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)
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 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 >
At 06:44 PM 7/20/2004 +0100, Adaikalavan Ramasamy wrote:>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.Another method which gives the p value etc. was shared with this list by Prof. Ripley several years ago: set.seed(1) x <- rnorm(20) x.hypoth <- 1 # i.e., Null hypothesis is that x != 1 y <- 2*x + rnorm(20) summary( m1 <- lm(y - x.hypoth*x~x) ) Produces: Call: lm(formula = y - x.hypoth * x ~ x) Residuals: Min 1Q Median 3Q Max -1.69133 -0.43739 -0.07132 0.68033 1.63937 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.03307 0.19981 0.166 0.870 x 0.79245 0.21951 3.610 0.002 ** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 0.8738 on 18 degrees of freedom Multiple R-Squared: 0.42, Adjusted R-squared: 0.3878 F-statistic: 13.03 on 1 and 18 DF, p-value: 0.002001> >> 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 > >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>> > >______________________________________________ >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 >With best wishes and kind regards I am Sincerely, Corey A. Moffet Rangeland Scientist ################################################################## #### USDA-ARS # Northwest Watershed Research Center # 800 Park Blvd, Plaza IV, Suite 105 ########### #### Boise, ID 83712-7716 # # # # Voice: (208) 422-0718 # # #### #### FAX: (208) 334-1502 # # # # #### ########### ##################################################################
see also the contributed document by John Verzani, Simple R, page 87f.> Adaikalavan Ramasamy wrote: > > > 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>> > > > ______________________________________________ > 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 ______________________________________________ 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 -------------------------------------------------------------------------------- The information contained herein is confidential and is inte...{{dropped}}
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