[R] Std. errors of intercept and slope

[Yao, Minghua]

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 
> 
> >
> 
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