Commit 8c269149 authored by Turnhout, M.C. van's avatar Turnhout, M.C. van
Browse files

ani tables, eqs

parent c08e40e7
\begin{equation}
R_\varepsilon^\text{l}(\sigma_x = 0.015\,\text{MPa}) = 9.53\cdot 10^{-1} -9.04\cdot 10^{-2} \mu + 2.07\cdot 10^{-2} \sigma + 2.53\cdot 10^{-1} P + \text{error} \label{anispace_Rel_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$R_\varepsilon^\text{l}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$9.53\cdot 10^{-1}$ & $\left[8.90\cdot 10^{-1} \quad 1.02\right]$ & & $0.000$&&\\
$-9.04\cdot 10^{-2} \mu$ & $\left[-1.32\cdot 10^{-1} \quad -4.89\cdot 10^{-2}\right]$ & $0.107$ & $0.000$ & $1.37\cdot 10^{-1}$ & $0.277$\\
$+2.07\cdot 10^{-2} \sigma$ & $\left[-9.77\cdot 10^{-2} \quad 1.39\cdot 10^{-1}\right]$ & $0.001$ & $0.729$ & $1.07\cdot 10^{-2}$ & $0.022$\\
$+2.53\cdot 10^{-1} P$ & $\left[1.90\cdot 10^{-1} \quad 3.15\cdot 10^{-1}\right]$ & $0.371$ & $0.000$ & $2.49\cdot 10^{-1}$ & $0.503$\\
$+\text{error}$ & & $0.521$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.484$ & \multicolumn{5}{c}{min: $8.37\cdot 10^{-1}$, mean: $1.01$, median: $9.94\cdot 10^{-1}$, max: $1.33$}\\
\end{tabular}
\begin{equation}
R_\varepsilon^\text{r}(\sigma_x = 0.015\,\text{MPa}) = 1.47 -1.97\cdot 10^{-1} \mu -3.34\cdot 10^{-2} \sigma + 3.07\cdot 10^{-1} P + \text{error} \label{anispace_Rer_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$R_\varepsilon^\text{r}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$1.47$ & $\left[1.33 \quad 1.60\right]$ & & $0.000$&&\\
$-1.97\cdot 10^{-1} \mu$ & $\left[-2.86\cdot 10^{-1} \quad -1.08\cdot 10^{-1}\right]$ & $0.148$ & $0.000$ & $2.99\cdot 10^{-1}$ & $0.312$\\
$-3.34\cdot 10^{-2} \sigma$ & $\left[-2.87\cdot 10^{-1} \quad 2.21\cdot 10^{-1}\right]$ & $0.001$ & $0.795$ & $1.73\cdot 10^{-2}$ & $0.018$\\
$+3.07\cdot 10^{-1} P$ & $\left[1.73\cdot 10^{-1} \quad 4.40\cdot 10^{-1}\right]$ & $0.158$ & $0.000$ & $3.02\cdot 10^{-1}$ & $0.314$\\
$+\text{error}$ & & $0.694$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.306$ & \multicolumn{5}{c}{min: $1.09$, mean: $1.45$, median: $1.39$, max: $2.05$}\\
\end{tabular}
\begin{equation}
\lambda_L^\text{l}(\sigma_x = 0.015\,\text{MPa}) = 1.00 -1.12\cdot 10^{-3} \mu -9.52\cdot 10^{-4} \sigma + 1.71\cdot 10^{-3} P + \text{error} \label{anispace_dLl_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\lambda_L^\text{l}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$1.00$ & $\left[1.00 \quad 1.00\right]$ & & $0.000$&&\\
$-1.12\cdot 10^{-3} \mu$ & $\left[-1.29\cdot 10^{-3} \quad -9.48\cdot 10^{-4}\right]$ & $0.377$ & $0.000$ & $1.70\cdot 10^{-3}$ & $0.454$\\
