Answer :
To determine which student had the strongest correlation from the given correlation coefficients:
1. Understand the Correlation Coefficient:
The correlation coefficient, denoted as [tex]\( r \)[/tex], measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.
- A value of 1 implies a perfect positive correlation.
- A value of -1 implies a perfect negative correlation.
- A value of 0 implies no linear correlation.
2. Examine the Absolute Values:
To find the strongest correlation, we look at the magnitude of the values, disregarding the sign. This is because a correlation of -1 is just as strong as a correlation of +1; they just have different directions. Therefore, we compare the absolute values of the correlation coefficients.
3. List the 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]
4. Calculate the Absolute Values:
- [tex]\(|-0.87| = 0.87\)[/tex]
- [tex]\(|-0.78| = 0.78\)[/tex]
- [tex]\(|0.79| = 0.79\)[/tex]
- [tex]\(|0.86| = 0.86\)[/tex]
5. Determine the Strongest Correlation:
Compare the absolute values:
- Student A: 0.87
- Student B: 0.78
- Student C: 0.79
- Student D: 0.86
The highest absolute value is 0.87, which comes from Student A's data.
6. Conclusion:
Student A had the strongest correlation with a correlation coefficient of [tex]\( r = -0.87 \)[/tex]. The negative sign just indicates direction, but the strength, as shown by the absolute value, is the greatest among the students.
1. Understand the Correlation Coefficient:
The correlation coefficient, denoted as [tex]\( r \)[/tex], measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.
- A value of 1 implies a perfect positive correlation.
- A value of -1 implies a perfect negative correlation.
- A value of 0 implies no linear correlation.
2. Examine the Absolute Values:
To find the strongest correlation, we look at the magnitude of the values, disregarding the sign. This is because a correlation of -1 is just as strong as a correlation of +1; they just have different directions. Therefore, we compare the absolute values of the correlation coefficients.
3. List the 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]
4. Calculate the Absolute Values:
- [tex]\(|-0.87| = 0.87\)[/tex]
- [tex]\(|-0.78| = 0.78\)[/tex]
- [tex]\(|0.79| = 0.79\)[/tex]
- [tex]\(|0.86| = 0.86\)[/tex]
5. Determine the Strongest Correlation:
Compare the absolute values:
- Student A: 0.87
- Student B: 0.78
- Student C: 0.79
- Student D: 0.86
The highest absolute value is 0.87, which comes from Student A's data.
6. Conclusion:
Student A had the strongest correlation with a correlation coefficient of [tex]\( r = -0.87 \)[/tex]. The negative sign just indicates direction, but the strength, as shown by the absolute value, is the greatest among the students.
