Thanks, Mr. Graves. This is exactly what I need.
-MY -----Original Message----- From: Spencer Graves [mailto:[EMAIL PROTECTED] Sent: Saturday, September 27, 2003 8:34 AM To: [EMAIL PROTECTED] 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:[EMAIL PROTECTED] >>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 >>> >>> >>> >>>______________________________________________ >>>[EMAIL PROTECTED] mailing list >>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help >>> >>> >>> >> >> > > > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
