Correlation Coefficient
A free Algebra I lesson from the “Statistics and Data Analysis” unit, with a worked example and practice problems including step-by-step solutions.
The correlation coefficient r measures how strongly two variables move together along a line. It ranges from -1 to 1. r = 1 is a perfect positive correlation, r = -1 a perfect negative, r = 0 no linear correlation. |r| close to 1 means strong; close to 0 means weak. Correlation never proves causation. In Statistics and Data Analysis, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.
What you'll learn
- Interpret the correlation coefficient r and its sign
- Match r-values to strength and direction (perfect, strong, weak)
- Distinguish correlation from causation
Worked example
Problem. What does r = 1 indicate?
- r ranges from -1 to 1.
- r = 1 is the highest possible value — a perfect positive linear correlation.
- Connect the result back to Correlation Coefficient so the method and meaning are both clear.
- Check the result against the original representation before writing the final answer.
Answer: Perfect positive correlation
Practice problems
1. r = 1 means:
Choices: Perfect positive · Perfect negative · No correlation
Show solution
- Warm-up: First identify exactly what the question is asking: r = 1 means:
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Highest possible r.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
- Identify the Algebra I structure before choosing a calculation.
Answer: Perfect positive
2. r = -1 means:
Choices: Perfect positive · Perfect negative · No correlation
Show solution
- Warm-up: First identify exactly what the question is asking: r = -1 means:
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- Lowest possible r.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
- Identify the Algebra I structure before choosing a calculation.
Answer: Perfect negative
3. r = 0 means:
Choices: No linear correlation · Perfect correlation
Show solution
- Warm-up: First identify exactly what the question is asking: r = 0 means:
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Zero indicates no linear relationship.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
- Identify the Algebra I structure before choosing a calculation.
Answer: No linear correlation
4. r = 0.95 indicates:
Choices: Strong positive · Weak positive
Show solution
- Core Practice: First identify exactly what the question is asking: r = 0.95 indicates:
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- |r| close to 1 is strong; sign positive.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
- Identify the Algebra I structure before choosing a calculation.
Answer: Strong positive
5. r = -0.8 indicates:
Choices: Strong negative · Weak negative
Show solution
- Core Practice: First identify exactly what the question is asking: r = -0.8 indicates:
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- |r| = 0.8 is strong; sign negative.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
- Identify the Algebra I structure before choosing a calculation.
Answer: Strong negative
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