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

[Duncan Murdoch]

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
>