4 Examples of No Correlation Between Variables


In statistics, correlation is a measure of the linear relationship between two variables.

The value for a correlation coefficient is always between -1 and 1 where:

  • -1 indicates a perfectly negative linear correlation between two variables
  • 0 indicates no linear correlation between two variables
  • 1 indicates a perfectly positive linear correlation between two variables

If two variables have a correlation of zero, it indicates that they’re not related in any way. In other words, knowing the value of one variable doesn’t give us any idea of what the value of the other variable may be.

If we create a scatterplot of two variables that have zero correlation, there will be no clear pattern in the plot:

Example of no correlation

Examples of No Correlation

The following examples illustrate scenarios where two variables have no correlation.

Example 1: Coffee Consumption vs. Intelligence

The amount of coffee that individuals consume and their IQ level has a correlation of zero. In other words, knowing how much coffee an individual drinks doesn’t give us an idea of what their IQ level might be.

If we created a scatterplot of daily coffee consumption vs. IQ level, it would look like this:

Example 2: Height & Exam Scores

The height of students and their average exam scores has a correlation of zero. In other words, knowing the height of an individual doesn’t give us an idea of what their average exam score might be.

If we created a scatterplot of height vs. average exam score, it would look like this:

Example 3: Shoe Size & Movies Watched

The shoe size of individuals and the number of movies they watch per year has a correlation of zero. In other words, knowing the shoe size of an individual doesn’t give us an idea of how many movies they watch per year.

If we created a scatterplot of shoe size vs. number of movies watched, it would look like this:

Example 4: Weight & Income

The weight of individuals and their annual income has a correlation of zero. In other words, knowing the weight of a person doesn’t give us an idea of what their annual income might be.

If we created a scatterplot of weight vs. income, it would look like this:

Additional Resources

An Introduction to the Pearson Correlation Coefficient
Correlation vs. Association: What’s the Difference?
Correlation vs. Regression: What’s the Difference?

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