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 (1)
Calculate the absolute value of each correlation coefficient.
Compare the absolute values to determine the largest.
The largest absolute value corresponds to the strongest correlation.
Student A's data has the strongest correlation: St u d e n t A .
Explanation
Understanding the Problem We are given the correlation coefficients for four students and asked to determine whose data had the strongest correlation. The strength of a correlation is determined by the absolute value of the correlation coefficient r . The closer ∣ r ∣ is to 1, the stronger the correlation.
Calculating Absolute Values To find the strongest correlation, we need to calculate the absolute value of each student's correlation coefficient:
Student A: ∣ r ∣ = ∣ − 0.87∣ = 0.87 Student B: ∣ r ∣ = ∣ − 0.78∣ = 0.78 Student C: ∣ r ∣ = ∣0.79∣ = 0.79 Student D: ∣ r ∣ = ∣0.86∣ = 0.86
Comparing Absolute Values Now, we compare the absolute values to determine which is the largest. Comparing the values, we have 0.86 > 0.79 > 0.78"> 0.87 > 0.86 > 0.79 > 0.78 . Therefore, Student A has the largest absolute value for their correlation coefficient.
Determining the Strongest Correlation Since Student A has the largest absolute value for their correlation coefficient, their data has the strongest correlation.
Examples
In data analysis, correlation coefficients help us understand the strength and direction of relationships between variables. For example, if we are analyzing the relationship between hours studied and exam scores, a strong positive correlation (close to 1) would indicate that more study time is associated with higher scores. Conversely, a strong negative correlation (close to -1) might indicate an inverse relationship, such as between exercise and resting heart rate. Understanding correlation helps in making predictions and informed decisions based on data.
