I don't recommend to put so much information on a single slide. The fontsize needs to be so small, nobody will to be able to read it anyway
Don't scale text, either reduce the amount of text on the slide or use a smaller font size. For more information, please have a look at Why not scale elements that contain text
\documentclass[xcolor=table]{beamer}
\setlength{\arrayrulewidth}{0.5mm}
\renewcommand{\arraystretch}{1}
\definecolor{wildblueyonder}{rgb}{0.64, 0.68, 0.82}
\newcolumntype{S}{>{\columncolor[HTML]{AAACED}}l}
\usepackage{lmodern}
\begin{document}
\begin{frame}
\fontsize{5.5pt}{8pt}\selectfont
\centering
\begin{tabular}{ |l|S|S|c| }
\hline
\rowcolor{lightgray} \multicolumn{4}{|c|}{Classical multiple lm} \\
\hline
\rowcolor{wildblueyonder}
& Estimate & Std. Error & p-value \\
\hline
intercept & 21.8100 & 0.5723 & $<2e-16$ \\
r.limit & 0.4872 & 0.3775 & 0.1997 \\
conc & -0.9541 & 0.0352 & $<2e-16$ \\
log.t & -2.7720 & 0.0377 & $<2e-16$ \\
log.rho & -1.4140 & 0.0186 & $<2e-16$ \\
V.esc & 0.0001 & 0.0001 & 0.2544 \\
V.t & 0.0021 & 0.0044 & 0.6368 \\
Metal & 0.0427 & 0.0145 & 0.0040 \\
\textbf{F test} & \cellcolor{lightgray} & \cellcolor{lightgray} & \textcolor{red}{$<2e-16$} \\
\hline
\end{tabular}
\hfill
\begin{tabular}{ |l|S|S|c| }
\hline
\rowcolor{lightgray} \multicolumn{4}{|c|}{Canonical multiple lm} \\
\hline
\rowcolor{wildblueyonder}
& Estimate & Std. Error & p-value \\
\hline
intercept & -7.4181 & 0.0067 & $<2e-16$ \\
Comp.1 & -0.2536 & 0.0038 & $<2e-16$ \\
Comp.2 & 0.6747 & 0.0053 & $<2e-16$ \\
Comp.3 & -0.4879 & 0.0645 & $<2e-16$ \\
Comp.4 & -0.0336 & 0.0081 & 0.0001 \\
Comp.5 & 0.1427 & 0.0097 & $<2e-16$ \\
Comp.6 & -2.2291 & 0.0284 & $<2e-16$ \\
Comp.7 & 1.5929 & 0.0409 & $<2e-16$ \\
\textbf{F test} & \cellcolor{lightgray} & \cellcolor{lightgray} & \textcolor{red}{$<2e-16$} \\
\hline
\end{tabular}
\smallskip\smallskip
\begin{tabular}{ |l|S|S|c| }
\hline
\rowcolor{lightgray} \multicolumn{4}{|c|}{Canonical multiple lm} \\
\hline
\rowcolor{wildblueyonder}
& Estimate & Std. Error & p-value \\
\hline
intercept & -7.4181 & 0.0067 & $<2e-16$ \\
Comp.1 & -0.2536 & 0.0038 & $<2e-16$ \\
Comp.2 & 0.6747 & 0.0053 & $<2e-16$ \\
Comp.3 & -0.4879 & 0.0645 & $<2e-16$ \\
Comp.4 & -0.0336 & 0.0081 & 0.0001 \\
Comp.5 & 0.1427 & 0.0097 & $<2e-16$ \\
Comp.6 & -2.2291 & 0.0284 & $<2e-16$ \\
Comp.7 & 1.5929 & 0.0409 & $<2e-16$ \\
\textbf{F test} & \cellcolor{lightgray} & \cellcolor{lightgray} & \textcolor{red}{$<2e-16$} \\
\hline
\end{tabular}
\end{frame}
\end{document}

To free the data from data prison

I suggest to use the booktabs package
\documentclass{beamer}
\usepackage{booktabs}
\usepackage{siunitx}
\begin{document}
\begin{frame}
\tiny
\centering
\begin{tabular}{@{}lS[table-format=-2.4]S[table-format=1.4]S[table-format=1e-2,table-comparator = true,table-number-alignment = center]@{}}
\toprule
\multicolumn{4}{c}{Classical multiple lm} \\
\midrule
& {Estimate} & {Std. Error} & {p-value} \\
\cmidrule(rl){2-2} \cmidrule(rl){3-3} \cmidrule(rl){4-4}
intercept & 21.8100 & 0.5723 & <2e-16 \\
r.limit & 0.4872 & 0.3775 & 0.1997 \\
conc & -0.9541 & 0.0352 & <2e-16 \\
log.t & -2.7720 & 0.0377 & <2e-16 \\
log.rho & -1.4140 & 0.0186 & <2e-16 \\
V.esc & 0.0001 & 0.0001 & 0.2544 \\
V.t & 0.0021 & 0.0044 & 0.6368 \\
Metal & 0.0427 & 0.0145 & 0.0040 \\
\midrule
F test & & & <2e-16 \\
\bottomrule
\end{tabular}
\hfill
\begin{tabular}{@{}lS[table-format=-2.4]S[table-format=1.4]S[table-format=1e-2,table-comparator = true,table-number-alignment = center]@{}}
\toprule
\multicolumn{4}{c}{Classical multiple lm} \\
\midrule
& {Estimate} & {Std. Error} & {p-value} \\
\cmidrule(rl){2-2} \cmidrule(rl){3-3} \cmidrule(rl){4-4}
intercept & 21.8100 & 0.5723 & <2e-16 \\
r.limit & 0.4872 & 0.3775 & 0.1997 \\
conc & -0.9541 & 0.0352 & <2e-16 \\
log.t & -2.7720 & 0.0377 & <2e-16 \\
log.rho & -1.4140 & 0.0186 & <2e-16 \\
V.esc & 0.0001 & 0.0001 & 0.2544 \\
V.t & 0.0021 & 0.0044 & 0.6368 \\
Metal & 0.0427 & 0.0145 & 0.0040 \\
\midrule
F test & & & <2e-16 \\
\bottomrule
\end{tabular}
\smallskip
\begin{tabular}{@{}lS[table-format=-2.4]S[table-format=1.4]S[table-format=1e-2,table-comparator = true,table-number-alignment = center]@{}}
\toprule
\multicolumn{4}{c}{Classical multiple lm} \\
\midrule
& {Estimate} & {Std. Error} & {p-value} \\
\cmidrule(rl){2-2} \cmidrule(rl){3-3} \cmidrule(rl){4-4}
intercept & 21.8100 & 0.5723 & <2e-16 \\
r.limit & 0.4872 & 0.3775 & 0.1997 \\
conc & -0.9541 & 0.0352 & <2e-16 \\
log.t & -2.7720 & 0.0377 & <2e-16 \\
log.rho & -1.4140 & 0.0186 & <2e-16 \\
V.esc & 0.0001 & 0.0001 & 0.2544 \\
V.t & 0.0021 & 0.0044 & 0.6368 \\
Metal & 0.0427 & 0.0145 & 0.0040 \\
\midrule
F test & & & <2e-16 \\
\bottomrule
\end{tabular}
\end{frame}
\end{document}

\tl? please provide complete bur small document with your frame beginning with\documentclass{beamer}followed with preamble with yours definition of new commands and frame with tables and ending with\end{document}– Zarko Apr 20 '18 at 20:29