## 4 Discussion
### Outcomes Analysis  
The investigation shows that min air temperature, max air temperature, curing method, and curing days are the principal components of concrete construction (see Table 3). A further linear discriminant analysis (LDA) shows that the curing method variable should be used to classify observations (see Table 4). For all the concrete specimens cured using Method #C1, the linear correlation regression equations in Table 5 have R-squared values of (a) 0.9750, (b) 0.9955, (c) 0.9889, (d) 0.9910, (e) 0.9958, (f) 0.9962, and (g) 0.9956, and the nonlinear correlation regression equation in Table 6 has an R-squared value of 0.9670. All the R-squared values are greater than 80%, which confirms the applicability of Gaussian process regression (GPR). The predictions of GPR for a new data point are based on the conditional distribution of the corresponding variable given observed data. Hence, GPR is applicable for the outcome analysis because, for a given set of function values, their \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{5}{c}{**MANOVA Tests for Specim Type**} \\ \hline \hline \multirow{2}{*}{**Criterion**} & \multirow{2}{*}{**Test Statistic**} & \multicolumn{3}{c}{**Degree of Freedom**} \\  & & **F** & **Num** & **Denominator** & \(p\)**-Value** \\ \hline [PERSON]\({}^{\prime}\) & 0.91681 & 3.856 & 2 & 85 & 0.025 \\ Lawley–Hotelling & 0.09074 & 3.856 & 2 & 85 & 0.025 \\ [PERSON]’s & 0.08319 & 3.856 & 2 & 85 & 0.025 \\ Roy’s & 0.09074 & & & & \\  & & s = 1 & m = 0 & n = 41.5 & \\ \hline \multicolumn{5}{c}{**MANOVA Tests for Method**} \\ \[PERSON]\({}^{\prime}\) & 0.29181 & 24.117 & 6 & 170 & 0 \\ Lawley–Hotelling & 2.05575 & 28.781 & 6 & 168 & 0 \\ [PERSON]’s & 0.81647 & 19.776 & 6 & 172 & 0 \\ [PERSON]’s & 1.85579 & & & & \\  & & s = 2 & m = 0 & n = 41.5 & \\ \hline \multicolumn{5}{c}{**MANOVA Tests for Season**} \\ \hline [PERSON]\({}^{\prime}\) & 0.06122 & 86.179 & 6 & 170 & 0 \\ Lawley–Hotelling & 10.79215 & 151.09 & 6 & 168 & 0 \\ Pillai’s & 1.21687 & 44.544 & 6 & 172 & 0 \\ [PERSON]’s & 10.3534 & & & & \\  & & s = 2 & m = 0 & n = 41.5 & \\ \hline \multicolumn{5}{c}{**MANOVA Tests for Specim Type \(\times\) Method**} \\ \hline [PERSON]\({}^{\prime}\) & 0.91727 & 1.25 & 6 & 170 & 0.283 \\ Lawley–Hotelling & 0.08935 & 1.251 & 6 & 168 & 0.283 \\ [PERSON]’s & 0.0835 & 1.249 & 6 & 172 & 0.284 \\ [PERSON]’s & 0.0787 & & & & \\  & & s = 2 & m = 0 & n = 41.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: MANOVA. combined distribution follows a pattern (a.k.a., multivariate Gaussian). This pattern and its specific details, like averages and variances, are already determined with prior knowledge. Similarly, for all the concrete specimens cured using Method #C2, the linear correlation regression equations in Table 7 have R-squared values of (a) 0.9130, (b) 0.9903, (c) 0.9889, (d) 0.9959, (e) 0.9910, (f) 0.9861, and (g) 0.9925, and the nonlinear correlation regression equation in Table 8 has an R-squared value of 0.9049. All the R-squared values are greater than 80%, which confirms the applicability of GPR. Further examination indicates that the multiple linear regression (MLR) model in Table 5 has different slopes in the correlation regression equations of the compressive strengths of the 4 in. and 6 in. cylinders when using Method #C1 to cure them. The slopes are in the range of [0.9603, 1.0497], with a 9.31% difference. Using the 24 MPa (3500 psi) design standard as an example, the difference is 24 \(\times\) 9.31% = 2.23 MPa (or 325 psi). The slope differences suggest that concrete construction in different seasons could have a nearly 2.24 MPa variation in compressive strength estimation when using 4 in. or 6 in. cylinders. Table 7 has the same influence factors as Table 5, except that the data are for Method #C2. The slopes are in the range of [0.9851, 1.1237], with a 14.07% difference, which suggests that the MLR model should consider construction season and curing duration.