Chapter 2.5, Problem 13HP

To determine

What can you determine about the correlation between statements $a$ and $d$ ?

Answer to Problem 13HP

  $\boxed{\text{Negative correlation}}$

Explanation of Solution

Given information:

If statements $a$ and $b$ have a positive correlation, $b$ and $c$ have a negative correlation, and $c$ and $d$ have a positive correlation, what can you determine about the correlation between statements $a$ and $d$ ? Explain your reasoning.

Calculation:

There are four statements $a$ , $b$ , $c$ and $d$ .

Statement $a$ and $b$ have positive correlation

Statement $b$ and $c$ have negative correlation

Statement $c$ and $d$ have positive correlation

Since, statement $a$ and $b$ have positive correlation, then both $a$ and $b$ are increasing.

Statement $b$ and $c$ have negative correlation, and then if $b$ is increasing (as per the previous condition (i)), then $c$ must be decreasing.

Statement $c$ and $d$ have positive correlation and if $c$ is decreasing (as per the previous condition (ii)), then $d$ must be decreasing as well.

If $a$ is increasing (as per (i)) and $d$ is decreasing (as per(ii)), then there is negative correlation between $a$ and $d$ .

Hence, there is negative correlation between $a$ and $d$ .