The posted code produces
! Extra alignment tab has been changed to \cr.
as it has 7 declared columns but 8 columns of data.
Adding an extra L to fix that then you get the warning
Package tabularx Warning: X Columns too narrow (table too wide)
(tabularx) on input line 26.
because
\newcolumntype{L}{>{\hsize=7.5\hsize}X}
forces at each iteration every column to be seven and a half times wider than the width calculated, so tabularx has no chance of ever converging to the requested table width.
Then delete the ! from
\begin{table}[!htbp]
which should only be used in exceptional circumstances.
then I added dcolumn to allow decimal aligned columns (you could instead use siunitx)
Then define a command for the headings,
then it sort of fits but it's still far too tight to be readable, you could use \tiny instead of \footnotesize but do you need to give so many decimal places?

\documentclass{article}
\usepackage[english]{babel}
\usepackage{booktabs,tabularx,caption,ragged2e}
\captionsetup{skip=0.333\baselineskip}
\usepackage{dcolumn}
\newcommand\hd[1]{\multicolumn{1}{c}{\begin{tabular}{@{}c@{}}#1\end{tabular}}}
\begin{document}
\begin{table}[htbp]
\centering
\footnotesize
\setlength\tabcolsep{1pt} % default: 6pt
\caption{} \label{}
\begin{tabular}{@{}rp{2cm} *{6}{D..{1.9}}@{}}
\toprule
&
\hd{Test} &
\hd{Trust}&
\hd{Demo-\\graphics} &
\hd{Immi-\\gration}&
\hd{Economic\\Model}&
\hd{Issue\\Satisfaction}&
\hd{Demo-\\graphic\\No\\Country}\\
\hline
1 & R2 & 0.016 & 0.2 & 0.086 & 0.007 & 0.021 & 0.027 \\
2 & Predicted & 83.20\% & 83.3\%\% & 83.40\% & 82.7\%\% & 83.20\% & 84.50\% \\
3 & AUC Index & 0.585 & 0.79 & 0.701 & 0.559 & 0.603 & 0.61 \\
4 & Sum of\newline squared errors & 4861.786003 & 4773.002716 & 1847.897222 & 1249.544564 & 5009.179836 & 5310.168732 \\
5 & Expected value$|$H0 & 4862.80413 & 4777.131906 & 1835.302972 & 1249.164639 & 5003.713449 & 5311.013662 \\
6 & SD & 0.545436987 & 3.006760697 & 1.739686944 & 0.10557875 & 0.673923831 & 0.953354286 \\
7 & Z & -1.866627646 & -1.373301832 & 7.239377177 & 3.598496041 & 8.111283371 & -0.886270167 \\
8 & P & 0.061953604 & 0.169658533 & 4.51E-13 & 0.000320063 & 5.01E-16 & 0.375471961 \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
\documentclass{article}
\usepackage[english]{babel}
\usepackage{booktabs,tabularx,caption,ragged2e}
\captionsetup{skip=0.333\baselineskip}
\usepackage{dcolumn}
\newcommand\hd[1]{\multicolumn{1}{c}{\begin{tabular}{@{}c@{}}#1\end{tabular}}}
\begin{document}
\begin{table}[htbp]
\centering
\footnotesize
\setlength\tabcolsep{1pt} % default: 6pt
\caption{} \label{}
\begin{tabular}{@{}rp{2cm} *{6}{D..{1.9}}@{}}
\toprule
&
\hd{Test} &
\hd{Trust}&
\hd{Demo-\\graphics} &
\hd{Immi-\\gration}&
\hd{Economic\\Model}&
\hd{Issue\\Satisfaction}&
\hd{Demo-\\graphic\\No\\Country}\\
\hline
1 & R2 & 0.016 & 0.2 & 0.086 & 0.007 & 0.021 & 0.027 \\
2 & Predicted & 83.20\% & 83.3\%\% & 83.40\% & 82.7\%\% & 83.20\% & 84.50\% \\
3 & AUC Index & 0.585 & 0.79 & 0.701 & 0.559 & 0.603 & 0.61 \\
4 & Sum of\newline squared errors & 4861.786003 & 4773.002716 & 1847.897222 & 1249.544564 & 5009.179836 & 5310.168732 \\
5 & Expected value$|$H0 & 4862.80413 & 4777.131906 & 1835.302972 & 1249.164639 & 5003.713449 & 5311.013662 \\
6 & SD & 0.545436987 & 3.006760697 & 1.739686944 & 0.10557875 & 0.673923831 & 0.953354286 \\
7 & Z & -1.866627646 & -1.373301832 & 7.239377177 & 3.598496041 & 8.111283371 & -0.886270167 \\
8 & P & 0.061953604 & 0.169658533 & 4.51E-13 & 0.000320063 & 5.01E-16 & 0.375471961 \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
Actually, you need a format of D..{2.9} to allow for the minus sign, but as noted above 9 decimal places seems excessive for a table.
\documentclass{article}
\usepackage[english]{babel}
\usepackage{booktabs,tabularx,caption,ragged2e}
\captionsetup{skip=0.333\baselineskip}
\usepackage{dcolumn}
\newcommand\hd[1]{\multicolumn{1}{c}{\begin{tabular}{@{}c@{}}#1\end{tabular}}}
\begin{document}
\begin{table}[htbp]
\centering
\footnotesize
\setlength\tabcolsep{1pt} % default: 6pt
\caption{} \label{}
\begin{tabular}{@{}r>{\raggedright}p{1.4cm} *{6}{D..{2.9}}@{}}
\toprule
&
\hd{Test} &
\hd{Trust}&
\hd{Demo-\\graphics} &
\hd{Immi-\\gration}&
\hd{Economic\\Model}&
\hd{Issue\\Satisfaction}&
\hd{Demo-\\graphic\\No\\Country}\\
\hline
1 & R2 & 0.016 & 0.2 & 0.086 & 0.007 & 0.021 & 0.027 \\
2 & Predicted & 83.20\% & 83.3\%\% & 83.40\% & 82.7\%\% & 83.20\% & 84.50\% \\
3 & AUC\\ Index & 0.585 & 0.79 & 0.701 & 0.559 & 0.603 & 0.61 \\
4 & Sum of\\ squared errors & 4861.786003 & 4773.002716 & 1847.897222 & 1249.544564 & 5009.179836 & 5310.168732 \\
5 & Expec-\\ted value$|$H0 & 4862.80413 & 4777.131906 & 1835.302972 & 1249.164639 & 5003.713449 & 5311.013662 \\
6 & SD & 0.545436987 & 3.006760697 & 1.739686944 & 0.10557875 & 0.673923831 & 0.953354286 \\
7 & Z & -1.866627646 & -1.373301832 & 7.239377177 & 3.598496041 & 8.111283371 & -0.886270167 \\
8 & P & 0.061953604 & 0.169658533 & 4.51E-13 & 0.000320063 & 5.01E-16 & 0.375471961 \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
\newcolumntype{L}{>{\hsize=7.5\hsize}X}what???????????? – David Carlisle May 09 '17 at 17:33flushleftis to add additional vertical space. – David Carlisle May 09 '17 at 17:36Ldefinition makes every column 7.5 times as wide as tabularx calculated that the column needs to be, I'm wondering what is the intended behaviour? – David Carlisle May 09 '17 at 17:39