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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 theyâ€™re not related in any way. In other words, knowing the value of one variable doesnâ€™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:

**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 doesnâ€™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 doesnâ€™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 doesnâ€™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 doesnâ€™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: Whatâ€™s the Difference?

Correlation vs. Regression: Whatâ€™s the Difference?