choose all values of the correlation coefficient, r, that indicate a strong, but not perfect, linear…

choose all values of the correlation coefficient, r, that indicate a strong, but not perfect, linear association between two variables.\na. $r = - 0.85$\nb. $r = - 0.10$\nc. $r = 0.15$\nd. $r = 0.90$\ne. $r = 1.00$

choose all values of the correlation coefficient, r, that indicate a strong, but not perfect, linear association between two variables.\na. $r = - 0.85$\nb. $r = - 0.10$\nc. $r = 0.15$\nd. $r = 0.90$\ne. $r = 1.00$

Answer

Explanation:

Step1: Recall correlation - coefficient rules

The correlation coefficient $r$ ranges from - 1 to 1. Values close to - 1 or 1 indicate a strong linear association. A value of 1 or - 1 is a perfect linear association. We want strong but not perfect linear associations.

Step2: Analyze each option

  • Option A: $r=-0.85$. The absolute value $|r| = 0.85$, which is close to 1, indicating a strong negative linear association.
  • Option B: $r=-0.10$. The absolute value $|r|=0.10$, which is close to 0, indicating a weak linear association.
  • Option C: $r = 0.15$. The absolute value $|r|=0.15$, which is close to 0, indicating a weak linear association.
  • Option D: $r = 0.90$. The absolute value $|r| = 0.90$, which is close to 1, indicating a strong positive linear association.
  • Option E: $r = 1.00$ is a perfect positive linear association.

Answer:

A. $r=-0.85$, D. $r = 0.90$