Which correlation best describes the strength of the linear association?
Understand the Problem
The question is asking to identify the type of correlation represented by the given statistical values (r and r²) and select the appropriate description of the strength of the linear association based on these values.
Answer
Strong negative correlation because $r = -0.9998$.
Answer for screen readers
Strong negative correlation because $r = -0.9998$.
Steps to Solve
-
Identify the Correlation Coefficient
The problem provides the correlation coefficient $r = -0.9998$. This value indicates the strength and direction of the linear relationship between the two variables. -
Determine the Type of Correlation
Since $r < 0$, it indicates a negative correlation. The closer $r$ is to $-1$, the stronger the negative linear relationship. Here, $r = -0.9998$ is very close to $-1$, suggesting a strong negative correlation. -
Check the Strength of the Correlation
Using the typical interpretation:- (0.0 < |r| < 0.3): weak
- (0.3 \leq |r| < 0.7): moderate
- (0.7 \leq |r| < 1.0): strong
Since $|-0.9998| \approx 1$, this indicates a strong correlation.
-
Final Decision
Given that the strength is strong and it is negative, the appropriate conclusion is that it is a "strong negative correlation."
Strong negative correlation because $r = -0.9998$.
More Information
A negative correlation means that as one variable increases, the other variable decreases. An $r$ value of nearly $-1$ signifies a very strong association between the two variables, indicating that predictions about one variable can be made with high accuracy using the other.
Tips
- Misinterpreting the sign of $r$. Remember that values close to $-1$ indicate strong negative relationships, while values close to $1$ indicate strong positive relationships.
- Overlooking the closeness to 1 or -1. High absolute values show strong correlation, so it's crucial to consider the entire scale.
AI-generated content may contain errors. Please verify critical information
