[R] Linear Models with mean as Intercept.

[Ghislain Vieilledent]

Dear advanced statisticians,

*******Objectif********

I try to set up linear models with mean as intercept:
Answer: y
Variable: x, as factor of two modalities: x(1), x(2).

I would like to have a model as:
y = mean(y)+A(i)+residuals,
with i in (1,2) and A(1) coefficient for x(1) and A(2) coefficient for x(2).

*******Trials in R*******

## Firstly:

I write in R:
 >Model<-lm(y~x,Data)
 >summary(Model)
...
I've got the coefficients for:
- the intercept (x(1) as been choosen) that we can call B(1)
- the second modality: x(2) that we can call B(2)

If I have well understood we have for the model and predictions:
if x(1): y=B(1)
if x(2): y=B(1)+B(2)
which is quite different as y=mean(y)+A(i)

## Secondly
I tried to skip the intercept
 >Model2<-lm(y~0+x,Data)
 >summary(Model2)
...
I've got the coefficients for:
- the first modality: x(1) that we can call C(1)
- the second modality: x(2) that we can call C(2)

And the model and predictions, if I'm right, are:
if x(1): y=C(1)
if x(2): y=C(2)

******* Questions ***********
How can I obtain a predictive model y=mean(y)+A(i) ?
Is it possible to settle mean(y) as intercept?

Thanks for your help.

Ghislain V., retarded statistician.