Question

which table shows no correlation?

Explanation:

Step1: Check for patterns

In a table with no - correlation, there should be no clear increasing or decreasing trend between the $x$ and $y$ values.
For the first table: As $x$ increases from 3 to 15, $y$ first decreases, then increases.
For the second table: As $x$ increases from 3 to 15, $y$ does not follow a consistent increasing or decreasing pattern.
For the third table: As $x$ increases from 3 to 15, $y$ consistently decreases. There is a negative - correlation.
For the fourth table (incomplete as only 3 rows are shown): As $x$ increases from 3 to 6, $y$ first decreases from - 2 to - 4 and then increases to 6.

Step2: Determine the table with no correlation

The table with no clear pattern of increase or decrease between $x$ and $y$ values is the second table.

Answer:

The second table shows no correlation.