Question

which table shows a negative correlation?

Explanation:

Step1: Recall negative - correlation concept

In a negative - correlation, as the value of $x$ increases, the value of $y$ decreases.

Step2: Check each table

For the first table: As $x$ increases from 2 to 12, $y$ values do not show a consistent decrease.
For the second table: As $x$ increases from 2 to 12, $y$ values do not show a consistent decrease.
For the third table: When $x = 2,y=-5$; as $x$ increases to 5, $y$ remains - 5; not a negative - correlation.
For the fourth table: When $x = 2,y=-8$; as $x$ increases to 5, $y=-5$; as $x$ increases to 6, $y=-6$; as $x$ increases to 7, $y=-3$; as $x$ increases to 10, $y=-2$; as $x$ increases to 12, $y=-1$. As $x$ increases, $y$ generally increases in a non - consistent way.

Let's re - check the fourth table more carefully. When $x$ goes from 2 to 5, although $y$ increases from - 8 to - 5, when $x$ goes from 5 to 6, $y$ decreases from - 5 to - 6, when $x$ goes from 6 to 7, $y$ decreases from - 6 to - 3, when $x$ goes from 7 to 10, $y$ decreases from - 3 to - 2, when $x$ goes from 10 to 12, $y$ decreases from - 2 to - 1. Overall, as $x$ increases, $y$ has a tendency to decrease.

Answer:

The fourth table shows a negative correlation.