[R] details about lm()

[Uwe Ligges]

vincent at 7d4.com wrote:

> Uwe Ligges a écrit :
> 
>> vincent at 7d4.com wrote:
>>
>>> Domenico Cozzetto a écrit :
>>>
>>>> Dear all,
>>>> I'd like to get a linear regression of some data, and impose that 
>>>> the line
>>>> goes through a given point P. I've tried to use the lm() method in the
>>>> package "stats", but I wasn't able to specify the coordinates of the 
>>>> point P. Maybe I should use another method?
>>>
>>>
>>> add directly P in your data is also a way
>>
>>
>> No!
> 
> 
> Sorry indeed for my not at all rigourous answer.
> Adding P in the data set will indeed not force the regression line
> to pass through P (P will only be one more points of the cloud,
> adding P will "attract" the regression line, not more.)
> 
> I did make this answer because I'm yet working with very small data
> sets, and adding P (in more than one exemplar when needed in order to
> give it more weight), is a fast, (a bit ugly I agree), way to do.
> But on the kind of data I use, it works good enough.
> I should have add this precision. Apologies.
> 
>> Please, both of you, consult a basic textbook on linear regression.
> 
> 
> If you have a good reference or link in mind,
> I would thank you.

E.g., among several other, the great comprehensive books by John Fox are 
really well written and easy to understand ...


>> You can transform the data (linear) so that P becomes (0,0), after 
>> that you can estimate the slope without intercept by specifying
>> lm(y ~ x - 1)
>> The slope estimate is still valid while your intercept can be 
>> calculated afterwards.
> 
> 
> Sorry for my lack of knowledge, but will the above trick really force
> the regression line to pass through P ?
> adding (0,0) in this new system of coordinates isn't it equivalent to 
> add P to the dataset in the original system ?

Well, you do not add that point, but transform the others:
Say you have (let's make a very simple 1-D example) points P_i = (x_i, 
y_i), and P = (x_0, y_0). Then calculate for all i:

   P'_i = (x_i - x_0, y_i - y_0)

Now you can calculate a regression without any Intercept by

   lm(y ~ x - 1)

You got the slope now and the Intercept is 0 so far for P'.

After that, you can re-transform to get the real data's intercept:

   Intercept = -(slope * x_0) + y_0


Uwe Ligges




> If my question is too basic and/or too stupid, just give it a rest.
> 
> Vincent