Question

which table shows no correlation? x 3 5 6 8 10 14 15 y -1 -2 -3 -2 -5 -4 -8 x 3 5 6 8 10 14 15 y -6 -7 -4 -2 0 -1 3 x 3 5 6 8 10 14 15 y -2 -4 6 8 12 10 -16 x 3 5 6 8 10 14 15 y -3 -5 -9 -11 -13 -15 -17

Explanation:

Step1: Analyze the first table

As \(x\) increases, \(y\) generally decreases (though not perfectly), so there is a negative correlation tendency.

Step2: Analyze the second table

Looking at the values of \(x\) and \(y\), there is no clear pattern (increasing - decreasing - increasing - etc.) that can be described as a positive or negative correlation.

Step3: Analyze the third table

There is a mix of positive and negative changes that don't form a consistent pattern (except for some initial negative values and then positive, but not a clear overall trend), but it's more erratic than the second table. Wait, no - actually, check again. Wait, no: for the second table, when \(x = 3,y=-6\); \(x = 5,y = - 7\); \(x=6,y=-4\); \(x = 8,y=-2\); \(x = 10,y = 0\); \(x=14,y=-1\); \(x = 15,y = 3\). There is no consistent upward or downward trend as \(x\) increases. For the third table, \(x = 3,y=-2\); \(x = 5,y=-4\) (negative trend part), but then \(x = 6,y = 6\) (positive jump), \(x=8,y = 8\) (positive trend part), \(x = 10,y=12\) (positive), \(x=14,y = 10\) (decrease), \(x=15,y=-16\) (big decrease). But the second table has more randomness. The fourth table: as \(x\) increases by \(2\) (from \(3\) to \(5\), \(5\) to \(6\) - no, wait \(x\) values: \(3,5,6,8,10,14,15\). The \(y\) values: \(y=-3,-5,-9,-11,-13,-15,-17\). As \(x\) increases (even if not by a constant increment), \(y\) decreases by a relatively constant amount (negative correlation).

Answer:

The second table (where \(x = 3,y=-6\); \(x = 5,y = - 7\); \(x=6,y=-4\); \(x = 8,y=-2\); \(x = 10,y = 0\); \(x=14,y=-1\); \(x = 15,y = 3\)) shows no correlation.