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 negative - correlation concept

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

Step2: Analyze the first table

For the first table, as $x$ increases from 2 to 12, $y$ values are not consistently decreasing. For example, when $x$ goes from 5 to 6, $y$ changes from - 5 to - 6 and then from 6 to 7, $y$ changes from - 6 to - 3.

Step3: Analyze the second table

In the second table, as $x$ increases, $y$ remains constant at - 5. There is no correlation (neither positive nor negative).

Step4: Analyze the third table

For the third table, as $x$ increases from 2 to 6, $y$ decreases from 6 to 1, but then as $x$ increases from 6 to 7, $y$ remains 1 and then increases as $x$ further increases. It is not a consistent negative - correlation.

Step5: Analyze the fourth table

In the fourth table, as $x$ increases from 2 to 5, $y$ decreases from 4 to 2. As $x$ increases from 5 to 6, $y$ decreases from 2 to - 4. As $x$ increases from 6 to 7, $y$ decreases from - 4 to - 3. As $x$ increases from 7 to 10, $y$ decreases from - 3 to - 11. As $x$ increases from 10 to 12, $y$ decreases from - 11 to - 12. This table shows a negative correlation.

Answer:

The fourth table (with $x$ values 2, 5, 6, 7, 10, 12 and $y$ values 4, 2, - 4, - 3, - 11, - 12)