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

[Peter Dalgaard]

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 using 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
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
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