[R] glm expand model to more values

[Jarek Jasiewicz]

Charles Annis, P.E. wrote:
> How many parameters are you trying to estimate?  How many observations do
> you have?
>
> What is wrong is that half of your parameter estimates are statistically
> meaningless:
>
> dd <- data.frame(a=c(1, 2, 3, 4, 5, 6), b=c(3,  5,  6,  7,  9, 10))
>
> overparameterized.model <- glm(b~poly(a,3),data=dd)
>
> summary(overparameterized.model)
>
>
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)    
>
> (Intercept)   6.6667     0.1725  38.644 0.000669 ***
>
> poly(a, 3)1   5.7371     0.4226  13.576 0.005382 ** 
>
> poly(a, 3)2  -0.1091     0.4226  -0.258 0.820395    
>
> poly(a, 3)3   0.2236     0.4226   0.529 0.649562  
>
>
>
>
> Charles Annis, P.E.
>
> Charles.Annis at StatisticalEngineering.com
> phone: 561-352-9699
> eFax:  614-455-3265
> http://www.StatisticalEngineering.com
>  
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of Jarek Jasiewicz
> Sent: Saturday, January 12, 2008 11:50 AM
> To: R-help at r-project.org
> Subject: [R] glm expand model to more values
>
> Hi
>
> I have the problem with fitting curve to data with lm and glm. When I 
> use polynominal dependiency, fitted values from model are OK, but I 
> cannot  recive proper values when I use coefficents to caltulate this.  
> Let me present simple example:
>
> I have simple data.frame: (dd)
>  a: 1 2 3 4 5 6
>  b:  3  5  6  7  9 10
>
> I try to fit it to model:
>
> model=glm(b~poly(a,3),data=dd)
>  I have following data fitted to model (as I expected)
>  > fitted(model)
>         1         2         3         4         5         6
>  3.095238  4.738095  6.095238  7.333333  8.619048 10.119048
>
> and coef(model)
> (Intercept) poly(a, 3)1 poly(a, 3)2 poly(a, 3)3
>   6.6666667   5.7370973  -0.1091089   0.2236068
>
> so when I try to expand the model to other data (simple extrapolation), 
> let say: s=seq(1:10,by=1)
>
> I do:
> extra=sapply(s,function(x) coef(model) %*% x^(0:3))
> and here is result:
> [1]  12.51826  19.49328  28.93336  42.18015  60.57528  85.46040 118.17714
>  [8] 160.06715 212.47207 276.73354
>
> the data form expanding coefs are completly differnd from fitted
>
> What's going wrong?
>
> Jarek
>
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>
>   
sorry but I cannot understand. What does it means data are statistically 
meanningless?

It is examle with very simple data which I use according to simpleR 
manual example to check why I cannot recive expected result. I need 
simple model y~x^3+x^2....+z to extrapolate data
Jarek