Use a computer program that enables you to do matrix operations (e.g., MINITAB, SAS, SPSS).
(a) Calculate the determinant of the correlation matrix of the five independent variables in Study Suggestion 1.
(b) What would the determinant be if the matrix was orthogonal?
(c) What would the determinant be if the matrix contained a linear dependency?
(d) If the determinant was equal to 1 .00, what would the regression equation be?
(e) Calculate the inverse of the correlation matrix of the five independent variables.
(f) Using. relevant values from the inverse and a formula given in this chapter, calculate 1 -
,where
is the squared multiple correlation of each independent variable with the remaining independent variables. Compare the results with those obtained under Study Suggestion 1(f). If you do not have access to a computer program for matrix operations, use the inverse given in the answers to this chapter to solve for 1 -
.
(g) What would the inverse of the correlation matrix among the independent variables be if all the correlations among them were equal to zero?