Subjects statistics

Correlation Coefficient 2A8774

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1. **State the problem:** We need to determine the most likely correlation coefficient for the given scatter plot data points: approximately (1,2), (2,4), (3,2), (4,3), and (5,3). 2. **Recall the correlation coefficient:** The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. It ranges from $-1$ (perfect negative correlation) to $1$ (perfect positive correlation). Values near $0$ indicate weak or no linear correlation. 3. **Analyze the scatter plot:** The points show a slight upward trend, meaning as $x$ increases, $y$ tends to increase slightly. This suggests a positive correlation. 4. **Evaluate the options:** - $-0.65$: negative moderate correlation, unlikely since trend is upward. - $-0.19$: weak negative correlation, unlikely. - $0.19$: weak positive correlation, possible but the line seems a bit stronger. - $0.75$: moderate to strong positive correlation, fits the slightly upward slope well. 5. **Conclusion:** The most likely correlation coefficient is $0.75$ because the data points show a moderate positive linear trend. **Final answer:** $0.75$