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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

Why it matters: Researchers report r when claiming two variables are related. A high r supports a strong linear relationship, but more evidence is needed to prove one variable causes the other.

Worked example

Problem. What does r = 1 indicate?

  1. r ranges from -1 to 1.
  2. r = 1 is the highest possible value — a perfect positive linear correlation.
  3. Connect the result back to Correlation Coefficient so the method and meaning are both clear.
  4. Check the result against the original representation before writing the final answer.

Answer: Perfect positive correlation

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. r = 1 means:

Choices: Perfect positive · Perfect negative · No correlation

Show solution
  1. Highest possible r.

Answer: Perfect positive

2. r = -1 means:

Choices: Perfect positive · Perfect negative · No correlation

Show solution
  1. Lowest possible r.

Answer: Perfect negative

3. r = 0 means:

Choices: No linear correlation · Perfect correlation

Show solution
  1. Zero indicates no linear relationship.

Answer: No linear correlation

4. r = 0.95 indicates:

Choices: Strong positive · Weak positive

Show solution
  1. |r| close to 1 is strong; sign positive.

Answer: Strong positive

5. r = -0.8 indicates:

Choices: Strong negative · Weak negative

Show solution
  1. |r| = 0.8 is strong; sign negative.

Answer: Strong negative

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