ACT (Enhanced)MathematicsMedium
A statistician is analyzing the relationship between two variables, x and y. She finds that as x increases, y generally decreases, but the points are widely scattered around a downward-sloping line. Which of the following is the most likely value for the correlation coefficient (r) between x and y?
- A-0.1
- B-0.7
- C0.9
- D0.2
Show answer & explanationAnswer & explanation
Correct answer: B. -0.7
A negative correlation coefficient indicates an inverse relationship (as one variable increases, the other decreases). A value of -0.7 suggests a moderately strong negative linear relationship with some scatter, matching the description.
Why the other options are wrong
- A. Incorrect. A value of -0.1 indicates a very weak negative linear correlation, almost no linear relationship.
- C. Incorrect. A value of 0.9 indicates a strong positive linear correlation (as x increases, y strongly increases).
- D. Incorrect. A value of 0.2 indicates a very weak positive linear correlation, with points highly scattered.
Correlation Coefficient (r)
The correlation coefficient (r) measures the strength and direction of a linear relationship between two quantitative variables. It ranges from -1 to +1.
- r > 0: positive linear relationship (as x increases, y increases).
- r < 0: negative linear relationship (as x increases, y decreases).
- |r| close to 1: strong linear relationship.
- |r| close to 0: weak or no linear relationship.
Memory trick: Correlation 'Cues' the 'Connection' between 'Variables'.