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Yao, Minghua

2003-Sep-26 21:10 UTC

[R] Std. errors of intercept and slope

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 
>

Ben Bolker

2003-Sep-26 21:33 UTC

head link

[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

Yao, Minghua

2003-Sep-26 21:49 UTC

head link

[R] Std. errors of intercept and slope

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

Yao, Minghua

2003-Sep-29 13:38 UTC

head link

[R] Std. errors of intercept and slope

Thanks, Mr. Graves.

This is exactly what I need.

-MY

-----Original Message-----
From: Spencer Graves [mailto:spencer.graves at pdf.com]
Sent: Saturday, September 27, 2003 8:34 AM
To: bolker at zoo.ufl.edu
Cc: Yao, Minghua; R Help (E-mail)
Subject: Re: [R] Std. errors of intercept and slope


See especially any discussion of "the matrix formulation of 
regression".  I'm sure this is in many books.  I'm not familiar
with the
recent literature, but I know it is in Draper and Smith, Applied 
Regression Analysis and Box, Hunter and Hunter, Statistics for 
Experimenters. 

Briefly, suppose we write the regression model as y = X b + e, where y 
and e are N x 1 vectors, X is an N x k matrix, and e is a vector of 
normal, independent errors with standard deviation s.e.  Then the least 
squares and maximum likelihood estimate of b is

      b.hat = (inverse(X' X))*(X'y),

and the covariance matrix for b.hat is

      var(b.hat) = s.e^2 * inverse(X'X). 

I apologize if this is too terse for you;  if so, please see any good 
book on regress. 

hope this helps.  spencer graves

Ben Bolker wrote:
>  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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