Question

(a) for which data - set is the sample correlation coefficient r closest to 0?
(b) which data - set indicates the strongest negative linear relationship between its two variables?
(c) for which data - set is the sample correlation coefficient r equal to - 1?
(d) which data - set has an apparent negative, but not perfect, linear relationship between its two variables?

Explanation:

Step1: Recall correlation coefficient properties

The correlation coefficient $r$ ranges from - 1 to 1. $r = 0$ means no linear relationship, $r=-1$ means a perfect negative linear relationship and values close to - 1 mean strong negative linear relationships. Values close to 0 mean weak or no linear relationship.

Step2: Answer part (a)

We are looking for a data - set with $r$ closest to 0. This is the data - set with little or no linear relationship.

Step3: Answer part (b)

The data - set with the strongest negative linear relationship has a value of $r$ closest to - 1.

Step4: Answer part (c)

The data - set with $r = - 1$ has a perfect negative linear relationship.

Step5: Answer part (d)

We want a data - set with an apparent negative but not perfect linear relationship. So $r$ is negative but not equal to - 1.

Since no data - sets are provided, we can't give specific answers. But the general approach is as above.

Answer:

(a) The data - set with little or no linear relationship.
(b) The data - set with $r$ closest to - 1.
(c) The data - set with a perfect negative linear relationship.
(d) The data - set with a negative non - perfect linear relationship.