To determine whose data had the strongest correlation, we need to look at the magnitude (absolute value) of the correlation coefficients provided by the four students. Correlation coefficients (denoted as [tex]\( r \)[/tex]) measure the strength and direction of a linear relationship between two variables, ranging from [tex]\(-1\)[/tex] to [tex]\(1\)[/tex]. The closer the absolute value of [tex]\( r \)[/tex] is to [tex]\(1\)[/tex], the stronger the correlation.
Here are the provided correlation coefficients for each student:
- Student A: [tex]\( r = -0.87 \)[/tex]
- Student B: [tex]\( r = -0.78 \)[/tex]
- Student C: [tex]\( r = 0.79 \)[/tex]
- Student D: [tex]\( r = 0.86 \)[/tex]
First, we calculate the absolute values of these correlation coefficients:
[tex]\[
\left| r_A \right| = \left| -0.87 \right| = 0.87
\][/tex]
[tex]\[
\left| r_B \right| = \left| -0.78 \right| = 0.78
\][/tex]
[tex]\[
\left| r_C \right| = \left| 0.79 \right| = 0.79
\][/tex]
[tex]\[
\left| r_D \right| = \left| 0.86 \right| = 0.86
\][/tex]
Now, we compare these absolute values to determine which one is the largest:
[tex]\[
0.87, \ 0.78, \ 0.79, \ 0.86
\][/tex]
Among these absolute values, [tex]\( 0.87 \)[/tex] is the highest. Therefore, Student A's data had the strongest correlation. The absolute value indicates the strength of the correlation, irrespective of whether it is positive or negative.
Answer: Student A
