# [R] regression slope

Sundar Dorai-Raj sundar.dorai-raj at PDF.COM
Tue Jul 20 20:28:05 CEST 2004

```

> I would try to construct the confidence intervals and compare them to
> the value that you want
>
>>x <- rnorm(20)
>>y <- 2*x + rnorm(20)
>>summary( m1 <- lm(y~x) )
>
>
> <snip>
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)
> (Intercept)   0.1418     0.1294   1.095    0.288
> x             2.2058     0.1289  17.108  1.4e-12 ***
> <snip>
>
> That says that the slope estimate is 2.2058 with standard error of
> 0.1289. So the approximate 99% CI is 2.2058 +/- 3*0.1289 = (1.819,
> 2.593) which is clearly greater than 1.
>
>
>>summary(m1)[[4]][2,1] + 3* summary(m1)[[4]][2,2]
>
> [1] 2.592629
>
>>summary(m1)[[4]][2,1] - 3* summary(m1)[[4]][2,2]
>
> [1] 1.819026
>

I think the preferred way of doing this is with confint:

# 3 sigma limits
confint(m1, parm = "x", level = 1 - pt(-3, m1\$df.resid) * 2)
# 95% confidence (default)
confint(m1, parm = "x")

> For your next question, you simply compare the CI of one slope to
> another and see if they overlap.
>
> There is probably a way to construct proper significance testing to get
> p-values and such. You can try reading MASS4 or hopefully someone in the
> list might provide with a neater answer.
>
>
> On Tue, 2004-07-20 at 17:02, Avril Coghlan wrote:
>
>>Hello,
>>
>>  I'm a newcomer to R so please
>>forgive me if this is a silly question.
>>
>>It's that I have a linear regression:
>>fm <- lm (x ~ y)
>>and I want to test whether the
>>slope of the regression is significantly
>>less than 1. How can I do this in R?
>>
>>I'm also interested in comparing the
>>slopes of two regressions:
>>fm1 <- lm (x ~ y)
>>fm2 <- lm (a ~ b)
>>and asking if the slope of fm1 is
>>less than the slope of fm2. Is this
>>easy to do in R?
>>
>>
>>I will be very grateful for any help.
>>
>>regards,
>>Avril Coghlan
>>(University College Dublin, Ireland)
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>>
>
>
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