Which table of paired values $(x,y)$ shows a negative correlation between $x$ and $y$?

• A. Table A: $x:1,2,3,4$ and $y:8,6,4,2$
• B. Table D: $x:1,2,3,4$ and $y:3,7,2,6$
• C. Table C: $x:1,2,3,4$ and $y:5,5,5,5$
• D. Table B: $x:1,2,3,4$ and $y:2,4,6,8$

Answer: (A)

Verified step by step guidance

1. Understand that a negative correlation between variables \(x\) and \(y\) means that as \(x\) increases, \(y\) tends to decrease. This relationship is often visualized as a downward slope when plotting \(y\) against \(x\).
2. Look at each table and observe the pattern of \(y\) values as \(x\) increases. For example, in Table A, \(x\) increases from 1 to 4, and \(y\) decreases from 8 to 2, which suggests a negative relationship.
3. In Table B, notice that as \(x\) increases, \(y\) also increases (from 2 to 8), indicating a positive correlation, not negative.
4. In Table C, \(y\) remains constant at 5 regardless of \(x\), which means there is no correlation between \(x\) and \(y\).
5. In Table D, \(y\) values do not consistently increase or decrease with \(x\) (values go 3, 7, 2, 6), so this does not show a clear negative correlation.