Table with caption too wide for standalone package document
I would break this into two parts.
(1) I would put the table in its own file.
(2) I would import the table using \includegraphics
Call the file for your table mytable.tex
\documentclass{standalone}
\usepackage{booktabs}
\begin{document}
\begin{tabular}{llllllllll}
\toprule
& \multicolumn{3}{c}{Model 1}
& \multicolumn{3}{c}{Model 2}
& \multicolumn{3}{c}{Model 3}
\\
\cmidrule(r){2-4}
\cmidrule(r){5-7}
\cmidrule(r){8-10}
%
Variable
& Coefficient & Std Error & $p$-value
& Coefficient & Std Error & $p$-value
& Coefficient & Std Error & $p$-value
\\
\midrule
Brand1:$\log p_t$
& -3.44 & 0.226 & 2e-16***
& -3.39 & 0.227 & 2e-16***
& -3.27 & 0.231 & 2e-16***
\\
Brand2:$\log p_t$
& -2.67 & 0.250 & 2e-16***
& -2.62 & 0.248 & 2e-16***
& -2.61 & 0.248 & 2e-16***
\\
Brand3:$\log p_t$
& -4.45 & 0.413 & 2e-16***
& -4.50 & 0.425 & 2e-16***
& -4.43 & 0.427 & 2e-16***
\\
Brand4:$\log p_t$
& -2.34 & 0.607 & 1e-4***
& -2.32 & 0.601 & 1e-4***
& -2.38 & 0.599 & 9e-5***
\\
Brand5:$\log p_t$
& -3.92 & 0.536 & 2e-12***
& -3.90 & 0.532 & 2e-12***
& -3.86 & 0.530 & 2e-12***
\\[5pt]
Brand1:$\log p_{t-1}$
& & &
& 0.435 & 0.227 & 0.056.
& 0.518 & 0.229 & 0.024*
\\
Brand2:$\log p_{t-1}$
& & &
& 0.226 & 0.248 & 0.362
& 0.256 & 0.248 & 0.302
\\
Brand3:$\log p_{t-1}$
& & &
& 1.024 & 0.410 & 0.012*
& 1.078 & 0.423 & 0.011*
\\
Brand4:$\log p_{t-1}$
& & &
& 0.547 & 0.602 & 0.364
& 0.543 & 0.598 & 0.364
\\
Brand5:$\log p_{t-1}$
& & &
& 0.151 & 0.532 & 0.777
& 0.183 & 0.531 & 0.731
\\[5pt]
Brand1:$\log p_{t-2}$
& & &
& & &
& 0.465 & 0.231 & 0.045*
\\
Brand2:$\log p_{t-2}$
& & &
& & &
& 0.241 & 0.248 & 0.332
\\
Brand3:$\log p_{t-2}$
& & &
& & &
& 0.067 & 0.413 & 0.870
\\
Brand4:$\log p_{t-2}$
& & &
& & &
& -0.508 & 0.599 & 0.397
\\
Brand5:$\log p_{t-2}$
& & &
& & &
& 0.047 & 0.530 & 0.979
\\[5pt]
Brand1:MAPE
& \multicolumn{3}{c}{0.146}
& \multicolumn{3}{c}{0.131}
& \multicolumn{3}{c}{0.114}
\\
Brand2:MAPE
& \multicolumn{3}{c}{0.111}
& \multicolumn{3}{c}{0.111}
& \multicolumn{3}{c}{0.109}
\\
Brand3:MAPE
& \multicolumn{3}{c}{0.108}
& \multicolumn{3}{c}{0.103}
& \multicolumn{3}{c}{0.099}
\\
Brand4:MAPE
& \multicolumn{3}{c}{0.192}
& \multicolumn{3}{c}{0.192}
& \multicolumn{3}{c}{0.194}
\\
Brand5:MAPE
& \multicolumn{3}{c}{0.110}
& \multicolumn{3}{c}{0.103}
& \multicolumn{3}{c}{0.099}
\\
\bottomrule
\end{tabular}
\end{document}
Then create another document from which to import the image:
\documentclass{standalone}
\usepackage{caption}
\usepackage{booktabs}
\usepackage{graphicx}
\begin{document}
\begin{minipage}{0.9\textwidth}
\includegraphics[width=\textwidth]{mytable}
\captionof{table}{Regression results for 5 brands of coffee in a single store.}
\end{minipage}
\end{document}
In your code, the problem arises because TeX tries to use the same font size (viz., \normalsize) for the tabular environment and the caption material. Because you're using the fairly narrow default value of \textwidth and, moreover, are using only 90% of that amount for the minipage, the table is simply too wide to fit in the space available.
