Plot points from pgfplotstableset

This has nothing to do with beamer vs. article but with the fact that a column is a group, so the loadedtable is not "known" in the right column. This can be solved by defining the table before the columns.

documentclass[]{beamer}
usepackage{pgfplots}
usepackage{pgfplotstable}
begin{document}
begin{frame}[t]
frametitle{Regression}
framesubtitle{Weight and Height}
pgfmathsetseed{1138}% set the random seed
pgfplotstableset{ % Define the equations for x and y
    create on use/x/.style={create col/expr={42+5*pgfplotstablerow}},
    create on use/y/.style={create col/expr={(0.6*thisrow{x}+130)+5*rand}},
}%
pgfplotstablenew[columns={x,y}]{10}loadedtable % create a new table with 10 rows and columns x and y:
begin{columns}[T]
begin{column}{0.22textwidth}
pgfplotstabletypeset[fixed]{loadedtable}
end{column}%
begin{column}{0.78textwidth}  
Consideremos la variable textit{Peso} en el eje X, es decir esta es la
variable independiente. Y luego consideremos la variable textit{Altura} en el 
eje Y, es decir, esta es la variable dependiente.

begin{tikzpicture}
begin{axis}[height=4.5cm,width=0.9textwidth,
xlabel=Weight (kg), % label x axis
ylabel=Height (cm), % label y axis
axis lines=left, %set the position of the axes
xmin=40, xmax=105, % set the min and max values of the x-axis
ymin=150, ymax=200, % set the min and max values of the y-axis
clip=false
]
addplot[only marks] table {loadedtable};
end{axis}
end{tikzpicture}
end{column}
end{columns}
end{frame}
end{document}

I had to make the left column a tiny bit wider and the plot smaller to avoid overfull hboxes. Needless to say that you could add the regression line with pgfplots, too, if needed.