College

Four students in Ms. Alton's class shared the correlation coefficients derived from their data as follows:

- 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]

Whose data had the strongest correlation?

A. Student A
B. Student B
C. Student C
D. Student D

Answer :

Sure, let's solve the problem step-by-step.

The task is to determine which student’s data had the strongest correlation based on the given correlation coefficients. Recall that the strength of a correlation is measured by the absolute value of the correlation coefficient [tex]\(r\)[/tex]. The closer the absolute value of [tex]\(r\)[/tex] is to 1, the stronger the correlation.

Here are the steps:

1. List the given correlation coefficients:
- 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]

2. Calculate the absolute value of each correlation coefficient:
- Absolute value for Student A: [tex]\(|r_A| = |-0.87| = 0.87\)[/tex]
- Absolute value for Student B: [tex]\(|r_B| = |-0.78| = 0.78\)[/tex]
- Absolute value for Student C: [tex]\(|r_C| = |0.79| = 0.79\)[/tex]
- Absolute value for Student D: [tex]\(|r_D| = |0.86| = 0.86\)[/tex]

3. Compare the absolute values:
- [tex]\(|r_A| = 0.87\)[/tex]
- [tex]\(|r_B| = 0.78\)[/tex]
- [tex]\(|r_C| = 0.79\)[/tex]
- [tex]\(|r_D| = 0.86\)[/tex]

4. Determine the maximum absolute value:
The maximum absolute value from the list is [tex]\(0.87\)[/tex].

Since the strongest correlation is indicated by the highest absolute value, the student with the strongest correlation is:

Student A: [tex]\(r = -0.87\)[/tex].

Thus, the data provided by Student A had the strongest correlation.