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

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

jean-philippe fontaine
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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Re: interpret a p-value result as a significance of a linear regression in terms of sigmas

Duncan Murdoch-2
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-help
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and provide commented, minimal, self-contained, reproducible code.
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Re: interpret a p-value result as a significance of a linear regression in terms of sigmas

Peter Dalgaard-2
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-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.