If I want to investigate how two continuous variables are linked, what is the difference between calculating the correlation coefficient (Pearson's $r$) versus calculating the (simple linear) regression coefficient?  I see people who, if the regression coefficient is significantly different from zero, talk about the two variables as if they are correlated, which is confusing as it suggests that the two coefficients (correlation, regression) are the same thing.  Having said that, isn't $r$ a measure of the (regression line) slope anyway? I'm confused!!
In particular, I am referring to the Pearson product-moment correlation coefficient.
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I reproduced this effect by tinkering:    The code is as follows:  \documentclass[aspectratio=1610]{beamer}  \usepackage[T1]{fontenc} \usepackage[french]{babel}  \usepackage{amsmath, amsfonts, amssymb} \usefonttheme[onlymath]{serif}  \begin{document} \begin{frame} Lorsque le \og \textit{carreau carré} \fg{}   mesure: \begin{itemize} \item $\rm 1\,cm$ de côté, l'unité d'aire est appelée le \og \textrm{centimètre carré} \fg{} et est noté $\rm cm^2$; \item $\rm 1\,dm$ \hspace{1mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}''\hspace{8mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{décimètre carré} \fg{} \hspace{2mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1.5mm} $\rm dm^2$; \item $\rm 1\,m$ \hspace{3mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}'' \hspace{7mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{mètre carré} \fg{}  \hspace{9mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1mm} $\rm m^2$; \item etc. \end{itemize} \end{frame} \end{document}   How can I get the same effect more simply than by tinkering like I just did? 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