An example of a lack of correlation is the relationship between a person's shoe size and their hours of sleep. When plotted on a scatterplot, the data points for these two variables show no systematic pattern, indicating that a change in shoe size is not associated with a predictable change in hours of sleep.

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A zero correlation exists when the correlation coefficient is exactly 0. This signifies that there is no discernible linear relationship between two variables. As a result, knowing the value of one variable provides no basis for predicting the value of the other.

Zero Correlation

Spielman, R. M., Jenkins, W. J., & Lovett, M. D. (2020, April 22). Psychology (2nd ed.). OpenStax. https://openstax.org/books/psychology-2e/pages/1-introduction

OpenStax Psychology (2nd ed.) Textbook

A researcher investigates the potential link between the number of books a person owns and their average daily screen time. After collecting data from a large sample, a scatterplot reveals that the data points are spread out randomly, forming no clear line or curve. What is the most accurate conclusion the researcher can draw from this visual representation of the data?

An example of no correlation, where two variables have no discernible relationship, is the connection between the number of hours a person sleeps and their shoe size. A scatterplot of this relationship shows data points scattered randomly with no clear pattern or line, indicating that knowing one variable provides no information for predicting the other.

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