Correlation coefficient

Definition

A correlation coefficient is a statistical measure that indicates the extent to which two variables fluctuate together. Values range from -1 to 1, where 1 and -1 indicate perfect linear relationships.

5 Must Know Facts For Your Next Test

1. The correlation coefficient is often denoted by $r$.
2. A correlation coefficient of 0 indicates no linear relationship between the variables.
3. Positive values of $r$ indicate a positive linear relationship, while negative values indicate a negative linear relationship.
4. The closer the value of $r$ is to 1 or -1, the stronger the linear relationship between the variables.
5. $r^2$, known as the coefficient of determination, explains the proportion of variance in one variable predictable from another.

Review Questions

• What does a correlation coefficient of -0.8 signify?
• How is the strength of a linear relationship indicated by the correlation coefficient?
• What value of $r$ would you expect if there is no linear relationship between two variables?

Related terms

Linear Regression: A method for modeling the relationship between a dependent variable and one or more independent variables using a straight line.

$r^2$ (Coefficient of Determination): $r^2$ measures how well observed outcomes are replicated by the model, based on the proportion of total variation explained by the model.

Scatter Plot:

A graph used to visually display and assess patterns or relationships between two numerical variables.