$-9.52\cdot 10^{-4} \sigma$ & $\left[-1.43\cdot 10^{-3} \quad -4.71\cdot 10^{-4}\right]$ & $0.034$ & $0.000$ & $4.93\cdot 10^{-4}$ & $0.132$\\
$+1.71\cdot 10^{-3} P$ & $\left[1.46\cdot 10^{-3} \quad 1.96\cdot 10^{-3}\right]$ & $0.391$ & $0.000$ & $1.68\cdot 10^{-3}$ & $0.451$\\
$+\text{error}$ & & $0.198$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.811$ & \multicolumn{5}{c}{min: $9.99\cdot 10^{-1}$, mean: $1.00$, median: $1.00$, max: $1.00$}\\
\end{tabular}
\begin{equation}
\lambda_L^\text{r}(\sigma_x = 0.015\,\text{MPa}) = 1.00 -9.63\cdot 10^{-4} \mu -9.24\cdot 10^{-4} \sigma + 1.51\cdot 10^{-3} P + \text{error} \label{anispace_dLr_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\lambda_L^\text{r}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$1.00$ & $\left[1.00 \quad 1.00\right]$ & & $0.000$&&\\
$-9.63\cdot 10^{-4} \mu$ & $\left[-1.15\cdot 10^{-3} \quad -7.75\cdot 10^{-4}\right]$ & $0.325$ & $0.000$ & $1.46\cdot 10^{-3}$ & $0.452$\\
$-9.24\cdot 10^{-4} \sigma$ & $\left[-1.46\cdot 10^{-3} \quad -3.89\cdot 10^{-4}\right]$ & $0.037$ & $0.001$ & $4.78\cdot 10^{-4}$ & $0.148$\\
$+1.51\cdot 10^{-3} P$ & $\left[1.22\cdot 10^{-3} \quad 1.79\cdot 10^{-3}\right]$ & $0.353$ & $0.000$ & $1.48\cdot 10^{-3}$ & $0.459$\\
$+\text{error}$ & & $0.285$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.727$ & \multicolumn{5}{c}{min: $1.00$, mean: $1.00$, median: $1.00$, max: $1.00$}\\
\end{tabular}
\begin{equation}
\Deltaup \kappa (\sigma_x = 0.015\,\text{MPa}) = -4.34\cdot 10^{-1} + 5.14\cdot 10^{-2} \mu + 3.71\cdot 10^{-2} \sigma + 5.89\cdot 10^{-2} P + \text{error} \label{anispace_dk_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\Deltaup \kappa (\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$-4.34\cdot 10^{-1}$ & $\left[-4.85\cdot 10^{-1} \quad -3.83\cdot 10^{-1}\right]$ & & $0.000$&&\\
$+5.14\cdot 10^{-2} \mu$ & $\left[1.77\cdot 10^{-2} \quad 8.52\cdot 10^{-2}\right]$ & $0.087$ & $0.003$ & $7.81\cdot 10^{-2}$ & $0.183$\\
$+3.71\cdot 10^{-2} \sigma$ & $\left[-5.90\cdot 10^{-2} \quad 1.33\cdot 10^{-1}\right]$ & $0.006$ & $0.445$ & $1.92\cdot 10^{-2}$ & $0.045$\\
$+5.89\cdot 10^{-2} P$ & $\left[8.27\cdot 10^{-3} \quad 1.10\cdot 10^{-1}\right]$ & $0.050$ & $0.023$ & $5.80\cdot 10^{-2}$ & $0.136$\\
$+\text{error}$ & & $0.858$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
\multicolumn{6}{l}{$n = 95$, $R_a^2 = 0.101$, min: $-4.57\cdot 10^{-1}$, mean: $-3.52\cdot 10^{-1}$, median: $-3.71\cdot 10^{-1}$, max: $-2.94\cdot 10^{-2}$}\\
\end{tabular}
\begin{equation}
