Dear Edwin,

Your first approach is correct. Since confidence intervals strongly 
related to one-sample tests, you can use one-sample t-test if you want 
p-values. Someone may suggest built-in function for this, but you can 
calculate it easily without such function.

Here is an example:

# creating data, the intercept is zero, the slope is 1.2
x<-seq(0,100)
y<-rnorm(length(x),mean=1.2*x,sd=15)

# plotting the data
plot(x,y)
abline(0,1)

# fitting linear equation
m<-lm(y~x)
summary(m)

# for test we need the slope and its standard error
# we can get both from the summary
sm<-summary(m)
sm$coefficients
(slope<-sm$coefficients[2,1])
(se.slope<-sm$coefficients[2,2])

# the last steps: calculating t-value and probability of type I error
(t.value<-(slope-1)/se.slope)
1-pt(t.value,df=length(x)-2)



Best regards,

Zoltan

2013.06.12. 13:46 keltezéssel, Pos, E.T. írta:
> Dear all,
>
> I'm having trouble with something that I presume is foolishly easy.
>
> I have a linear model with a slope slightly higher than the slope of y=x. Now I wish to test if the slope of this lm is actually significantly different from the slope of y=x (i.e. 1)
>
> One option to do this obviously is testing whether 1 falls within the 95% confidence interval of the original lm. I've done this and it gives me an indication but I would like a hard p-value for testing this significance. The problem I run into is that I don't know how to test for the significance of this difference between the slope of my lm and the line y=x.
>
> Thus far:
>
> Method #1
>
> data1.y = "some data"
> data1.x = "some more data"
> data1 = lm(data1.y~data1.x)
> abline(data1, col = "red", lwd = 2) #draw a line through the regression
> abline(a = 0, b = 1)                    # which gives me the line for x=y but this doesn't work for ANOVA but is nicely ilustrative
>
> #Check the 95% confidence interval
> confint(data1)
>
> Method #2
>
> # I used offset because I found that on the mailinglist in the archives but I'm not sure why this would indicate the difference is significant from the slope y=x? Any suggestions?
> data1.y = "some data"
> data1.x = "some more data"
> data1 = lm(data1.y~data1.x)
> data1.offset = lm(data1.y~data1.x+offset(data1.x))
> summary(data1.offset) #then check if the slope is significantly different from 1
>
> But I'm not convinced that method number 2 gives me the correct answer. Any idea's here?
>
> Thanks a lot,
>
> Edwin.
>
>
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>
>
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology@r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology


-- 
Botta-Dukát Zoltán
--------------------------------
Ökológiai és Botanikai Intézet
Magyar Tudományos Akadémia
Ökológiai Kutatóközpont
--------------------------------
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zoltan@okologia.mta.hu
www.okologia.mta.hu


Zoltán BOTTA-Dukát
--------------------------------
Institute of Ecology and Botany
Hungarian Academy of Sciences
Centre for Ecological Research
--------------------------------
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zoltan@okologia.mta.hu
www.okologia.mta.hu


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