Exam 1

1. Question

   The following figure shows a scatterplot. Which of the following statements are correct?
   

   
   
   1. The absolute value of the correlation coefficient is at least $0.8$.
   2. The slope of the regression line is about $1$.
   3. The standard deviation of $Y$ is at least $6$.
   4. For $X = 0.3$, $Y$ can be expected to be about $0$.
   5. The mean of $X$ is at most $5$.
   
   

   Solution

   1. False. No association between the variables is observed in the scatterplot. This implies a correlation coefficient close to $0$.
   2. False. The slope of the regression line is given by $r \cdot s_y/s_x$ and hence not about equal to $1$.
   3. False. The standard deviation of $Y$ is about equal to $1$ and is therefore smaller than $6$.
   4. True. The regression line at $X=0.3$ implies a value of about $Y = 0$.
   5. True. The mean of $X$ is about equal to $0$ and hence is smaller than $5$.