Exam 1

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

The absolute value of the correlation coefficient is at most
$0.8$.

The standard deviation of
$X$ is at least
$6$.

For
$X=17.1$,
$Y$ can be expected to be about 19.9 .

The scatterplot is standardized.

The mean of
$Y$ is at least
$30$.
Solution

False. A strong association between the variables is given in the scatterplot. Hence the absolute value of the correlation coefficient is close to
$1$ and therefore larger than
$0.8$.

True. The standard deviation of
$X$ is about equal to
$20$ and is therefore larger than
$6$.

True. The regression line at
$X=17.1$ implies a value of about
$Y=19.9$.

False. The scatterplot is not standardized, because
$X$ and
$Y$ do not both have mean
$0$ and variance
$1$.

False. The mean of
$Y$ is about equal to
$20$ and hence is smaller than
$30$.