Linear Scatter Plots Practice worksheet with four exercises involving scatter plots, correlation analysis, and data interpretation.
A worksheet titled "Linear Scatter Plots Practice" featuring four sections with scatter plots and questions about correlation, including identifying correlation types, estimating correlation coefficients, and analyzing data from real-world scenarios like soccer practice and grocery spending.
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Step-by-step solution for: Scatter Plots Notes and Worksheets - Lindsay Bowden
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Show Answer Key & Explanations
Step-by-step solution for: Scatter Plots Notes and Worksheets - Lindsay Bowden
Here is the complete solution and explanation for all four problems on the “Linear Scatter Plots Practice” worksheet.
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Problem 1: Use the scatter plot to answer the questions below.
*(Note: The scatter plot shows points trending upward from left to right, indicating a positive relationship.)*
a. What type of correlation is shown?
✔ Positive correlation
> Explanation: As the x-values increase, the y-values generally increase too. The points form an upward-sloping pattern from bottom-left to top-right.
b. Estimate the correlation coefficient.
✔ Approximately 0.7 to 0.8
> Explanation: The correlation coefficient (r) ranges from -1 to +1. A value close to +1 means a strong positive linear relationship. In this plot, the points show a clear upward trend but are somewhat scattered — not perfectly aligned. So, it’s moderately to strongly positive, but not perfect. An estimate of 0.7–0.8 is reasonable.
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Problem 2: Soccer team data — plot and answer questions.
Step 1: Plot the data
The table gives:
| Hours Practiced (x) | 0 | 1 | 2 | 3 | 4 | 5 |
|---------------------|-----|-----|-----|-----|-----|-----|
| Avg Goals per Game (y) | 0 | 0.4 | 1 | 1.5 | 2 | 2.5 |
Plot these points on the grid:
- (0, 0)
- (1, 0.4)
- (2, 1)
- (3, 1.5)
- (4, 2)
- (5, 2.5)
You’ll see they form a nearly straight line going up to the right.
a. What type of correlation is shown?
✔ Positive correlation
> Explanation: As hours practiced increases, average goals per game also increase — clear positive relationship.
b. Estimate the correlation coefficient.
✔ Approximately 0.95 to 1.0
> Explanation: The points lie very close to a straight line with a positive slope. This indicates a very strong positive linear correlation. Since it’s almost perfectly linear, r is very close to +1.
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Problem 3: Surveyor at grocery store
> “She found that the more a person spent, the more pets they had. She concludes that spending a lot at the grocery store causes people to want more pets.”
a. What type of correlation did the surveyor find?
✔ Positive correlation
> Explanation: Spending more money is associated with having more pets — as one variable increases, so does the other. That’s a positive correlation.
b. Was the surveyor’s conclusion correct? Why or why not?
✔ No, the conclusion is not correct.
> Explanation: Correlation does NOT imply causation. Just because two variables are correlated doesn’t mean one causes the other. There could be a third factor (confounding variable) — for example, wealthier people may spend more at the grocery store AND are more likely to afford multiple pets. Or perhaps people with larger families (who need to buy more groceries) also have more pets. The surveyor confused association with cause-and-effect.
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Problem 4: Parents’ number of children vs. hours of sleep
*(Scatter plot shows points trending downward from left to right — as number of children increases, hours of sleep tend to decrease.)*
a. Is there a correlation between number of children and hours of sleep?
✔ Yes, there is a negative correlation.
> Explanation: As the number of children (x) increases, the hours of sleep (y) generally decreases. The points show a downward trend — classic negative correlation.
b. Name one thing that could have affected this data.
✔ Example: Parents with more children may have less time to sleep due to nighttime care, feeding, or child-related responsibilities.
> Other possible answers:
> - Stress levels increasing with more children
> - Age of children (e.g., infants require more nighttime attention)
> - Work schedules or childcare arrangements
> - Parental health or energy levels
> Key point: These are confounding factors that may explain the observed correlation — not necessarily direct cause-and-effect, but plausible influences.
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✔ Final Summary of Answers:
1a. Positive correlation
1b. ~0.7–0.8
2a. Positive correlation
2b. ~0.95–1.0
3a. Positive correlation
3b. No — correlation ≠ causation; other factors may explain both spending and pet ownership.
