# [R] Std. errors of intercept and slope

Ben Bolker bolker at zoo.ufl.edu
Fri Sep 26 23:33:53 CEST 2003

```  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
>
> >
>
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>

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