## 3 Results
### Prediction of the Number of Orders--Exponential Smoothing
In total, 33 time series simulations were conducted, each spanning 21 months (with a three-month delay for the initial forecast). The total number of regular forecasts was 693, with an additional 33 weekend forecasts. Figure 4 provides a few examples of individual forecasts. A prediction plot with confidence intervals overlaid on plotted historical data from the same period is shown in Figure 4. The forecasts were calculated based on data from two \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **TEST\_CODE** & **NAME** & **Number of Tests** \\ \hline
1 & 100 & TSH & 1,364,261 \\
2 & 20 & ALT & 858,255 \\
3 & 61 & CRP & 763,815 \\
4 & 21 & AST & 581,132 \\
5 & 101 & FT4 & 483,112 \\
6 & 13 & Potassium & 465,509 \\
7 & 40 & Iron & 335,365 \\
8 & 12 & Sodium & 287,343 \\
9 & 114 & Prolactin & 102,062 \\
10 & 112 & Estradiol & 72,785 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
43 & 116 & Beta-HCG & 55,689 \\ \hline \end{tabular}
\end{table} 
Table 1: Number of tests on individual parameters. Figure 4: A few examples of individual time series simulations. The blue line indicates the actual course, while the bold orange line indicates the forecast, while the thinner orange lines indicate the confidence interval. three-month periods from each of the three previous years; therefore, the timeline (x-axis) cannot be regarded as a continuous range but rather as individual measurement points. Each of the plots depicts the trend and prediction for a different examined parameter. It can be observed that at some points, the prediction lags by one time step from the historical data; however, the confidence intervals cover the variability quite well, especially considering that the studied period includes the time of the pandemic. It is also worth noting that the period during which the models were examined coincided with the pandemic, which disrupted the blood research market, affecting its dynamics. Table 2 presents the results of forecasts for 11 factors, including the 10 most commonly performed plus bHCG, over a six-month period. The forecasts were calculated based on data from two three-month periods from each of the three previous years during the same periods of the year. The table compares the averages and standard deviations of these samples. The Mean Absolute Percentage Error (MAPE) is the percentage error calculated separately for each parameter within a given set of forecasts and then averaged. The MAPE value of 2.16% indicates the precision of the models. Figure 5 shows a scatter plot of the model predictions compared to the observed order quantities. Figure 5 shows a graphical representation where, on the Y axis, we have the predictions made by a model and, on the X axis, we have the actual observed quantities of orders. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **No. of Tests (Parameters)** & **11** \\ \hline RSS & Residual Sum of Squares & 4,711,975 \\ MAE & Mean Absolute Error & 1559 \\ RMSE & Relative Mean Square Error & 0.01 \\ d & Relative Average Deviation & 0.08 \\ r & Correlation Coefficient & 0.99 \\ R\({}^{2}\) & Determination Coefficient & 0.98 \\ MAPE & Mean Absolute Percentage Error & 2.16\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results regarding the number of forecasts and the corresponding parameters. Figure 5: A scatter plot of model predictions against observed order quantities. The blue dots indicates the actual values, while the red line indicates the predicted model, while the dotted red lines indicate the confidence interval. Lines representing confidence intervals in a scatter plot indicate the range within which the true values of the data points are likely to fall with a 90% level of confidence. In other words, they provide an estimation of the uncertainty associated with the predicted values. Typically, the narrower the confidence interval, the more precise the predictions are considered to be.