We need to calculate the regression coefficients using canonical correlation approach (in this case one of the sets, Y set is a singleton and all the other variables of the other set as covariates in MANOVA-model without factors). We have the following R matrix but we are making a mistake with the geometric solution end up with numbers that does not resemble the actual coefficients. Any ideas how to do it?

correlation matrix

x1 x2 y

x1 1 0,10652 0,84946

x2 0,10652 1 0,46722

y 0,84946 0,46722 1