[R] Forcing best-fit lines to go through the origin

[Henric Nilsson]

Jim Milks said the following on 2005-04-18 03:08:

> Dear All,
> 
> I have a rather unusual problem.  I have a set of data for a class in 
> subsurface processes.  From that dataset, I must calculate the slope of 
> the best-fit line (which is the parameter of interest).  The problem I 
> have is twofold: 1) for the purposes of the exercise, I must force my 
> best-fit line to go through the origin (0,0), and 2) the line must be 
> linear, even though the data is not.  I would like to use R to help me 
> calculate the line, but am unaware of any code or packages that will 
> allow me to force the line through the origin.
> 
> The dataset is as follows:
> 
>    C           C*
> 4.1         17.4
> 6.2         24.9
> 27.9         39.5
> 91.1         57.4
> 168.0     75.5

Depending on your definition of `best-fit', you may use the `lm' 
function where `best-fit' corresponds to solving a least-squares 
problem. Try ?lm at the R prompt.

Not that I know if you want to regress C on C*, or the other way 
around.. Let's do both:

 > (dta <- read.table("clipboard", header = TRUE))
       C   C.
1   4.1 17.4
2   6.2 24.9
3  27.9 39.5
4  91.1 57.4
5 168.0 75.5
 > fit1 <- lm(C ~ C. -1 , data = dta)
 > coef(fit1)
       C.
1.676325
 > fit2 <- lm(C. ~ C -1, data = dta)
 > coef(fit2)
         C
0.5150568

To convince yourself, take a look at the data with the least-squares 
line superimposed:

 > plot(C ~ C., data = dta, xlim = c(0, 200), ylim = c(0, 100))
 > abline(fit1)

Plotting `fit2' is left as an exercise... ;-)


HTH,
Henric

> 
> Thank you in advance for any advice you can give me.
> 
> Sincerely,
> 
> Jim Milks
> Graduate Student
> Environmental Sciences Ph.D. Program
> Wright State University
> 3640 Colonel Glenn Hwy
> Dayton, OH 45435
> 
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