
linear regression and multicollinearity
Posted:
Nov 5, 2007 11:25 PM


Hi,
I have 2 questions:
1) I know that multicollinearity may cause some problems, but may be not? Suppose I've X1, X2 predictors and Y response variable with the following data: X1 X2 Y  1 2 3 2 4 6 3 6 9 4 8 12
X2 = 2*X1, there exists multicollinearity between X1 and X2.
When I try a least squares regression for Y = b0 + b1*X1 + b2*X2 I expect Y =X1 + X2 (b0 = 0 and b1= b2 = 1), the unbiased and minimum variance estimator But with a software package, exactly R, I get that the system is singular. It's ok, if I have the X matrix > X [,1] [,2] [,3] [1,] 1 1 2 [2,] 1 2 4 [3,] 1 3 6 [4,] 1 4 8
X and then R try to invert X' X (in R notation t(X) %*% X) that is not invertible and I get an error.
Of course is not a real world case problem but, this is an error? is common in other packages than R?
Thanks! hb

