# [R] Linear Model with curve fitting parameter?

Peter Ehlers ehlers at ucalgary.ca
Fri Apr 1 18:14:39 CEST 2011

```On 2011-04-01 05:44, stephen sefick wrote:
> Setting Z=Q-A would be the incorrect dimensions.  I could Z=Q/A.  Is
> fitting a nls model the same as fitting an ols?  These data are
> hydraulic data from ~47 sites.  To access predictive ability I am
> removing one site fitting a new model and then accessing the fit with
> a myriad of model assessment criteria.  I should get the same answer
> with ols vs nls?  Thank you for all of your help.

No, ols and nls won't give the same result.
If you use ols on the logged data, you're assuming
additive errors on the log scale. With nls, you
assume additive errors on the original scale.
But your model looks simple enough - why not run
it through both functions and see what the difference is.
Ultimately, everything depends on what assumptions
you're comfortable with.

Peter Ehlers

>
> Stephen
>
> On Thu, Mar 31, 2011 at 8:34 PM, Steven McKinney<smckinney at bccrc.ca>  wrote:
>>
>>> -----Original Message-----
>>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of stephen sefick
>>> Sent: March-31-11 3:38 PM
>>> To: R help
>>> Subject: [R] Linear Model with curve fitting parameter?
>>>
>>> I have a model Q=K*A*(R^r)*(S^s)
>>>
>>> A, R, and S are data I have and K is a curve fitting parameter.  I
>>> have linearized as
>>>
>>> log(Q)=log(K)+log(A)+r*log(R)+s*log(S)
>>>
>>> I have taken the log of the data that I have and this is the model
>>> formula without the K part
>>>
>>> lm(Q~offset(A)+R+S, data=x)
>>>
>>> What is the formula that I should use?
>>
>> Let Z = Q - A for your logged data.
>>
>> Fitting lm(Z ~ R + S, data = x) should yield
>> intercept parameter estimate = estimate for log(K)
>> R coefficient parameter estimate = estimate for r
>> S coefficient parameter estimate = estimate for s
>>
>>
>>
>> Steven McKinney
>>
>> Statistician
>> Molecular Oncology and Breast Cancer Program
>> British Columbia Cancer Research Centre
>>
>>
>>
>>>
>>> Thanks for all of your help.  I can provide a subset of data if necessary.
>>>
>>>
>>>
>>> --
>>> Stephen Sefick
>>> ____________________________________
>>> | Auburn University                                         |
>>> | Biological Sciences                                      |
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>>> | Auburn, Alabama                                         |
>>> | 36849                                                           |
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