how to test this

This is two tests: Whether the slope != 1 and whether the intercept != 0.

Neither model given has an intercept ....

To do this, include an offset in your model:

fit  <- lm(y ~ x + offset(x), data=dat)

but no intercept, so use

summary(lm(y ~ 0 + x + offset(1.05*x), data=dat))

and look if the coefficient of x is significantly different from zero.

E.g.

x <- 1:10
set.seed(1)
y <- 1.05*x + rnorm(10)
summary(lm(y ~ 0 + x + offset(1.05*x)))

Coefficients:
   Estimate Std. Error t value Pr(>|t|)
x  0.03061    0.03910   0.783    0.454

is not.

HTH,

Simon.


At 03:44 PM 3/08/2005, Jin.Li at csiro.au wrote:

I am wondering how to test whether a simple linear regression model
(e.g. y=1.05x) is significantly different from a 1 to 1 line (i.e. y=x).

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595