Which value of correlation coefficient indicates the strongest negative linear relationship? (A) -1 (B) 1 (C) 0 (D) 0.5
Answer (1)
The value of the correlation coefficient that indicates the strongest negative linear relationship is − 1 . So, the correct choice for this question is option (A) -1.
Understanding the Correlation Coefficient:
What is it? The correlation coefficient, denoted as r , is a statistical measure that describes the strength and direction of a linear relationship between two variables. Its value ranges from − 1 to 1 .
Interpretation of Values:
r = 1 : A perfect positive linear relationship. As one variable increases, the other also increases in perfect proportion.
r = − 1 : A perfect negative linear relationship. As one variable increases, the other decreases in perfect proportion.
r = 0 : No linear relationship between the variables.
Values between − 1 and 1 indicate the degree of linear relationship, with values closer to − 1 or 1 indicating stronger relationships, either negative or positive.
Why is − 1 the strongest negative relationship? When r = − 1 , the data points on a scatter plot lie perfectly on a downward sloping line, indicating a perfectly inverse relationship between the variables.
Understanding these fundamentals helps in analyzing data and predicting relationships between variables, which is essential in various fields, including economics, biology, and more. Knowing how to interpret the correlation coefficient can help in making data-driven decisions and understanding the dynamics within datasets.
