> >Hassane ABIDI wrote:
> >When the IDV variable (X) is random is it correct to use simple linear
> >regression ?????
> Dennis Robert wrote:
> in what way would it make sense to say that X is random (and what do you
> mean by this?) and Y is fixed (and what do you mean by this?)?
>
> all regression analysis does (in the linear case) is to find a least
> squares line (and the equation for it) through the data plot ... that
> minimizes squared deviations around the regression line ...
>
> now, if one were doing an analysis of experimental data ... where X is a
> treatment variable ... that has dosage levels of 3, 6, and 9 miligrams ...
> you might (???) consider that fixed in that these are the ONLY levels of
> the treatment you are interested in ... so you could plot the means on some
> criterion variable against these 3 dosage levels ... here X might be
> 'fixed' and Y not ...
>
> i don't really see how you can fix Y ... if that is the criterion ... ONLY
> in the sense that you might have a measure that ONLY gives you 'fixed'
> possible values .... but, that is a stretch ...
>
> in what sense would height and weight be fixed or not fixed if we did a
> regression using height to estimate or predict weight, or vice versa?
> notion of 'fixed' really makes no sense here ... and regression does not care
>
> but, my point to the original poster was simple:
>
> make a plot of the data ... see what you see ... and go from there
>
> this is not about using pearson or spearman, it is about seeing if the data
> look linear ... and IF they do ... then summarize it via a regression
> equation ... this will give the means to 'link' X to Y ... proxy to true
>
> if they don't ... you have to think about a different strategy
Thanks to Dennis, I'm sorry for my poor english,
In mathematical sense, I agree with you, but not in the statistical sense.
No probleme in the estimation of the coefficients of regression with the
ordinary or generalised least square or maximum likelihood :
B = Inv(X'*X)*X'*Y (Inv=Inverse, X'=Transpose of X)
This relation remains true even if X's are random.
But to obtain the variances of B, the classical linear regression
supposes that X's as fixed to obtain:
Var(B)=s^2*Inv(X'*X) (s^2 is an estimation of residual variance)
Else I do not know how to calculate this variance.
|=======================================================|
| Hassane ABIDI (PhD) |
| Unite d'Epidemiologie; Centre Hospitalier Lyon-Sud |
| Pavillon 1.M, 69495 Pierre Benite Cedex, France |
| Tel: (33) 04 78 86 56 87 ; Fax: (33) 04 78 86 33 31 |
| E. mail: [EMAIL PROTECTED] |
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