Semipartial Correlation Coefficient

A squared, semipartial correlation coefficient can be used in connection with multiple regression analysis to measure the strength of the association between the dependent and an independent variable, taking into account the relationships among all the variables. A squared semipartial correlation coefficient is also called a squared part correlation. To illustrate the squared semipartial correlation coefficient, consider data that include final mathematics grades (MA), student perception of teacher's academic support (TAS) in mathematics class, and positive affect (PA) in mathematics class. The sample size is N = 200. A multiple regression model for these variables is

where α denotes the intercept; β1 and β2 denote the regression coefficients (slopes) for PA and TAS, respectively; and ε denotes the residual. The sample squared multiple correlation coefficient for ...