 |
the matrix of coefficients of correlation (Analysis I, Correlation Matrices) is
Hierarchical Regression Analysis
Hierarchical regression analysis is based on the fact that predictor variable X correlates 1.00 with the predicted variable Y' and .00 with the error variable Y^. For the data on the vector display below - obtained by clicking (Data, Bivariate Prototypes) and (Analysis I, Regression Analysis)
|
|
the matrix of coefficients of correlation (Analysis I, Correlation Matrices) is
 |
From the correlational viewpoint, the variable Y' is redundant and can be deleted. If we replace the variable Y with the variable Y^, the variables X and Y^ will be orthogonal. Clicking on (Data, Replace Variables) and selecting Variable to be Moved as Y^ and Variable to be Replaced as Y, changes the vector display as
 |
Clicking (Data, Delete Variables) and selecting variable Y' results in the vector display
 |
where variables X and Y^ are orthogonal. Hierarchical regression analysis with multiple predictor variables is obtained by repeated application of the above steps, changing the data matrix with correlated predictor variables and a criterion variable Y to a matrix of orthogonalized predictor variables with the criterion variable Y.