2707.sagews

X=cbind(c(1,1,1,1),c(-1,1,0,-2),c(2,2,-2,-2))
Y=cbind(c(8,16,64,32))
betahat=solve(crossprod(X))%*%t(X)%*%Y
betahat
Mx=diag(4)-X%*%solve(crossprod(X))%*%t(X)
Uhat=Mx%*%Y
Uhat

[,1] [1,] 35.0 [2,] 10.0 [3,] -11.5 [,1] [1,] 6 [2,] -6 [3,] 6 [4,] -6