To determine which table shows no correlation, we need to analyze the strength and direction of the correlation between the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values for each table. A correlation coefficient (often denoted by [tex]\( r \)[/tex]) close to 0 indicates no correlation, meaning there is no linear relationship between the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values.
We have the following correlation coefficients for each table:
1. [tex]\([-0.8548]\)[/tex]
2. [tex]\([0.8789]\)[/tex]
3. [tex]\([0.9647]\)[/tex]
4. [tex]\([-0.9666]\)[/tex]
Let's analyze each correlation coefficient:
1. The first correlation coefficient is [tex]\(-0.8548\)[/tex], which indicates a strong negative correlation.
2. The second correlation coefficient is [tex]\(0.8789\)[/tex], indicating a strong positive correlation.
3. The third correlation coefficient is [tex]\(0.9647\)[/tex], indicating a very strong positive correlation.
4. The fourth correlation coefficient is [tex]\(-0.9666\)[/tex], indicating a very strong negative correlation.
Since we are looking for the table that shows no correlation, we observe that all the correlation coefficients are either strongly positive or strongly negative. Since none of the coefficients is close to 0, all tables exhibit a significant correlation, either positive or negative. Therefore, based on the given correlations, none of the provided tables shows no correlation.
