Multiple correlation coefficient
Definition
The multiple correlation coefficient ($R$) measures the strength and direction of the linear relationship between one dependent variable and two or more independent variables. It ranges from 0 to 1, where higher values indicate a stronger relationship.
5 Must Know Facts For Your Next Test
- The multiple correlation coefficient is denoted by $R$.
- It summarizes how well the independent variables predict the dependent variable in a multiple regression model.
- $R^2$, the squared multiple correlation coefficient, represents the proportion of variance in the dependent variable explained by all independent variables combined.
- The value of $R$ ranges from 0 (no linear relationship) to 1 (perfect linear relationship).
- A higher $R$ value indicates a better fit for the regression model.
Review Questions
- What does a multiple correlation coefficient of 0 signify?
- How is $R^2$ related to the multiple correlation coefficient?
- What does an $R$ value close to 1 imply about the linear relationship?
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Related terms
Linear Regression: A statistical method that models the relationship between a dependent variable and one or more independent variables using a linear equation.
Coefficient of Determination ($R^2$): A statistic that indicates what proportion of variance in the dependent variable can be explained by the independent variables.
Adjusted $R^2$: A modified version of $R^2$ that has been adjusted for the number of predictors in the model, providing a more accurate measure when there are multiple independent variables.
