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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
Re: linear regression and multicollinearity
Posted: Nov 11, 2007 1:55 PM
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Thanks for answer!

I agree with you and R, in my second message I've tryed to explain
that R shows me the right results.

My difficulties are: understand how multicollinearity affects the
regression analysis and how it's related with a computational problems
(like ill and possed X'X matrix) and statistical problem (like with a
"small" change in predictors data may arrive to very different results
in the model).
I know the definitions eigenvalue, singular matrix and condition
number but I'm trying to understand implications in the statistics
area.
Again, thanks for answer!

On 7 nov, 02:26, David Winsemius <doe_s...@comcast.n0T> wrote:
> Dear DP;
>
> You _should_ get an error when you try to invert a singular matrix. R is
> behaving correctly.
>
> When I run you your data through the function lm() the output contains
> the line:
> "Coefficients: (1 not defined because of singularities)".
> Again R is giving appropriate warnings.
>

> > str(x.df)
>
> 'data.frame': 4 obs. of 4 variables:
> $ V1: num 1 1 1 1
> $ V2: num 2 4 6 8
> $ V3: num 3 6 9 12
> $ y : num 3 6 9 12
>

> > xdf.mdl<-lm(y ~ V2+V3,data=x.df)
> > summary(xdf.mdl)

>
> Call:
> lm(formula = y ~ V2 + V3, data = x.df)
>
> Residuals:
> 1 2 3 4
> 3.680e-16 -6.134e-16 1.227e-16 1.227e-16
>
> Coefficients: (1 not defined because of singularities)
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 1.110e-15 6.374e-16 1.742e+00 0.224
> V2 1.500e+00 1.164e-16 1.289e+16 <2e-16 ***
> V3 NA NA NA NA
>
> I do not understand what difficulties you are having because you are not
> producing the output that you feel is incorrect. It appears you may need
> to further study the meanings of "singular", "eigenvalue", and
> "condition number".
>
> --
> David Winsemius






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