# [R] Std. errors of intercept and slope

Yao, Minghua yao6889 at msmailhub.oulan.ou.edu
Fri Sep 26 23:49:59 CEST 2003

```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
>

--
620B Bartram Hall                            bolker at zoo.ufl.edu
Zoology Department, University of Florida    http://www.zoo.ufl.edu/bolker
Box 118525                                   (ph)  352-392-5697
Gainesville, FL 32611-8525                   (fax) 352-392-3704

```