[R] Plot different regression models on one graph

[Peter Ehlers]

kMan wrote:
> Peter wrote:
>> You like to live dangerously.
> 
> Clue me in, Professor.
> 
> Sincerely,
> KeithC.
> 

Okay, Keith, here goes:

dat <-
structure(list(x = c(62.5, 68.5, 0, 52, 0, 52, 0, 52, 23.5, 86,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0), y = c(0.054, 0.055, 0.017, 0.021,
0.02, 0.028, 0.032, 0.073, 0.076, 0.087, 0.042, 0.042, 0.041,
0.045, 0.021, 0.018, 0.017, 0.018, 0.028, 0.022)), .Names = c("x",
"y"), row.names = c(NA, -20L), class = "data.frame")

fm1 <- lm(y ~ poly(x,3), data = dat)
fm2 <- lm(y ~ poly(x,3), data = dat, subset = -9)

xx <- 0:86
yhat1 <- predict(fm1, list(x = xx))
yhat2 <- predict(fm2, list(x = xx))

plot(x,y)
lines(xx, yhat1, col="blue", lwd=2)
lines(xx, yhat2, col="red", lwd=2)


That's how much difference *one* point makes in a cubic fit!
I'm not much of a gambler, so I wouldn't base any important
decisions on the results of the fit.

Cheers,

  -Peter Ehlers

> -----Original Message-----
> From: Peter Ehlers [mailto:ehlers at ucalgary.ca] 
> Sent: Sunday, February 14, 2010 6:49 PM
> To: kMan
> Cc: 'David Winsemius'; 'Rhonda Reidy'; r-help at r-project.org
> Subject: Re: [R] Plot different regression models on one graph
> 
> kMan wrote:
>> I would use all of the data. If you want to "drop" one, control for it in
>> the model & sacrifice a degree of freedom.
> 
> You like to live dangerously.
> 
>   -Peter Ehlers
> 
>> Why the call to poly() by the way?
>>
>> KeithC.
>>
>> -----Original Message-----
>> From: Peter Ehlers [mailto:ehlers at ucalgary.ca] 
>> Sent: Saturday, February 13, 2010 1:35 PM
>> To: David Winsemius
>> Cc: Rhonda Reidy; r-help at r-project.org
>> Subject: Re: [R] Plot different regression models on one graph
>>
>> Rhonda:
>>
>> As David points out, a cubic fit is rather speculative. I think that one
>> needs to distinguish two situations: 1) theoretical justification for a
>> cubic model is available, or 2) you're dredging the data for the "best"
> fit.
>> Your case is the second. That puts you in the realm of EDA (exploratory
> data
>> analysis). You're free to fit any model you wish, but you should assess
> the
>> value of the model. One convenient way is to use the influence.measures()
>> function, which will show that points 9 and 10 in your data have a strong
>> influence on your cubic fit (as, of course, your eyes would tell you). A
>> good thing to do at this point is to fit 3 more cubic models:
>> 1) omitting point 9, 2) omitting point 10, 3) omitting both.
>>
>> Try it and plot the resulting fits. You may be surprised.
>>
>> Conclusion: Without more data, you can conclude nothing about a
>> non-straightline fit.
>>
>> (And this hasn't even addressed the relative abundance of x=0 data.)
>>
>>   -Peter Ehlers
>>
>> David Winsemius wrote:
>>> On Feb 13, 2010, at 1:35 PM, Rhonda Reidy wrote:
>>>
>>>> The following variables have the following significant relationships 
>>>> (x is the explanatory variable): linear, cubic, exponential, logistic.
>>>> The linear relationship plots without any trouble.
>>>>
>>>> Cubic is the 'best' model, but it is not plotting as a smooth curve 
>>>> using the following code:
>>>>
>>>> cubic.lm<- lm(y~poly(x,3))
>>> Try:
>>>
>>> lines(0:80, predict(cubic.lm, data.frame(x=0:80)),lwd=2)
>>>
>>> But I really must say the superiority of that relationship over a 
>>> linear one is far from convincing to my eyes. Seems to be caused by 
>>> one data point. I hope the quotes around "best" mean tha tyou have the
>> same qualms.
>>>> lines(x,predict(cubic.lm),lwd=2)
>>>>
>>>> How do I plot the data and the estimated curves for all of these 
>>>> regression models in the same plot?
>>>>
>>>> x <- c(62.5,68.5,0,52,0,52,0,52,23.5,86,0,0,0,0,0,0,0,0,0,0)
>>>>
>>>> y <-
>>>> c(0.054,0.055,0.017,0.021,0.020,0.028,0.032,0.073,0.076,0.087,0.042,0
>>>> .042,0.041,0.045,0.021,0.018,0.017,0.018,0.028,0.022)
>>>>
>>>>
>>>> Thanks in advance.
>>>>
>>>> Rhonda Reidy
>>>>
>> --
>> Peter Ehlers
>> University of Calgary
>>
>>
>>