jean-philippe
2018-Jun-20 10:53 UTC
[R] interpret a p-value result as a significance of a linear regression in terms of sigmas
dear R community,
I am running a linear regression for my dataset between 2 variables
(disk mass and velocities).
This is the result returned by the summary function onto the lm object
for one of my dataset.
Call:
lm(formula = df$md1 ~ df$logV, data = df)
Residuals:
Min 1Q Median 3Q Max
-0.64856 -0.16492 0.04127 0.18027 0.45727
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.2582 0.2682 23.333 < 2e-16 ***
df$logV 1.2926 0.2253 5.738 6.5e-06 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 0.3067 on 24 degrees of freedom
Multiple R-squared: 0.5784, Adjusted R-squared: 0.5609
F-statistic: 32.93 on 1 and 24 DF, p-value: 6.504e-06
I am interested to give the significance in terms of sigmas (as
generally done in particle physics, see for instance the 7 \sigma
discovery of the Higgs particle)
of my regression.
For this, if I understood well, I should look at the p-value for the
F-statistic which is in this univariate linear regression the same as
the one for logV.
My question is, am I right if I state that the significance in terms of
sigmas (sign) is given by: p = 2*(1-pnorm(sign)) since I guess the
p-value returned by R is for a two sided test (and assuming Gaussianity
for my dataset)?
Otherwise is there any way to get the significance of this linear
regression in terms of sigmas?
I would have a similar question also, as extension, for a multivariate
linear regression for which the p-value associated to F statistics is
not the same as the p-value for each variable of the regression.
Thanks in advance,
Best Regards
Jean-Philippe Fontaine
--
Jean-Philippe Fontaine
PhD Student in Astroparticle Physics,
Gran Sasso Science Institute (GSSI),
Viale Francesco Crispi 7,
67100 L'Aquila, Italy
Mobile: +393487128593, +33615653774
Duncan Murdoch
2018-Jun-20 11:42 UTC
[R] interpret a p-value result as a significance of a linear regression in terms of sigmas
On 20/06/2018 6:53 AM, jean-philippe wrote:> dear R community, > > I am running a linear regression for my dataset between 2 variables > (disk mass and velocities). > This is the result returned by the summary function onto the lm object > for one of my dataset. > > Call: > lm(formula = df$md1 ~ df$logV, data = df) > > Residuals: > Min 1Q Median 3Q Max > -0.64856 -0.16492 0.04127 0.18027 0.45727 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 6.2582 0.2682 23.333 < 2e-16 *** > df$logV 1.2926 0.2253 5.738 6.5e-06 *** > --- > Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 > > Residual standard error: 0.3067 on 24 degrees of freedom > Multiple R-squared: 0.5784, Adjusted R-squared: 0.5609 > F-statistic: 32.93 on 1 and 24 DF, p-value: 6.504e-06 > > > I am interested to give the significance in terms of sigmas (as > generally done in particle physics, see for instance the 7 \sigma > discovery of the Higgs particle) > of my regression. > For this, if I understood well, I should look at the p-value for the > F-statistic which is in this univariate linear regression the same as > the one for logV.The t value is probably what you want, but I think you'll have to ask your supervisor for the definition used in your area. Duncan Murdoch> > My question is, am I right if I state that the significance in terms of > sigmas (sign) is given by: p = 2*(1-pnorm(sign)) since I guess the > p-value returned by R is for a two sided test (and assuming Gaussianity > for my dataset)? > > Otherwise is there any way to get the significance of this linear > regression in terms of sigmas? > > I would have a similar question also, as extension, for a multivariate > linear regression for which the p-value associated to F statistics is > not the same as the p-value for each variable of the regression. > > > > Thanks in advance, > > > Best Regards > > > Jean-Philippe Fontaine >
Peter Dalgaard
2018-Jun-20 11:45 UTC
[R] interpret a p-value result as a significance of a linear regression in terms of sigmas
Sorry to say so, but you seem confused. The "sigma" in physics parlance is presumably the s.e. of the estimate so the "number of sigmas" equal the t statistic, in this case 5.738. However, use of that measure ignores the t distribution, effectively assuming that there are infinite df (and 24 in not quite infinite). - pd> On 20 Jun 2018, at 12:53 , jean-philippe <jeanphilippe.fontaine at gssi.infn.it> wrote: > > dear R community, > > I am running a linear regression for my dataset between 2 variables (disk mass and velocities). > This is the result returned by the summary function onto the lm object for one of my dataset. > > Call: > lm(formula = df$md1 ~ df$logV, data = df) > > Residuals: > Min 1Q Median 3Q Max > -0.64856 -0.16492 0.04127 0.18027 0.45727 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 6.2582 0.2682 23.333 < 2e-16 *** > df$logV 1.2926 0.2253 5.738 6.5e-06 *** > --- > Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 > > Residual standard error: 0.3067 on 24 degrees of freedom > Multiple R-squared: 0.5784, Adjusted R-squared: 0.5609 > F-statistic: 32.93 on 1 and 24 DF, p-value: 6.504e-06 > > > I am interested to give the significance in terms of sigmas (as generally done in particle physics, see for instance the 7 \sigma discovery of the Higgs particle) > of my regression. > For this, if I understood well, I should look at the p-value for the F-statistic which is in this univariate linear regression the same as the one for logV. > > My question is, am I right if I state that the significance in terms of sigmas (sign) is given by: p = 2*(1-pnorm(sign)) since I guess the p-value returned by R is for a two sided test (and assuming Gaussianity for my dataset)? > > Otherwise is there any way to get the significance of this linear regression in terms of sigmas? > > I would have a similar question also, as extension, for a multivariate linear regression for which the p-value associated to F statistics is not the same as the p-value for each variable of the regression. > > > > Thanks in advance, > > > Best Regards > > > Jean-Philippe Fontaine > > -- > Jean-Philippe Fontaine > PhD Student in Astroparticle Physics, > Gran Sasso Science Institute (GSSI), > Viale Francesco Crispi 7, > 67100 L'Aquila, Italy > Mobile: +393487128593, +33615653774 > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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.-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com