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Topic: linear regression and multicollinearity
Replies: 13   Last Post: Nov 15, 2007 4:28 PM

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hberig@gmail.com

Posts: 10
Registered: 11/5/07
linear regression and multicollinearity
Posted: Nov 5, 2007 11:25 PM
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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




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