Quiz on identifying linear association strength from scatter plots

📚 Quick Study Guide

🔍 Linear Association: Describes the strength and direction of a linear relationship between two variables displayed on a scatter plot.

➕ Positive Association: As one variable increases, the other tends to increase. The scatter plot slopes upwards.

➖ Negative Association: As one variable increases, the other tends to decrease. The scatter plot slopes downwards.

💪 Strength of Association:
• Strong: Points are closely clustered around a line.
• Moderate: Points are somewhat scattered but still show a clear trend.
• Weak: Points are widely scattered with a barely discernible trend.
• No Association: Points appear randomly scattered; no trend is visible.

📏 Correlation Coefficient ($r$): A numerical measure of the strength and direction of a linear association. Ranges from -1 to +1.
• $r \approx 1$: Strong positive association
• $r \approx -1$: Strong negative association
• $r \approx 0$: Weak or no association

Practice Quiz

1. Which scatter plot shows the strongest positive linear association?
1. Points widely scattered with an upward trend.
2. Points tightly clustered around a line sloping downwards.
3. Points randomly scattered.
4. Points tightly clustered around a line sloping upwards.
2. Which of the following correlation coefficients indicates the weakest linear association?
1. $r = 0.9$
2. $r = -0.8$
3. $r = 0.1$
4. $r = -0.5$
3. A scatter plot shows points that are moderately scattered, sloping downwards. Which statement best describes the linear association?
1. Strong positive association
2. Weak positive association
3. Moderate negative association
4. No association
4. Which scatter plot demonstrates no linear association between the variables?
1. Points forming a clear upward curve.
2. Points tightly clustered around a straight line.
3. Points randomly scattered with no discernible pattern.
4. Points forming a clear downward curve.
5. A correlation coefficient of $r = -0.95$ indicates what kind of linear association?
1. Strong positive association
2. Weak positive association
3. Strong negative association
4. Weak negative association
6. Which scatter plot would likely have a correlation coefficient closest to $r = 0.6$?
1. Points tightly clustered around a line sloping downwards.
2. Points randomly scattered.
3. Points moderately scattered with an upward trend.
4. Points tightly clustered around a line sloping upwards.
7. If as 'x' increases, 'y' tends to increase, but the points are quite scattered, what is the likely linear association?
1. Strong negative association
2. Weak positive association
3. Strong positive association
4. No association