# [R] glm expand model to more values

Charles Annis, P.E. Charles.Annis at StatisticalEngineering.com
Sat Jan 12 19:39:01 CET 2008

```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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