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.
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The correlation coefficient is often denoted by $r$.
A correlation coefficient of 0 indicates no linear relationship between the variables.
Positive values of $r$ indicate a positive linear relationship, while negative values indicate a negative linear relationship.
The closer the value of $r$ is to 1 or -1, the stronger the linear relationship between the variables.
$r^2$, 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.