Definition

1. Noun:
   • A statistical measure: The multiple correlation coefficient is a single numerical value, typically denoted by R, that estimates the strength and direction of the linear relationship between a dependent variable and a combination of two or more independent variables. It represents the combined influence of the predictor variables on the outcome variable.

Usage

• The multiple correlation coefficient is used primarily in multiple regression analysis.
• It indicates how well the set of independent variables, taken together, can predict the value of the dependent variable.
• Its value always ranges from 0 to 1, where 0 indicates no linear relationship and 1 indicates a perfect linear relationship.

Examples

• Noun:
  • The multiple correlation coefficient for the model, which used age, income, and education level to predict spending, was 0.85.
  • A high multiple correlation coefficient suggests that the independent variables collectively explain a large portion of the variance in the dependent variable.
  • Researchers reported a multiple correlation coefficient of R = .72 in their study.

Advanced Usage

• "Squared multiple correlation coefficient (R²)": This is the coefficient of determination. It represents the proportion of variance in the dependent variable that is predictable from the independent variables.
  • While the multiple correlation coefficient was 0.9, the R² value of 0.81 tells us that 81% of the variance is explained by the model.

Variants and Related Words

• Multiple correlation (n): The broader concept of the correlation between one variable and a set of other variables.
• Coefficient of multiple determination (n): Synonymous with R², the squared multiple correlation coefficient.
• Multiple regression analysis (n): The statistical method in which the multiple correlation coefficient is a key output.

Synonyms

• R (Symbol): The standard symbol used to denote the multiple correlation coefficient.
• Multiple R: A common term used in statistical software output for this coefficient.

Related Terms (Conceptual)

• Partial correlation coefficient: A measure of the association between two variables, while controlling for the effect of one or more other variables.
• Simple correlation coefficient: The correlation between just two variables (e.g., Pearson's r), as opposed to multiple variables.

Noun

1. an estimate of the combined influence of two or more variables on the observed (dependent) variable