The multiple correlation coefficient, also known as the multiple R or the coefficient of multiple determination, is a statistical measure that represents the strength and direction of the linear relationship between a dependent variable and two or more independent variables in a multiple regression analysis. It is denoted by the symbol R.
The multiple correlation coefficient evaluates how well the independent variables collectively predict the dependent variable. It ranges from -1 to +1, where a positive value indicates a positive relationship, a negative value indicates a negative relationship, and a value of zero indicates no linear relationship.
The multiple correlation coefficient is a composite measure of the correlation between the independent variables and the dependent variable, which considers the interrelationships among all the independent variables simultaneously. It can be interpreted as the proportion of the variance in the dependent variable that can be explained by the independent variables collectively.
A higher multiple correlation coefficient suggests a stronger and more accurate prediction of the dependent variable by the independent variables. Conversely, a lower multiple correlation coefficient indicates a weaker relationship and a less accurate prediction.
The multiple correlation coefficient is often used in various fields, such as economics, psychology, and social sciences, to assess the predictive power of a set of independent variables on a dependent variable, and to understand the strength and direction of their relationships.
