Question

which table shows a negative correlation?
(the tables are presented with x and y values as follows:
first table: x: 2,5,6,7,10,12; y: -8,-5,-6,-3,-2,-1
second table: x: 2,5,6,7,10,12; y: -5,-5,-5,-5,-5,-5
third table: x: 2,5,6,7,10,12; y: 6,3,1,1,3,6
fourth table: x: 2,5,6,7,10,12; y: 4,2,-4,-3,-11,-12)

Explanation:

Step1: Recall negative correlation

Negative correlation means as \( x \) increases, \( y \) generally decreases.

Step2: Analyze first table

\( x \): 2, 5, 6, 7, 10, 12 (increasing)
\( y \): -8, -5, -6, -3, -2, -1 (no clear decrease, inconsistent)

Step3: Analyze second table

\( x \): 2, 5, 6, 7, 10, 12 (increasing)
\( y \): -5, -5, -6, -6, -5, -5 (constant, no correlation)

Step4: Analyze third table

\( x \): 2, 5, 6, 7, 10, 12 (increasing)
\( y \): 6, 3, 1, 1, 3, 6 (decreases then increases, positive correlation trend at end)

Step5: Analyze fourth table

\( x \): 2, 5, 6, 7, 10, 12 (increasing)
\( y \): 4, 2, -4, -3, -11, -12 (as \( x \) increases, \( y \) generally decreases)

Answer:

The table with \( x \) values 2, 5, 6, 7, 10, 12 and \( y \) values 4, 2, -4, -3, -11, -12 (the fourth table) shows a negative correlation.