Question

which table shows positive correlation? identifying correlation

Explanation:

Step1: Recall positive - correlation concept

In a positive correlation, as the value of $x$ increases, the value of $y$ also increases.

Step2: Analyze first table

When $x$ decreases from 5 to 1, $y$ values are 18, 11, 14, 12, 15 with no clear increasing or decreasing trend.

Step3: Analyze second table

When $x$ decreases from 5 to 1, $y$ decreases from 19 to 11. This is a negative - correlation.

Step4: Analyze third table

When $x$ decreases from 5 to 1, $y$ increases from 11 to 18. Since as $x$ decreases (opposite of the general increasing - $x$ case, but still a consistent relationship), as $x$ gets smaller, $y$ gets larger. If we consider the reverse (increase $x$ from 1 to 5), $y$ decreases. But if we re - order the $x$ values in ascending order (1, 2, 3, 4, 5), $y$ values 18, 16, 14, 12, 11 show that as $x$ increases, $y$ decreases. This is a negative - correlation.

Step5: Analyze fourth table

When $x$ decreases from 5 to 1, $y$ increases from 11 to 18. If we re - order the $x$ values in ascending order (1, 2, 3, 4, 5), $y$ values are 18, 16, 14, 12, 11. This is a negative - correlation.

In a positive correlation, as $x$ increases, $y$ increases. The third table shows that as $x$ (when arranged in ascending order 1, 2, 3, 4, 5) has $y$ values 11, 12, 14, 16, 18 which means as $x$ increases, $y$ increases.

Answer:

The third table (where $x$ values are 5, 4, 3, 2, 1 and $y$ values are 11, 12, 14, 16, 18)