. Precise measurement of oil level is critical to maintain the requisite tolerance bands in a real-world setting, particularly under degraded measurement conditions.