# Partially versus Purely Data-Driven Approaches in SARS-CoV-2 Prediction
## 4 Results  
### Linear Regression Model Results  
A linear trend model is computed for the sum of confirmed, new, and death cases (actual and forecast) given date of day. The confidence level is taken at 95%, so the model is significant at \(p\leq 0.05\); the results of applying the linear regression model for US, Jordan, and Italy are shown in Table 1.  
Figure 6: SIR (Susceptible, Infected, and Removed) Model Components. As shown in Table 1, SSE is the sum of the squared differences between each point and its group point's mean; it shows how variant each point is from the others. The results in Table 1 show very high variants in the three selected countries, which indicate that the confirmed, new, and death cases vary randomly in all countries, with the lowest value in Jordan death cases. MSE shows the difference between the predicted and actual values; the lowest rate is shown in Jordan death cases (i.e., 12.5). \(R^{2}\) is calculated as the sum of squared errors, divided by the total sum of squared errors, as shown in Equation (6):  
\[R^{2}=\frac{SSM}{SST} \tag{6}\]  
The larger \(R^{2}\) means the ability of the predictor to predict the dependent variable. R-squared is maximum in Jordan, US, and Italy confirmed cases, respectively. This demonstrates that the time variable is a very good predictable variable for the confirmed cases being more than new and death cases. For example, 97% of the confirmed cases in Jordan can be predicted using the independent variable (time). \(p\) value \(<\) 0.05 indicates that the overall model is significant. The result shows significant models in all countries' confirmed, death, and new cases, except for the death cases model in Jordan, which means the model cannot be considered. However, the null hypothesis that assumes that there is no relation between time and death cases in Jordan is taken. Table 2 lists the prediction numbers for confirmed, new, and death cases using the generated linear regression models. The table shows a prediction number for 24 th of August 2020, and the date of first future zero cases. Table 2 shows that Italy will see zero new cases from 17 th of August 2020; zero death cases in Jordan began from 9 th of April 2020 and will be seen in the US from 18 th of July 2020. The results show no zero cases for confirmed cases in the future for the selected countries using the linear regression model. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Country** & \multicolumn{3}{c}{**Italy**} & \multicolumn{3}{c}{**Jordan**} & \multicolumn{3}{c}{**US**} \\ \hline Model & & & & & & & & \\ Formula & & & & & & & & \\ \hline \multirow{2}{*}{Cases} & Confirmed & \multirow{2}{*}{New Cases} & \multirow{2}{*}{Death Cases} & Confirmed & \multirow{2}{*}{New Cases} & \multirow{2}{*}{Death Cases} & \multirow{2}{*}{New Cases} & \multirow{2}{*}{Death Cases} \\  & Cases & & & Cases & Cases & Cases & Cases & & \\ \hline SSE (sum & & & & & & & & \\ squared & \(3.3344\times 10^{11}\) & \(1.21758\times 10^{9}\) & \(1.05497\times 10^{7}\) & \(1.31218\times 10^{6}\) & 15846.4 & 12.5244 & \(1.9417\times 10^{13}\) & \(2.05371\times 10^{10}\) & \(1.50322\times 10^{6}\) \\ error: & & & & & & & & \\ MSE (mean & & & & & & & \\ squared & \(1.58781\times 10^{9}\) & \(5.79801\times 10^{6}\) & \(50,236.4\) & 6278.39 & 89.0245 & 0.0599252 & \(9.24653\times 10^{10}\) & \(9.77958\times 10^{10}\) & \(715\),821 \\ error: & & & & & & & & \\ R-Squared: & & & & & & & & \\ Standard & & & & & & & & \\ error: & & & & & & & & \\ error: & & & & & & & & \\ \(p\) value & & & & & & & & \\ \hline \end{tabular} \({}^{*}\) The prediction is made for August 24 2020.  
\end{table} 
Table 1: Linear Regression Results for Confirmed, New, and Death Cases for Italy, US, and Jordan.