\kappa_\varepsilon^\text{l}(\sigma_x = 0.015\,\text{MPa}) = 6.36\cdot 10^{-1} -3.17\cdot 10^{-1} \mu -1.66\cdot 10^{-1} \sigma + 5.21\cdot 10^{-2} P + \text{error} \label{anispace_kel_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\kappa_\varepsilon^\text{l}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$6.36\cdot 10^{-1}$ & $\left[5.67\cdot 10^{-1} \quad 7.05\cdot 10^{-1}\right]$ & & $0.000$&&\\
$-3.17\cdot 10^{-1} \mu$ & $\left[-3.62\cdot 10^{-1} \quad -2.72\cdot 10^{-1}\right]$ & $0.658$ & $0.000$ & $4.81\cdot 10^{-1}$ & $0.497$\\
$-1.66\cdot 10^{-1} \sigma$ & $\left[-2.96\cdot 10^{-1} \quad -3.66\cdot 10^{-2}\right]$ & $0.022$ & $0.013$ & $8.59\cdot 10^{-2}$ & $0.089$\\
$+5.21\cdot 10^{-2} P$ & $\left[-1.62\cdot 10^{-2} \quad 1.20\cdot 10^{-1}\right]$ & $0.008$ & $0.133$ & $5.13\cdot 10^{-2}$ & $0.053$\\
$+\text{error}$ & & $0.312$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.682$ & \multicolumn{5}{c}{min: $7.15\cdot 10^{-2}$, mean: $3.61\cdot 10^{-1}$, median: $3.44\cdot 10^{-1}$, max: $1.04$}\\
\end{tabular}
\begin{equation}
\kappa_\varepsilon^\text{r}(\sigma_x = 0.015\,\text{MPa}) = 6.39\cdot 10^{-1} -3.56\cdot 10^{-1} \mu -1.52\cdot 10^{-1} \sigma -3.33\cdot 10^{-2} P + \text{error} \label{anispace_ker_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\kappa_\varepsilon^\text{r}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$6.39\cdot 10^{-1}$ & $\left[5.47\cdot 10^{-1} \quad 7.31\cdot 10^{-1}\right]$ & & $0.000$&&\\
$-3.56\cdot 10^{-1} \mu$ & $\left[-4.17\cdot 10^{-1} \quad -2.96\cdot 10^{-1}\right]$ & $0.590$ & $0.000$ & $5.41\cdot 10^{-1}$ & $0.496$\\
$-1.52\cdot 10^{-1} \sigma$ & $\left[-3.25\cdot 10^{-1} \quad 2.11\cdot 10^{-2}\right]$ & $0.013$ & $0.084$ & $7.86\cdot 10^{-2}$ & $0.072$\\
$-3.33\cdot 10^{-2} P$ & $\left[-1.25\cdot 10^{-1} \quad 5.79\cdot 10^{-2}\right]$ & $0.002$ & $0.470$ & $3.28\cdot 10^{-2}$ & $0.030$\\
$+\text{error}$ & & $0.395$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.589$ & \multicolumn{5}{c}{min: $5.06\cdot 10^{-2}$, mean: $2.94\cdot 10^{-1}$, median: $2.50\cdot 10^{-1}$, max: $1.14$}\\
\end{tabular}
\begin{equation}
\frac{l}{L}(\sigma_x = 0.015\,\text{MPa}) = 8.17\cdot 10^{-1} -4.05\cdot 10^{-1} \mu -5.64\cdot 10^{-2} \sigma + 3.63\cdot 10^{-2} P + \text{error} \label{anispace_lL_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\frac{l}{L}(\sigma_x = 0.015\,\text{MPa}) = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$8.17\cdot 10^{-1}$ & $\left[7.66\cdot 10^{-1} \quad 8.68\cdot 10^{-1}\right]$ & & $0.000$&&\\
$-4.05\cdot 10^{-1} \mu$ & $\left[-4.39\cdot 10^{-1} \quad -3.71\cdot 10^{-1}\right]$ & $0.858$ & $0.000$ & $6.15\cdot 10^{-1}$ & $0.895$\\
$-5.64\cdot 10^{-2} \sigma$ & $\left[-1.52\cdot 10^{-1} \quad 3.95\cdot 10^{-2}\right]$ & $0.002$ & $0.246$ & $2.91\cdot 10^{-2}$ & $0.042$\\
