## 5 Results and Discussion
### Analysis on Performance Indexes (Regression) Supported in SVM--Dot Model  
Performance index operators were used to test the regression task with statistical performance and provided a list of the regression task's accuracy criteria values. The operator output (regression) was selected as it decides the type of learning task and measures the most common requirements for that category automatically. Regression operation is also a method used for numerical analysis and is a statistical measure that evaluates the intensity of the relationship between a dependent variable (label attribute) and a set of other changing variables known as independent variables (regular attributes). This type of operator has been constantly used in previous studies to evaluate specific factors, such as commodity price, interest rates, and certain industries, that affect the price movement of an asset [91; 92; 93]. To evaluate the statistical efficiency of the regression model, the dataset must be labeled and must have a label function attribute and a predictive role attribute. The attribute of the label stores the actual observed values, and the attribute of the prediction stores the label values predicted by the regression model under discussion. For this research, three types of index regression (as in Table 5) were used to refine and reduce the difference/gap between measured and predicted crack widths, and are shown in Figure 13.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No** & **Parameter** & **Description** \\ \hline
1. & Absolute error (AE) & AE is determined by adding the variance of all expected values from the label attribute’s actual values and dividing the amount by the total number of predictions. PA is determined by adding all the real label values and dividing the total number of examples by this figure. RMSE is a quadratic scoring method calculating the error’s average magnitude. It is the cumulative square root of variations between predictive and real observation. \\ \hline \hline \end{tabular}
\end{table}
Table 5: Types of performance index (regression) used for SVM—dot model.  
From the above figure, RMSE can be seen to exhibit a more consistent standard deviation of residuals (prediction errors) up to 5%, approaching actual crack widths compared to AE (26-37%) and PA (50%). The inconsistent prediction performance was found over-fitting in the case of AE and under-fitting in the case of PA from the reference lines, respectively. The extent of error found in the prediction model associated with AE and PA may be considered from the point of view of accuracy. The accuracy of measurement reflects the error or variance of the measurement from the average of a large number of measurements of the same quantity, whereas the precision of a measured value expresses the deviation of the measurement from the real quantity value. Error is viewed from the point of view of precision when the true value is known, but it must be used instead of accuracy when the true value of a quantity is not known. Accuracy cannot be achieved if the precision cannot be reached; however, precision does not guarantee accuracy. Residuals were calculated as to how far the data points were from the regression line; RMSE was assessed as to how these residuals were spread out. In other words, it shows how clustered the data is around the best fit axis, thus supporting the argument through a previous study in which RMSE was able to avoid over-fitting in positive identification [62; 65]. This parameter of the RMSE index is, therefore, a simple, quick, and reliable metric compared to other parameters, widely used in climate analysis, forecasting, and regression to validate experimental results [50; 64; 94].  
Figure 13: The distribution of predicted crack width for: (**a**) Absolute error (AE), (**b**) prediction average (AE), and (**c**) root mean square error (RMSE).