which table shows a positive correlation? x y 1 5 2 5 2 5 4 5 5 5 x y 1 10 2 18 3 31 4 37 5 52 x y 1 24 2 15…

Explanation:

Step1: Recall positive - correlation definition

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

Step2: Analyze the first table

When $x$ increases from 1 to 5, $y$ remains 5. There is no positive correlation.

Step3: Analyze the second table

When $x = 1,y = 10$; when $x = 2,y = 18$; when $x = 3,y = 31$; when $x = 4,y = 37$; when $x = 5,y = 52$. As $x$ increases, $y$ increases. This shows a positive correlation.

Step4: Analyze the third table

When $x$ increases from 1 to 5, $y$ decreases from 24 to 6. There is a negative - correlation, not a positive one.

Step5: Analyze the fourth table

Since $x$ has a constant value of 8, we cannot determine a correlation based on the change of $x$.

Answer:

The second table (with $x$ values 1, 2, 3, 4, 5 and corresponding $y$ values 10, 18, 31, 37, 52) shows a positive correlation.