## 3 Results  
### Statistical Models (Polynomials Time Regression)  
The statistical methods used to obtain the models are based on linear regressions (first-degree polynomials), quadratic regressions (second-degree polynomials), cubic regressions (third-degree polynomials), and the polynomials regression by fourth-degree poly. Polynomial regressions, and non-polynomial regressions, are obtained by applying the least squares method. In the cases of the polynomial regressions, the sought coefficients are obtained by solving linear equations systems, coming from the calculation of the critical points. The calculations of the coefficients from the interpolation polynomials were made using the interpolation function of the MathCAD 15 program, whose algorithm is described in study [25]. In addition to the regression polynomial coefficients, the polyfit function of the MathCAD 15 program also provides other important statistical features:  
Figure 4: Variation of eight parameters of the plant after contaminating the soil, using the normalized standard deviation, in consideration of Zn accumulation (where humid.pl. : plant water content; soil moist. : soil moisture; soil h.m.c. : soil heavy metal concentration; plant h.m.c. : plant heavy metal concentration). Figure 3: Box plot diagrams for mass (**a**), height (**b**), and diameter (**c**) distributions for the three cases of soil contamination with a solution of 1.5%, 3.0%, and 4.5% zinc concentration. the standard error for the regression coefficient, the lower and upper boundary for the confidence interval of the regression coefficient, the variance inflation factor--the measure of the inflation of the regression coefficient due to multicollinearity, Student's t-test statistic if the term is significant, and \(p\)-value--probability of rejecting the term based on its t-statistic, when in fact it is significant. The terms used in statistical analysis are presented schematically in Table 1.  
As an example, Table 2 shows the final and intermediate results of the interpolation for the evolution of the mass of plants grown in soil with a zinc concentration of 4.5%. The significance and calculation algorithms of these characteristics were calculated according to [25] and the PTC MathCAD prime linear regression, (2018). According to Tables 2-5, the equation that gives the time dependence of the plant mass of lettuces grown in soil with a concentration of 4.5%, through the polynomial function, are the following:  
\[ \begin{array}{rl}m1_{4.5}(t)&=2.25+0.117t\\ m2_{4.5}(t)&=1.656+0.175t-0.0008428t^{2}\\ m3_{4.5}(t)&=0.59+0.424t-0.01t^{2}+0.00009331t^{3}\\ m4_{4.5}(t)&=0.142+0.657t-0.028t^{2}+0.0005041t^{3}-0.000003033t^{4}\end{array}  \tag{2}\]  
where: \(t\) is the time (in days). \begin{table}
\begin{tabular}{c c} \hline
**Term** & **Labels for Each Term Reported Upon** \\ \hline Coefficient & Regression coefficient for each term \\ \hline Std Error & Standard error for the regression coefficient \\ \hline
95\% CI low & Lower boundary for the confidence interval of the regression coefficient \\ \hline
95\% CI High & Upper boundary for the confidence interval of the regression coefficient \\ \hline VIF & Variance inflation factor: measure of the inflation of the regression coefficient due to multicollinearity \\ \hline T & Student’s t test statistic to test if the term is significant \\ \hline P & \(p\)-value: probability of rejecting the term based on its \\ t-statistic when in fact it is significant \\ \hline \end{tabular}
\end{table} 
Table 1: Presentation of the main terms used in statistical analysis. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Term** & **Coefficient** & **Std Error** & **95\% CI Low** & **95\% CI High** & **VIF** & **T** & **P** \\ \hline \(t^{0}\) & 2.25 & 0.874 & 0.272 & 4.228 & NaN & 2.573 & 0.025 \\ T & 0.117 & 0.021 & 0.069 & 0.166 & 1 & 5.517 & 0.0002401 \\ \hline \end{tabular}
\end{table}