## 3 Results
ROS models had the lowest absolute valued coefficients on average. Models were also created with cell death, represented by the CA variable, as the effect. These models are displayed in Table 4, for 3 min CHCP treatment. Cell proliferation was omitted as a causal variable because a lack of cell proliferation does not have any definite causal linkage to cell death. All inputted variables were causal for the MCF-7 and SK-BR-3, while none were causal for MDA-MB-231. Only Ki-67 and G1 activity showed causality for the BT-474 models. Ki-67 had the greatest causal relationship to CA across all cell lines. Shown in Table 5, the same causality testing was then done for cell death using data from cells that underwent CHCP treatment for 5 min. When comparing the 3 min and 5 min cell death models, it was seen that the G1 variable for BT-474 and the ROS and Ki-67 variables for MCF-7 did not have significant causal link after 5 min CHCP treatment. However, the same variables were considered significantly causal for the 3 min models. This was inconsistent with the cell proliferation models, where all 5 min models were statistically significant, including those that had \(p\)-values \(>\) 0.05 in the 3 min models. The standard errors for the ROS, CA, Ki-67, and G1 models are presented in Table 6. The error of the models varied greatly among cell types. The standard of error for each model was computed from the causality() function in R, alongside the estimated \(p\)-values. The SK-BR-3 ROS models had the smallest error on average, while the MCF-7 caspase models had the largest. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cell Line**} & \multicolumn{6}{c}{**Standard of Error**} \\ \cline{2-9}  & \multicolumn{2}{c}{**ROS Model**} & \multicolumn{2}{c}{**Caspase Model**} & \multicolumn{2}{c}{**Ki-67 Model**} & \multicolumn{2}{c}{**G1 Model**} \\ \cline{2-9}  & **3 min** & **5 min** & **3 min** & **5 min** & **3 min** & **5 min** & **3 min** & **5 min** \\ \hline BT-474 & 0.0005668 & 0.0001282 & 0.0447 & 0.002926 & 0.01545 & 0.02515 & 0.001665 & 0.003625 \\ \hline MCF-7 & 0.005106 & 0.0005075 & 0.67176 & 0.01969 & 0.11736 & 0.02316 & 0.005439 & 0.003437 \\ \hline MDA-MB-231 & 0.0003843 & 0.0001438 & 0.03487 & 0.01409 & 0.07541 & 0.04053 & 0.003762 & 0.001562 \\ \hline SK-BR-3 & \(8.99\times 10^{-5}\) & \(4.14\times 10^{-5}\) & 0.006755 & 0.006358 & 0.02371 & 0.01421 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Standard of error for cell proliferation models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Cell Line**} & \multirow{2}{*}{**Result**} & **Cause:** & **Cause:** & **Cause:** \\  & & **ROS** & **Ki-67** & **G1** \\ \hline \multirow{2}{*}{BT-474} & \(p\)-value & 0.01091 * & 4.726 \(\times\) 10\({}^{-7}\) * & 0.4513 \\ \cline{2-5}  & Coefficient of Regression & 0.00223 & 0.26380 & 0.005350 \\ \hline \multirow{2}{*}{MCF-7} & \(p\)-value & 0.2384 & 0.1001 & 0.01122 * \\ \cline{2-5}  & Coefficient of Regression & 0.0007537 & 0.06361 & 0.023061 \\ \hline \multirow{2}{*}{MDA-MB-231} & \(p\)-value & 0.01123 * & 0.01146 * & 0.05247 \\ \cline{2-5}  & Coefficient of Regression & 0.0005037 & 0.23959 & 0.009367 \\ \hline \multirow{2}{*}{SK-BR-3} & \(p\)-value & \(5.98\times 10^{-5}\) * & 0.006272 * & - \\ \cline{2-5}  & Coefficient of Regression & \(2.46\times 10^{-4}\) & 0.55293 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: \(p\)-values and coefficients of linear regression for all cell death models for cells treated for 5 min (* \(p\) \(<\) 0.05).