Correlation Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Correlation.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Correlation is a statistical relationship between two variables where changes in one are associated with changes in the other. Positive correlation means both increase together; negative correlation means one increases as the other decreases; no correlation means no consistent pattern.

When one thing goes up and another tends to go up with it (like study time and test scores), that's positive correlation. When one goes up and the other goes down (like TV time and exercise), that's negative correlation. They 'move together' in some pattern.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Correlation measures the direction and strength of the linear relationship between two variables. It ranges from −1 (perfect negative) to +1 (perfect positive).

Common stuck point: Students often confuse the strength of a correlation with its direction — a correlation of −0.9 is very strong, just negative.

Sense of Study hint: First, plot both variables on a scatter plot and look at the overall pattern. Then determine the direction: upward trend means positive, downward means negative. Finally, judge the strength by how tightly the points cluster around a line — tighter clustering means stronger correlation.

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Correlation vs Causation Mistakes

Worked Examples

Example 1

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A scatter plot shows that as hours of study increase, test scores tend to increase. Describe the correlation and state whether it implies causation.

Solution

  1. 1
    Step 1: As one variable increases, the other also increases — this is a positive correlation.
  2. 2
    Step 2: Correlation describes a pattern but does not prove causation. There may be other factors (e.g., motivation, prior knowledge).
  3. 3
    Step 3: We can say study hours and test scores are positively correlated, but we cannot conclude that studying more directly causes higher scores without a controlled experiment.

Answer

Positive correlation. Correlation does not imply causation.
Correlation measures the strength and direction of a linear relationship between two variables. Establishing causation requires controlled experiments that rule out confounding variables.

Example 2

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Classify each as positive correlation, negative correlation, or no correlation: (a) Temperature and ice cream sales. (b) Shoe size and IQ. (c) Hours of TV watched and exercise done.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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A study finds a strong positive correlation between the number of firefighters at a fire and the damage caused. Does this mean sending more firefighters causes more damage? Explain.

Example 2

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A scatter plot shows that as outside temperature increases, hot chocolate sales decrease. Describe the correlation and explain why this pattern does not by itself prove temperature is the only cause.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

stat scatter plotdata collection