\begin{question}
The following figure shows a scatterplot. Which of the
following statements are correct?
\setkeys{Gin}{width=0.7\textwidth}
\includegraphics{scatterplot-002}
\begin{answerlist}
\item The absolute value of the correlation coefficient is at least $0.8$.
\item The slope of the regression line is about $1$.
\item The standard deviation of $Y$ is at least $6$.
\item For $X = 0.3 $, $Y$ can be expected to be about 0 .
\item The mean of $X$ is at most $5$.
\end{answerlist}
\end{question}
\begin{solution}
\begin{answerlist}
\item False. No association between the variables is observed in the scatterplot. This implies a correlation coefficient close to $0$.
\item False. The slope of the regression line is given by $r \cdot s_y/s_x$ and hence not about equal to $1$.
\item False. The standard deviation of $Y$ is about equal to $ 1 $ and is therefore smaller than $6$.
\item True. The regression line at $X=0.3$ implies a value of about $Y = 0$.
\item True. The mean of $X$ is about equal to $ 0 $ and hence is smaller than $5$.
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{mchoice}
%% \exsolution{00011}
%% \exname{Scatterplot}