interpret a p-value result as a significance of a linear regression in terms of sigmas

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 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code. Reply | Threaded Open this post in threaded view | Re: 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 > ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
 In reply to this post by jean-philippe fontaine 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 <[hidden email]> 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 > > ______________________________________________ > [hidden email] 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: [hidden email]  Priv: [hidden email] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.