Question

which table shows no correlation?

option 1:

x	3	5	6	8	10	14	15
y	-1	-2	-3	-2	-5	-4	-8

option 2:

x	3	5	6	8	10	14	15
y	-6	-7	-4	-2	0	-1	3

option 3:

x	3	5	6	8	10	14	15
y	-2	-4	6	8	12	10	-16

option 4:

x	3	5	6	8	10	14	15
y	-3	-5	-9	-11	-13	-15	-17

Explanation:

Step1: Define no correlation

No correlation means as $x$ increases, $y$ has no consistent upward/downward trend.

Step2: Analyze Table 1

$x$ increases, $y$ mostly decreases (weak negative correlation).

Step3: Analyze Table 2

$x$ increases, $y$ mostly increases (weak positive correlation).

Step4: Analyze Table 3

$x$ increases, $y$ fluctuates randomly: $-2\to-4\to6\to8\to12\to10\to-16$ (no consistent trend).

Step5: Analyze Table 4

$x$ increases, $y$ steadily decreases (strong negative correlation).

Answer:

The table with $x$ values 3, 5, 6, 8, 10, 14, 15 and $y$ values -2, -4, 6, 8, 12, 10, -16 (the third option) shows no correlation.