[R] Linear Regression with slope equals 0
Hi there, am trying to run a linear regression with a slope of 0. I have a dataset as follows t d 1 303 2 302 3 304 4 306 5 307 6 303 I would like to test the significance that these points would lie on a horizontal straight line. The standard regression lm(d~t) doesn't seem to allow the slope to be set. Any help very welcome. ed __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Linear Regression with slope equals 0
On Tue, 14 Aug 2007, [EMAIL PROTECTED] wrote: Hi there, am trying to run a linear regression with a slope of 0. I have a dataset as follows t d 1 303 2 302 3 304 4 306 5 307 6 303 I would like to test the significance that these points would lie on a horizontal straight line. The standard regression lm(d~t) doesn't seem to allow the slope to be set. lm(d ~ 1) does, though, to zero. More generally you can use offset(), e.g. lm(d ~ offset(7*t)) forces a slope of 7. -- Brian D. Ripley, [EMAIL PROTECTED] 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, UKFax: +44 1865 272595 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Linear Regression with slope equals 0
On 14-Aug-07 11:36:37, [EMAIL PROTECTED] wrote: Hi there, am trying to run a linear regression with a slope of 0. I have a dataset as follows t d 1 303 2 302 3 304 4 306 5 307 6 303 I would like to test the significance that these points would lie on a horizontal straight line. The standard regression lm(d~t) doesn't seem to allow the slope to be set. The model d~1 will fit a constant (the mean), i.e. a regressio with slope = 0. The model d~t will fit the usual linear regression. The two con be compared with anova(), as well as getting the details of the individual fits with summary(). E.g. (with your example): d-c(303,302,304,306,207,303) t-c(1,2,3,4,5,6) lm0-lm(u~1);lm1-lm(u~t);anova(lm0,lm1) ##Analysis of Variance Table ##Model 1: u ~ 1 ##Model 2: u ~ t ## Res.DfRSS Df Sum of Sq F Pr(F) ##1 5 7785.5 ##2 4 6641.4 11144.1 0.6891 0.4531 summary(lm0) ## Call: lm(formula = u ~ 1) ## Residuals: ##1 2 3 4 5 6 ## 15.5 14.5 16.5 18.5 -80.5 15.5 ## Coefficients: ##Estimate Std. Error t value Pr(|t|) ## (Intercept) 287.50 16.11 17.85 1.01e-05 *** ##Residual standard error: 39.46 on 5 degrees of freedom mean(d) ## [1] 287.5 summary(lm1) ## Call: lm(formula = u ~ t) ## Residuals: ## 1 2 3 4 5 6 ## -4.714 2.371 12.457 22.543 -68.371 35.714 ## Coefficients: ## Estimate Std. Error t value Pr(|t|) ## (Intercept) 315.800 37.934 8.325 0.00114 ** ## t -8.086 9.740 -0.830 0.45314 ## Residual standard error: 40.75 on 4 degrees of freedom ## Multiple R-Squared: 0.147, Adjusted R-squared: -0.0663 ## F-statistic: 0.6891 on 1 and 4 DF, p-value: 0.4531 The P-value for the slope in lm1 is the same as the P-value returned by anova(). If you want to force a particular non-zero slope (e.g. s0) for comparison with the data, you can use lm0 - lm(d - s0*t ~ 1), compared with lm1- lm(d- s0*t ~ t) for instance. Hoping this helps, Ted. E-Mail: (Ted Harding) [EMAIL PROTECTED] Fax-to-email: +44 (0)870 094 0861 Date: 14-Aug-07 Time: 13:16:05 -- XFMail -- __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Linear Regression with slope equals 0
Dear Ed,
In my opinion you don't need to set the slope to zero. Just test if the
slope in lm(d ~ t) is significant. If it is significant then you have
evidence that the slope is NOT zero. But when it is not significant (and
in your example it is), you can't say that it is zero. But doing some
power calculations allows you to estimate the smallest detectable slope.
The estimated slope in your example is 0.49. Your design has a power of
13% to detect slopes of this size. The real slope has to be about 1.75
in order to have 80% power. Let's say that it would matter if the slope
is about 2 or larger and it won't matter is it is below 2. The power to
detect a slope of 2 is 89%, hence you would likely get a significant
slope if it was larger then 2. Since the slope was not significant, it's
safe to say that the slope is not larger then 2.
But if a slope of 0.5 would matter, you couldn't make this kind of
assumptions because the power to detect a slope of 0.5 is only 13%. So
the change of rejecting the null hypothesis (slope = 0) when slope = 0.5
is too small.
HTH,
Thierry
power.trend - function(repetitions = 5, x = c(0, 1), sd = 1, slope =
1, alpha = 0.05){
+ X - rep(x, repetitions)
+ ncp - slope ^ 2 * sum((X - mean(X))^2) / sd ^ 2
+ return(1 - pf(qf(1 - alpha, 1, length(X) - 2), 1, length(X) - 2, ncp
= ncp))
+ }
df - data.frame(t = 1:6, d = c(303, 302, 304, 306, 307, 303))
fit - lm(d ~ t, data = df)
summary(fit)
Call:
lm(formula = d ~ t, data = df)
Residuals:
123456
0.04762 -1.43810 0.07619 1.59048 2.10476 -2.38095
Coefficients:
Estimate Std. Error t value Pr(|t|)
(Intercept) 302.4667 1.7849 169.45 7.28e-09 ***
t 0.4857 0.45831.060.349
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.917 on 4 degrees of freedom
Multiple R-Squared: 0.2192, Adjusted R-squared: 0.02402
F-statistic: 1.123 on 1 and 4 DF, p-value: 0.349
power.trend(repetitions = 1, x = df$t, sd = sd(df$d), slope =
coef(fit)[t])
[1] 0.1292668
power.trend(repetitions = 1, x = df$t, sd = sd(df$d), slope = 1.75)
[1] 0.8021454
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium
tel. + 32 54/436 185
[EMAIL PROTECTED]
www.inbo.be
Do not put your faith in what statistics say until you have carefully
considered what they do not say. ~William W. Watt
A statistical analysis, properly conducted, is a delicate dissection of
uncertainties, a surgery of suppositions. ~M.J.Moroney
-Oorspronkelijk bericht-
Van: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] Namens
[EMAIL PROTECTED]
Verzonden: dinsdag 14 augustus 2007 13:37
Aan: r-help@stat.math.ethz.ch
Onderwerp: [R] Linear Regression with slope equals 0
Hi there, am trying to run a linear regression with a slope of 0.
I have a dataset as follows
t d
1 303
2 302
3 304
4 306
5 307
6 303
I would like to test the significance that these points
would lie on a horizontal straight line.
The standard regression lm(d~t) doesn't seem to allow the
slope to be set.
Any help very welcome.
ed
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
