Question: A scatter plot of $y$ versus $x$ with points showing no clear linear trend, positioned in the top-left. Select all the correct answers. positive correlation negative correlation no correlation $r = 0.9$ $r = -0.6$ $r = 0.02$ $r = -0.006$

1. **Problem Statement:** We are given a scatter plot of $y$ versus $x$ with points showing no clear linear trend, positioned in the top-left. 2. **Understanding Correlation:** Correlation measures the strength and direction of a linear relationship between two variables. - Positive correlation means as $x$ increases, $y$ tends to increase. - Negative correlation means as $x$ increases, $y$ tends to decrease. - No correlation means there is no linear relationship between $x$ and $y$. 3. **Correlation Coefficient ($r$):** The value of $r$ ranges from $-1$ to $1$. - $r$ close to $1$ indicates strong positive correlation. - $r$ close to $-1$ indicates strong negative correlation. - $r$ close to $0$ indicates no correlation. 4. **Analyzing the given options:** - $r = 0.9$: Strong positive correlation (not consistent with no clear trend). - $r = -0.6$: Moderate negative correlation (not consistent with no clear trend). - $r = 0.02$: Very close to zero, indicating no correlation. - $r = -0.006$: Very close to zero, indicating no correlation. 5. **Conclusion:** Since the scatter plot shows no clear linear trend, the correct answers are: - no correlation - $r = 0.02$ - $r = -0.006$