Scatter Plots and Trend Lines
A free Algebra I lesson from the “Statistics and Data Analysis” unit, with a worked example and practice problems including step-by-step solutions.
A scatter plot graphs paired data on two axes. The pattern shows the type and strength of the relationship: rising (positive), falling (negative), random (none); straight-line (linear) or curved (nonlinear); tightly clustered (strong) or spread out (weak). Even strong correlation does not prove that one variable causes the other.
What you'll learn
- Read a scatter plot for positive, negative, or no association
- Distinguish linear and nonlinear trends
- Recognize that correlation does not prove causation
Worked example
Problem. A scatter plot of (hours studied, test score) rises to the right. What type of association is this?
- Both variables increase together.
- That is a positive association.
Answer: Positive
Practice problems
1. Hours practiced vs. free throws made (rising). Association?
Choices: Positive · Negative · None
Show solution
- Warm-up: First identify exactly what the question is asking: Hours practiced vs. free throws made (rising). Association?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Both increase together.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Positive
2. Drink size vs. soda calories (rising). Association?
Choices: Positive · Negative · None
Show solution
- Warm-up: First identify exactly what the question is asking: Drink size vs. soda calories (rising). Association?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Bigger drinks have more calories.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Positive
3. Ice-cream sales and drowning incidents both rise in summer. Does ice cream cause drowning?
Choices: Yes (causation) · No (just correlation)
Show solution
- Warm-up: First identify exactly what the question is asking: Ice-cream sales and drowning incidents both rise in summer. Does ice cream cause drowning?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A third variable (hot weather) drives both.
- Correlation does not imply causation.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: No (just correlation)
4. Hours of TV vs. grades (falling). Association?
Choices: Positive · Negative · None
Show solution
- Core Practice: First identify exactly what the question is asking: Hours of TV vs. grades (falling). Association?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- More TV, lower grades — opposite directions.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Negative
5. Random scatter with no pattern. Association?
Choices: Positive · Negative · None
Show solution
- Core Practice: First identify exactly what the question is asking: Random scatter with no pattern. Association?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- No discernible trend.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: None
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