Question

which table shows a negative correlation? x 2 5 6 7 10 12 y -8 -5 -6 -3 -2 -1 x 2 5 6 7 10 12 y -5 -5 -5 -5 -5 -5 x 2 5 6 7 10 12 y 6 3 1 1 3 6 x 2 5 6 7 10 12 y 4 2 -4 -3 -11 -12

Explanation:

Step1: Recall the definition of negative correlation

In a negative correlation, as \(x\) increases, \(y\) decreases.

Step2: Analyze each table

• First table: When \(x = 2,y=-8\); \(x = 5,y = - 5\). As \(x\) increases from \(2\) to \(5\), \(y\) increases from \(-8\) to \(-5\). So, it is not a negative - correlation.
• Second table: \(y=-5\) for all \(x\) values. There is no correlation (neither positive nor negative).
• Third table: When \(x = 2,y = 6\); \(x=5,y = 3\); \(x = 6,y=1\); \(x=7,y = 1\) (here \(x\) increases from \(6\) to \(7\) and \(y\) remains the same). Then \(x = 10,y = 3\) ( \(x\) increases from \(7\) to \(10\) and \(y\) increases from \(1\) to \(3\)). So, it is not a perfect negative correlation.
• Fourth table: When \(x = 2,y = 4\); \(x=5,y = 2\); \(x = 6,y=-4\); \(x=7,y=-3\); \(x = 10,y=-11\); \(x=12,y=-12\). As \(x\) increases, \(y\) generally decreases.

Answer:

The fourth table.