[R] glm expand model to more values

Sat Jan 12 21:13:46 CET 2008

Jarek:

Although it is not universally agreed on, I believe the first step in any
data analysis is to PLOT YOUR DATA.

dd <- data.frame(a=c(1, 2, 3, 4, 5, 6), b=c(3,  5,  6,  7,  9, 10))
plot(b ~ a, data=dd)
simple.model <- lm(b~a,data=dd)
abline(simple.model)

Why to you think you need a cubic model to describe 6 observations?

Your model is overparameterized - it has two more parameters than the number
of observations can reasonably justify, something that would be obvious from
your plot.

The summary of the simple.linear model shows both the intercept and the
slope are statistically meaningful.  (That's what the asterisks mean.)

Call:
lm(formula = b ~ a, data = dd)

Residuals:
       1        2        3        4        5        6 
-0.23810  0.39048  0.01905 -0.35238  0.27619 -0.09524 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.86667    0.30132   6.195  0.00345 ** 
a            1.37143    0.07737  17.725 5.95e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.3237 on 4 degrees of freedom
Multiple R-Squared: 0.9874,     Adjusted R-squared: 0.9843 
F-statistic: 314.2 on 1 and 4 DF,  p-value: 5.952e-05

I think you should invest a small amount of your time, and an even smaller
amount of your money to purchase and read - cover-to-cover - one of the
several very good books on elementary statistics and R.  My recommendation
is _Introductory Statistics with R_ by Peter Dalgaard (Paperback - Jan 9,
2004).  Amazon.com carries it.

Best wishes.

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 2:06 PM
To: Charles.Annis at statisticalengineering.com
Cc: R-help at r-project.org
Subject: Re: [R] glm expand model to more values

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

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