Chapter 13.3, Problem 38E

To determine

To match: The correct graphs corresponding to the given values of the correlation coefficient r.

Answer to Problem 38E

The correct matches are:

  $\begin{array}{l}\left(a\right)\to \left(iv\right)\\ \left(b\right)\to \left(i\right)\\ \left(c\right)\to \left(iii\right)\\ \left(d\right)\to \left(ii\right)\end{array}$

Explanation of Solution

Given:

The graphs are:

  

Figure 1

The values of r are:

(a) $r=0.04$	(b) $r=1$
(c) $r=-0.92$	(d) $r=0.81$

Calculation:

Based on the value of the correlation coefficient, following 5 deductions are implied:

1) For $r=-1$ , there is a perfect negative correlation.

2) For $-1<r<0$ , the relation moves from strong to weak negative linear relationship.

3) For $r=0$ , there is no linear relationship.

4) For $0<r<1$ , the relation moves from weak to strong positive linear relationship.

5) For $r=1$ , there is a perfect positive correlation.

So,

(a) For $r=0.04$ , the data is not linearly related and the graph that portrays this is numbered (iv).

(b) For $r=1$ , the graph represents a perfect positive linear relation which is portrayed by the graph numbered (i).

(c) For $r=-0.92$ , the graph represents a strong negative linear relation which is portrayed in the graph numbered (iii).

(d) For $r=0.81$ , the graph represents a strong positive linear relation which is portrayed in the graph numbered (ii).