Question

Orthogonal explanatory variables. suppose in the modelx2 to xk are all uncorrelated. such variables are called orthogonal variables. if this is the case:

a. what will be the structure of the (x’x) matrix?
b. how would you obtain = (x’x)−1x’y?
c. what will be the nature of the var–cov matrix of ?
d. suppose you have run the regression and afterward you want to introduce another orthogonal variable, say, xk 1 into the model. do you have to recompute all the previous coefficients 1 to k? why or why not?

Answer 1

d. suppose you have run the regression and afterward you want to introduce another orthogonal variable, say, xk 1 into the model. do you have to recompute all the previous coefficients 1 to k? why or why not?