Question

which table shows no correlation?
o x 3 5 6 8 10 14 15
y -1 -2 -3 -2 -5 -4 -8
o x 3 5 6 8 10 14 15
y -6 -7 -4 -2 0 -1 3
o x 3 5 6 8 10 14 15
y -2 -4 6 8 12 10 -16
o x 3 5 6 8 10 14 15
y -3 -5 -9 -11 -13 -15 -17

Explanation:

Step1: Recall correlation concept

In a no - correlation situation, as $x$ values change, $y$ values show no consistent increasing or decreasing pattern.

Step2: Analyze first table

As $x$ increases ($3,5,6,\cdots$), $y$ values ($- 1,-2,-3,\cdots$) seem to have some randomness but also a bit of a decreasing trend initially.

Step3: Analyze second table

As $x$ increases ($3,5,6,\cdots$), $y$ values ($-6,-7,-4,\cdots$) have no clear increasing or decreasing pattern overall. There is no consistent relationship between $x$ and $y$ changes.

Step4: Analyze third table

As $x$ increases ($3,5,6,\cdots$), $y$ values ($-2,-4,6,\cdots$) seem to have some irregularity but also some signs of a non - linear relationship.

Step5: Analyze fourth table

As $x$ increases ($3,5,6,\cdots$), $y$ values ($-3,-5,-9,\cdots$) have a clear decreasing trend.

Answer:

The second table (where $x = 3,5,6,8,10,14,15$ and $y=-6,-7,-4,-2,0,-1,3$) shows no correlation.