Final answer:
The squared multiple correlation (R²) between three or more variables is typically greater than any individual squared bivariate correlation (r²) because it encompasses the variance explained by all independent variables in the model.
Step-by-step explanation:
The squared multiple correlation (R²) between three or more variables should almost always be greater than any individual squared bivariate correlation between two of those same variables (r²). This is because R² takes into account the collective explanatory power of multiple independent variables regarding the variance in the dependent variable, while r² measures the strength of association on a one-to-one basis between two variables. When calculating the correlation coefficient r, we must remember that its value always falls between -1 and +1, indicating the strength of the linear relationship (the closer to 1, be it positive or negative, the stronger the relationship).
A useful interpretation of the coefficient of determination, r², which is the square of r, is that when expressed as a percentage, it represents the percentage of variation in the dependent variable that can be explained by the independent variable using the regression line. For example, if r is 0.70, then r² is 0.49, meaning 49% of the variation in the dependent variable can be explained by the independent variable(s). If multiple variables are included in the model, the R² value will include the variance explained by all of them collectively, which is why R² is generally higher than any individual r².