To determine the best description of the correlation for an [tex]\( r \)[/tex]-value of -0.93, let's break down the process step-by-step:
1. Understanding the [tex]\( r \)[/tex]-value:
- The [tex]\( r \)[/tex]-value, also known as the correlation coefficient, measures the strength and direction of a linear relationship between two variables.
- The [tex]\( r \)[/tex]-value ranges from -1 to 1.
- A positive [tex]\( r \)[/tex]-value indicates a positive correlation, while a negative [tex]\( r \)[/tex]-value indicates a negative correlation.
2. Determine the absolute value of [tex]\( r \)[/tex]:
- Since [tex]\( r = -0.93 \)[/tex], the absolute value is [tex]\( |r| = 0.93 \)[/tex].
3. Assessing the strength of the correlation:
- A correlation is generally considered strong when the absolute value of [tex]\( r \)[/tex] is closer to 1. Specifically:
- If [tex]\( |r| \geq 0.8 \)[/tex], the correlation is strong.
- If [tex]\( 0.5 \leq |r| < 0.8 \)[/tex], the correlation is moderate.
- If [tex]\( |r| < 0.5 \)[/tex], the correlation is weak.
- Since [tex]\( |r| = 0.93 \)[/tex], which is greater than 0.8, it indicates a strong correlation.
4. Determine the direction of the correlation:
- If [tex]\( r \)[/tex] is positive, the correlation is positive.
- If [tex]\( r \)[/tex] is negative, the correlation is negative.
- Since [tex]\( r = -0.93 \)[/tex] is negative, this indicates a negative correlation.
5. Combine strength and direction:
- We have determined that the correlation is strong because [tex]\( |r| = 0.93 \)[/tex].
- We have also determined that the correlation is negative because [tex]\( r = -0.93 \)[/tex].
Therefore, the best description of the correlation for an [tex]\( r \)[/tex]-value of -0.93 is:
a strong negative correlation.
The answer is:
a strong negative correlation.