4a. Yes — negative correlation
4b. Example: More children → more nighttime interruptions → less sleep
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Let me know if you’d like to graph the soccer data or visualize any of these scatter plots!
---
Problem 1: Use the scatter plot to answer the questions below.
*(Note: The scatter plot shows points trending upward from left to right, indicating a positive relationship.)*
a. What type of correlation is shown?
✔ Positive correlation
> Explanation: As the x-values increase, the y-values generally increase too. The points form an upward-sloping pattern from bottom-left to top-right.
b. Estimate the correlation coefficient.
✔ Approximately 0.7 to 0.8
> Explanation: The correlation coefficient (r) ranges from -1 to +1. A value close to +1 means a strong positive linear relationship. In this plot, the points show a clear upward trend but are somewhat scattered — not perfectly aligned. So, it’s moderately to strongly positive, but not perfect. An estimate of 0.7–0.8 is reasonable.
---
Problem 2: Soccer team data — plot and answer questions.
Step 1: Plot the data
The table gives:
| Hours Practiced (x) | 0 | 1 | 2 | 3 | 4 | 5 |
|---------------------|-----|-----|-----|-----|-----|-----|
| Avg Goals per Game (y) | 0 | 0.4 | 1 | 1.5 | 2 | 2.5 |
Plot these points on the grid:
- (0, 0)
- (1, 0.4)
- (2, 1)
- (3, 1.5)
- (4, 2)
- (5, 2.5)
You’ll see they form a nearly straight line going up to the right.
a. What type of correlation is shown?
✔ Positive correlation
> Explanation: As hours practiced increases, average goals per game also increase — clear positive relationship.
b. Estimate the correlation coefficient.
✔ Approximately 0.95 to 1.0
> Explanation: The points lie very close to a straight line with a positive slope. This indicates a very strong positive linear correlation. Since it’s almost perfectly linear, r is very close to +1.
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Problem 3: Surveyor at grocery store
> “She found that the more a person spent, the more pets they had. She concludes that spending a lot at the grocery store causes people to want more pets.”
a. What type of correlation did the surveyor find?
✔ Positive correlation
> Explanation: Spending more money is associated with having more pets — as one variable increases, so does the other. That’s a positive correlation.
b. Was the surveyor’s conclusion correct? Why or why not?
✔ No, the conclusion is not correct.
> Explanation: Correlation does NOT imply causation. Just because two variables are correlated doesn’t mean one causes the other. There could be a third factor (confounding variable) — for example, wealthier people may spend more at the grocery store AND are more likely to afford multiple pets. Or perhaps people with larger families (who need to buy more groceries) also have more pets. The surveyor confused association with cause-and-effect.
---
Problem 4: Parents’ number of children vs. hours of sleep
*(Scatter plot shows points trending downward from left to right — as number of children increases, hours of sleep tend to decrease.)*
a. Is there a correlation between number of children and hours of sleep?
✔ Yes, there is a negative correlation.
> Explanation: As the number of children (x) increases, the hours of sleep (y) generally decreases. The points show a downward trend — classic negative correlation.
b. Name one thing that could have affected this data.
✔ Example: Parents with more children may have less time to sleep due to nighttime care, feeding, or child-related responsibilities.
> Other possible answers:
> - Stress levels increasing with more children
> - Age of children (e.g., infants require more nighttime attention)
> - Work schedules or childcare arrangements
> - Parental health or energy levels
> Key point: These are confounding factors that may explain the observed correlation — not necessarily direct cause-and-effect, but plausible influences.
---
✔ Final Summary of Answers:
1a. Positive correlation
1b. ~0.7–0.8
2a. Positive correlation
2b. ~0.95–1.0
3a. Positive correlation
3b. No — correlation ≠ causation; other factors may explain both spending and pet ownership.
4a. Yes — negative correlation
4b. Example: More children → more nighttime interruptions → less sleep
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Let me know if you’d like to graph the soccer data or visualize any of these scatter plots!
Parent Tip: Review the logic above to help your child master the concept of scatter plot worksheet printable.
