The correlation coefficient, denoted as $r$, measures the strength and direction of a linear relationship between two variables on a scatterplot. Its value ranges from -1 to 1.
5 Must Know Facts For Your Next Test
The value of $r$ close to 1 indicates a strong positive linear relationship, while a value close to -1 indicates a strong negative linear relationship.
If $r = 0$, it implies no linear relationship between the variables.
The correlation coefficient is sensitive to outliers, which can significantly affect its value.
$r$ is dimensionless, meaning it has no units and is purely a measure of correlation strength and direction.
Both variables need to be continuous for the correlation coefficient calculation.
Review Questions
What does an $r$ value of 0.85 indicate about the relationship between two variables?
How would outliers in your data set impact the correlation coefficient?
Why can't you use the correlation coefficient for categorical data?
Related terms
Linear Regression: A statistical method that models the relationship between two variables by fitting a linear equation to observed data.
A type of data visualization that displays values for typically two variables for a set of data using Cartesian coordinates.
Coefficient of Determination ($R^2$): $R^2$ measures the proportion of variability in one variable that can be explained by its linear relationship with another variable.