Question

which table shows a positive correlation?

Explanation:

Step1: Recall the definition of positive correlation

In a positive - correlation, as \(x\) increases, \(y\) also increases.

Step2: Analyze the first table

For the first table, when \(x\) increases (\(x = 1,2,4,5\)), \(y = 5\) remains constant. So, there is no positive correlation.

Step3: Analyze the second table

When \(x = 1,y = 10\); \(x=2,y = 18\); \(x = 3,y=31\); \(x = 4,y = 37\); \(x=5,y = 52\). As \(x\) increases (\(1\to2\to3\to4\to5\)), \(y\) also increases (\(10\to18\to31\to37\to52\)).

Step4: Analyze the third table

When \(x\) increases (\(1\to2\to3\to4\to5\)), \(y\) decreases (\(24\to15\to13\to9\to6\)). So, there is a negative correlation.

Step5: Analyze the fourth table

When \(x = 8\) (constant), \(y\) increases (\(9\to12\to17\to21\to22\)). Since \(x\) is not increasing, there is no positive correlation.

Answer:

The second table.