which table shows no correlation?\no x 3 5 6 8 10 14 15\ny -1 -2 -3 -2 -5 -4 -8\no x 3 5 6 8 10 14 15\ny -6…

Explanation:

Step1: Recall correlation concept

Correlation implies a relationship between $x$ and $y$ values. In a positive - correlation, as $x$ increases, $y$ generally increases. In a negative - correlation, as $x$ increases, $y$ generally decreases. No - correlation means there is no clear pattern.

Step2: Analyze first table

As $x$ increases ($3,5,6,8,10,14,15$), $y$ values ($-1,-2,-3,-2,-5,-4,-8$) seem to have no clear increasing or decreasing trend.

Step3: Analyze second table

As $x$ increases ($3,5,6,8,10,14,15$), $y$ values ($-6,-7,-4,-2,0,-1,3$) show a general increasing trend (although not perfectly linear), indicating a positive correlation.

Step4: Analyze third table

As $x$ increases ($3,5,6,8,10,14,15$), $y$ values ($-2,-4,6,8,12,10,-16$) have no clear overall trend, but the large fluctuations suggest no simple linear correlation.

Step5: Analyze fourth table

As $x$ increases ($3,5,6,8,10,14,15$), $y$ values ($-3,-5,-9,-11,-13,-15,-17$) show a clear decreasing trend, indicating a negative correlation.

Answer:

The first table (with $x = 3,5,6,8,10,14,15$ and $y=-1,-2,-3,-2,-5,-4,-8$) shows no correlation.