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 ($2,5,6,7,10,12$), $y$ does not consistently decrease. For example, when $x$ goes from $5$ to $6$, $y$ goes from $- 5$ to $-6$ and then from $6$ to $7$, $y$ goes from $-6$ to $-3$.

Step3: Analyze the second table

Here, $y=-5$ for all values of $x$. There is no correlation (neither positive nor negative).

Step4: Analyze the third table

As $x$ increases, $y$ first decreases from $6$ to $1$ and then increases from $1$ to $6$. So, it is not a negative - correlation.

Step5: Analyze 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 further, $y$ continues to decrease overall. This table shows a negative correlation.

Answer:

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