R help - Jul 2005 - Non-linear "linear" models?

Hi,
    I'm new to R (though I have spent hours trying to learn how to use 
it) and also not very knowledgeable
about statistics, so I hope you will excuse what may seem like a very 
basic question. I'm trying to use
R to do an ANOVA analysis for some data with an unbalanced design, and 
while I was trying to figure that out, I got confused about the purpose 
of the "lm". All definitions I can find of "linear model"
are of the
form:
y = a + b * x + e

  In other words, y is only linear in the dependent variable(s) x. 
However, the lm model seems to support higher order polynomials, e.g.:
> lm(dist ~ speed + I(speed^2)+I(speed^3), cars)
  Is there some sense in which that model is "linear", or is R's
lm()
providing extra functionality?

Thanks,
--Paul


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Paul:

Even when the model includes polynomial terms as you have below, it is
still a linear model because it is linear in the parameters. It is your
coefficients that are not linear. There are other functions in R for
non-linear models.

help.search('non linear') 

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
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Sent: Saturday, July 23, 2005 10:24 AM
To: r-help at stat.math.ethz.ch
Subject: [R] Non-linear "linear" models?

Hi,
    I'm new to R (though I have spent hours trying to learn how to use
it) and also not very knowledgeable
about statistics, so I hope you will excuse what may seem like a very
basic question. I'm trying to use R to do an ANOVA analysis for some
data with an unbalanced design, and while I was trying to figure that
out, I got confused about the purpose of the "lm". All definitions I
can
find of "linear model" are of the
form:
y = a + b * x + e

  In other words, y is only linear in the dependent variable(s) x. 
However, the lm model seems to support higher order polynomials, e.g.:
> lm(dist ~ speed + I(speed^2)+I(speed^3), cars)
  Is there some sense in which that model is "linear", or is R's
lm()
providing extra functionality?

Thanks,
--Paul


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http://about.mailblocks.com/info

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