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

As $x$ increases ($2,5,6,7,10,12$), $y$ values ($-8,-5,-6,-3,-2,-1$) do not show a consistent decrease.

Step3: Analyze the second table

$y = - 5$ for all $x$ values. There is no correlation.

Step4: Analyze the third table

As $x$ increases ($2,5,6,7,10,12$), $y$ values ($6,3,1,1,3,6$) do not show a consistent decrease.

Step5: Analyze the fourth table

As $x$ increases from $2$ to $12$ ($2,5,6,7,10,12$), $y$ values decrease from $4$ to $-12$ ($4,2, - 4,-3,-11,-12$). This shows a negative correlation.

Answer:

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