I suggest you do the following: (i) use narrower column headers, (ii) reduce the value of the \tabcolsep parameter (which governs the width of the intercolumn space), (iii) don't use any whitespace at the start and end of the table, as well as (iv) use the dcolumn pacakge to align the numbers in four of the six data columns on the decimal points. With these changes, you'll get a table that uses the same font size for the caption and the contents of the tabular environment -- and fits into the text block.
\documentclass{standalone}
\usepackage[margin=1in]{geometry}
\usepackage{booktabs}
\usepackage{dcolumn}
\usepackage{caption}
\newcolumntype{z}{D{.}{.}{2.3}}
\newcommand{\mc}[1]{\multicolumn{1}{c}{#1}}
\addtolength{\tabcolsep}{-0.5pt}
\begin{document}
\begin{minipage}{\textwidth}
\begin{tabular}{@{}lzzlzzlzzl@{}}
\toprule
Variable
& \multicolumn{3}{c}{Model 1}
& \multicolumn{3}{c}{Model 2}
& \multicolumn{3}{c@{}}{Model 3}
\\
\cmidrule(lr){2-4}
\cmidrule(lr){5-7}
\cmidrule(l){8-10}
%
& \mc{Coeff} & \mc{Std Err} & $p$-value
& \mc{Coeff} & \mc{Std Err} & $p$-value
& \mc{Coeff} & \mc{Std Err} & $p$-value\\
\midrule
Brand1:$\log p_t$
& -3.44 & 0.226 & 2e-16***
& -3.39 & 0.227 & 2e-16***
& -3.27 & 0.231 & 2e-16***
\\
Brand2:$\log p_t$
& -2.67 & 0.250 & 2e-16***
& -2.62 & 0.248 & 2e-16***
& -2.61 & 0.248 & 2e-16***
\\
Brand3:$\log p_t$
& -4.45 & 0.413 & 2e-16***
& -4.50 & 0.425 & 2e-16***
& -4.43 & 0.427 & 2e-16***
\\
Brand4:$\log p_t$
& -2.34 & 0.607 & 1e-4***
& -2.32 & 0.601 & 1e-4***
& -2.38 & 0.599 & 9e-5***
\\
Brand5:$\log p_t$
& -3.92 & 0.536 & 2e-12***
& -3.90 & 0.532 & 2e-12***
& -3.86 & 0.530 & 2e-12***
\\[5pt]
Brand1:$\log p_{t-1}$
& & &
& 0.435 & 0.227 & 0.056.
& 0.518 & 0.229 & 0.024*
\\
Brand2:$\log p_{t-1}$
& & &
& 0.226 & 0.248 & 0.362
& 0.256 & 0.248 & 0.302
\\
Brand3:$\log p_{t-1}$
& & &
& 1.024 & 0.410 & 0.012*
& 1.078 & 0.423 & 0.011*
\\
Brand4:$\log p_{t-1}$
& & &
& 0.547 & 0.602 & 0.364
& 0.543 & 0.598 & 0.364
\\
Brand5:$\log p_{t-1}$
& & &
& 0.151 & 0.532 & 0.777
& 0.183 & 0.531 & 0.731
\\[5pt]
Brand1:$\log p_{t-2}$
& & &
& & &
& 0.465 & 0.231 & 0.045*
\\
Brand2:$\log p_{t-2}$
& & &
& & &
& 0.241 & 0.248 & 0.332
\\
Brand3:$\log p_{t-2}$
& & &
& & &
& 0.067 & 0.413 & 0.870
\\
Brand4:$\log p_{t-2}$
& & &
& & &
& -0.508 & 0.599 & 0.397
\\
Brand5:$\log p_{t-2}$
& & &
& & &
& 0.047 & 0.530 & 0.979
\\[5pt]
Brand1:MAPE
& \multicolumn{3}{c}{0.146}
& \multicolumn{3}{c}{0.131}
& \multicolumn{3}{c}{0.114}
\\
Brand2:MAPE
& \multicolumn{3}{c}{0.111}
& \multicolumn{3}{c}{0.111}
& \multicolumn{3}{c}{0.109}
\\
Brand3:MAPE
& \multicolumn{3}{c}{0.108}
& \multicolumn{3}{c}{0.103}
& \multicolumn{3}{c}{0.099}
\\
Brand4:MAPE
& \multicolumn{3}{c}{0.192}
& \multicolumn{3}{c}{0.192}
& \multicolumn{3}{c}{0.194}
\\
Brand5:MAPE
& \multicolumn{3}{c}{0.110}
& \multicolumn{3}{c}{0.103}
& \multicolumn{3}{c}{0.099}
\\
\bottomrule
\end{tabular}
\captionof{table}{Regression results for 5 brands of coffee in a single store.}
\end{minipage}
\end{document}