Question

choose the most appropriate completion of the sentence.
in order to indicate a strong correlation between variables, the correlation coefficient will be
○ near -1 or 1
○ near -1
○ near 10
○ near 1
○ near 0
○ near 1/2

Explanation:

Step1: Recall correlation coefficient range

The correlation coefficient \( r \) ranges between \(-1\) and \( 1 \), i.e., \( -1 \leq r \leq 1 \).

Step2: Interpret correlation strength

• A value near \( 0 \) means weak or no correlation.
• A value near \( 1 \) means a strong positive correlation.
• A value near \( -1 \) means a strong negative correlation.
• Values like near \( 10 \) (outside the range) or near \( \frac{1}{2} \) (moderate) don't indicate strong correlation. So, a strong correlation is indicated when \( r \) is near \( -1 \) or \( 1 \).

Answer:

A. near -1 or 1