# [R] fitting with lm

Arne Mueller a.mueller at icrf.icnet.uk
Tue Mar 19 17:03:53 CET 2002

```Dear All,

I'm getting confused with the concept R uses to do regression using lm.
I'm afmiliar with gnuplot and the build-in fit command, but couldn't get
R's lm to work on my data.

I know that my data follows a powerlaw or maybe an exponential function,
and I'd like to determine the best fitting factors for the formula:
a*x^b where b < 0.

I've tried thge follwoing:

s <- lm(y ~ x)

> summary(s)

Call:
lm(formula = y ~ x)

Residuals:
Min      1Q  Median      3Q     Max
-18.454  -7.577  -2.861   3.909  60.988

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21.209171   1.431472  14.816  < 2e-16 ***
x           -0.065609   0.008799  -7.456 7.45e-12 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

Residual standard error: 11.87 on 145 degrees of freedom
Multiple R-Squared: 0.2772,     Adjusted R-squared: 0.2722
F-statistic:  55.6 on 1 and 145 DF,  p-value: 7.454e-12

What has R done? I assume the formula is just a+b*x and I can get a and
b via

> coef(s)
(Intercept)           x
21.20917074 -0.06560878

But:

> s <- lm(y ~ a*x^b)
Error in terms.formula(formula, data = data) :
invalid power in formula

I went through the formula section of the R-manual, but I realy don't
get it.

Finally, I'd like to have the raw data-points together with a line
representing the function used to fit the data in a plot? How can I plot
function, e.g. sin(x) ?

I hope I just need a primer on this to get going.

thanks very much for any help,

Arne

--
Arne Mueller
Biomolecular Modelling Laboratory
Imperial Cancer Research Fund
44 Lincoln's Inn Fields
London WC2A 3PX, U.K.
phone : +44-(0)207 2693405      | fax :+44-(0)207-269-3534
email : a.mueller at icrf.icnet.uk | http://www.bmm.icnet.uk
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```