Question

which table shows a negative correlation?
x 2 5 6 7 10 12
y -8 -5 -6 -3 -2 -1
x 2 5 6 7 10 12
y -5 -5 -5 -5 -5 -5
x 2 5 6 7 10 12
y 6 3 1 1 3 6
x 2 5 6 7 10 12
y 4 2 -4 -3 -11 -12

Explanation:

Step1: Recall negative - correlation concept

In a negative correlation, as the value of \(x\) increases, the value of \(y\) decreases.

Step2: Analyze the first table

As \(x\) increases (\(2,5,6,7,10,12\)), \(y\) does not consistently decrease. For example, when \(x\) goes from \(5\) to \(6\), \(y\) goes from \(- 5\) to \(-6\) and then from \(6\) to \(7\), \(y\) goes from \(-6\) to \(-3\).

Step3: Analyze the second table

Here, \(y=-5\) for all values of \(x\). There is no correlation (neither positive nor negative).

Step4: Analyze the third table

As \(x\) increases (\(2,5,6,7,10,12\)), \(y\) first decreases from \(6\) to \(1\) and then increases from \(1\) to \(6\). There is no consistent negative - trend.

Step5: Analyze the fourth table

As \(x\) increases (\(2,5,6,7,10,12\)), \(y\) decreases (\(4,2, - 4,-3,-11,-12\)). This shows a negative correlation.

Answer:

The fourth table (where \(x = 2,5,6,7,10,12\) and \(y = 4,2,-4,-3,-11,-12\))