# [R] Std. errors of intercept and slope

Ben Bolker bolker at zoo.ufl.edu
Sat Sep 27 03:59:55 CEST 2003

```  I'm afraid you're going to have to look it up in a basic statistics
textbook.

Ben Bolker

On Fri, 26 Sep 2003, Yao, Minghua wrote:

> Thanks, Ben.
>
> Could you tell me the formula for calculating this sd., given (x_i, y_i)
> (i=1,2,...,N)?
> We only have one intercept and slope for them.
>
> -Minghua
>
> -----Original Message-----
> From: Ben Bolker [mailto:bolker at zoo.ufl.edu]
> Sent: Friday, September 26, 2003 4:34 PM
> To: Yao, Minghua
> Cc: R Help (E-mail)
> Subject: Re: [R] Std. errors of intercept and slope
>
>
>
>   Since the intercept and slope are estimated parameters, they have
> sampling distributions described by their means and standard deviations.
> The s.d. tells you the size of the uncertainty in intercept & in slope.
>
>   This is a pretty basic stats question -- you need to refer to a standard
> textbook or reference material ...
>
>   Ben Bolker
>
> On Fri, 26 Sep 2003, Yao, Minghua wrote:
>
> > Dear all,
> >
> > I have the following output generated by linear regression. Since there is
> > only one regression intercept and one slope for one set of data, what is
> the
> >
> > meaning of std. error for intercept and that of slope? Thanks in advance.
> >
> > Sincerely,
> >
> > Minghua
> >
> >
> > > data(thuesen)
> > > attach(thuesen)
> > > lm(short.velocity~blood.glucose)
> >
> > Call:
> > lm(formula = short.velocity ~ blood.glucose)
> >
> > Coefficients:
> >   (Intercept)  blood.glucose
> >       1.09781        0.02196
> >
> > > summary(lm(short.velocity~blood.glucose))
> >
> > Call:
> > lm(formula = short.velocity ~ blood.glucose)
> >
> > Residuals:
> >      Min       1Q   Median       3Q      Max
> > -0.40141 -0.14760 -0.02202  0.03001  0.43490
> >
> > Coefficients:
> >               Estimate Std. Error t value Pr(>|t|)
> > (Intercept)    1.09781    0.11748   9.345 6.26e-09 ***
> > blood.glucose  0.02196    0.01045   2.101   0.0479 *
> > ---
> > Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
> >
> > Residual standard error: 0.2167 on 21 degrees of freedom
> > Multiple R-Squared: 0.1737,     Adjusted R-squared: 0.1343
> > F-statistic: 4.414 on 1 and 21 DF,  p-value: 0.0479
> >
> > >
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> >
>
>

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