$+3.63\cdot 10^{-2} P$ & $\left[-1.43\cdot 10^{-2} \quad 8.68\cdot 10^{-2}\right]$ & $0.003$ & $0.157$ & $3.57\cdot 10^{-2}$ & $0.052$\\
$+\text{error}$ & & $0.136$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 95$, $R_a^2 = 0.861$ & \multicolumn{5}{c}{min: $2.44\cdot 10^{-1}$, mean: $4.95\cdot 10^{-1}$, median: $4.36\cdot 10^{-1}$, max: $9.31\cdot 10^{-1}$}\\
\end{tabular}
\begin{equation}
\overline{\min l(\sigma)} = 3.05\cdot 10^{-2} + 5.04\cdot 10^{-2} \mu -2.27\cdot 10^{-2} \sigma -3.52\cdot 10^{-2} P + \text{error} \label{anispace_md_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\overline{\min l(\sigma)} = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$3.05\cdot 10^{-2}$ & $\left[7.96\cdot 10^{-4} \quad 6.02\cdot 10^{-2}\right]$ & & $0.044$&&\\
$+5.04\cdot 10^{-2} \mu$ & $\left[3.08\cdot 10^{-2} \quad 6.99\cdot 10^{-2}\right]$ & $0.203$ & $0.000$ & $7.64\cdot 10^{-2}$ & $0.531$\\
$-2.27\cdot 10^{-2} \sigma$ & $\left[-7.86\cdot 10^{-2} \quad 3.32\cdot 10^{-2}\right]$ & $0.005$ & $0.423$ & $1.17\cdot 10^{-2}$ & $0.081$\\
$-3.52\cdot 10^{-2} P$ & $\left[-6.48\cdot 10^{-2} \quad -5.57\cdot 10^{-3}\right]$ & $0.043$ & $0.020$ & $3.47\cdot 10^{-2}$ & $0.241$\\
$+\text{error}$ & & $0.748$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 100$, $R_a^2 = 0.244$ & \multicolumn{5}{c}{min: $0.00$, mean: $4.62\cdot 10^{-2}$, median: $2.77\cdot 10^{-2}$, max: $1.44\cdot 10^{-1}$}\\
\end{tabular}
\begin{equation}
\max \sigma_x = 2.17\cdot 10^{-2} + 2.45\cdot 10^{-3} \mu + 4.46\cdot 10^{-3} \sigma -7.08\cdot 10^{-3} P + \text{error} \label{anispace_msig_eq}
\end{equation}
\begin{tabular}{l c c r r r}
\hline\noalign{\smallskip}
$\max \sigma_x = $ &95\,\% CI & SS/SS$_\text{tot}$ & $p$ & range & fraction\\
\noalign{\smallskip}\hline\noalign{\bigskip}
$2.17\cdot 10^{-2}$ & $\left[2.07\cdot 10^{-2} \quad 2.27\cdot 10^{-2}\right]$ & & $0.000$&&\\
$+2.45\cdot 10^{-3} \mu$ & $\left[1.79\cdot 10^{-3} \quad 3.11\cdot 10^{-3}\right]$ & $0.146$ & $0.000$ & $3.72\cdot 10^{-3}$ & $0.286$\\
$+4.46\cdot 10^{-3} \sigma$ & $\left[2.57\cdot 10^{-3} \quad 6.36\cdot 10^{-3}\right]$ & $0.060$ & $0.000$ & $2.31\cdot 10^{-3}$ & $0.178$\\
$-7.08\cdot 10^{-3} P$ & $\left[-8.08\cdot 10^{-3} \quad -6.07\cdot 10^{-3}\right]$ & $0.533$ & $0.000$ & $6.97\cdot 10^{-3}$ & $0.536$\\
$+\text{error}$ & & $0.261$ & &&\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$n = 100$, $R_a^2 = 0.750$ & \multicolumn{5}{c}{min: $1.20\cdot 10^{-2}$, mean: $2.14\cdot 10^{-2}$, median: $2.20\cdot 10^{-2}$, max: $2.50\cdot 10^{-2}$}\\
\end{tabular}
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