To determine which table shows a negative correlation, we need to consider the correlation coefficients for each set of data points.
1. For the first table, the values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
- [tex]\( x: 2, 5, 6, 7, 10, 12 \)[/tex]
- [tex]\( y: -5, -5, -5, -5, -5, -5 \)[/tex]
The correlation coefficient between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in this table is NaN (Not a Number). This typically indicates that there is no variation in [tex]\( y \)[/tex], meaning the correlation cannot be calculated or is undefined.
2. For the second table, the values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
- [tex]\( x: 2, 5, 6, 7, 10, 12 \)[/tex]
- [tex]\( y: 6, 3, 1, 1, 3, 6 \)[/tex]
The correlation coefficient between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in this table is approximately 0.0497. This value is very close to zero, indicating a very weak positive correlation or no meaningful correlation at all.
3. For the third table, the values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
- [tex]\( x: 2, 5, 6, 7, 10, 12 \)[/tex]
- [tex]\( y: 4, 2, -4, -3, -11, -12 \)[/tex]
The correlation coefficient between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in this table is approximately -0.9656. This value is very close to -1, indicating a strong negative correlation.
Since a negative correlation means that as [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] tends to decrease, the third table is the one that shows a negative correlation.
