Chapter 13.3, Problem 35E

To determine

To find:If the statement “a correlation coefficient of $r\approx 0.021$ implies that the data have weak or no linear correlation” is true or false.

Answer to Problem 35E

The given statement is true based on the reason given below.

Explanation of Solution

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.

For $r\approx 0.021$ , according to point (4), the linear relationship among the data is weak or does not exist at all.

Hence, the statement is true.