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No correlation between variables means that there is no relationship between two variables. Examples of this include the amount of time spent studying and a student’s height; the number of people in a room and the number of books in that room; the temperature of a room and the number of people in it; and the amount of money spent on food and the age of the person who bought it.
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 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 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
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:
