The standard errors for parameters in the fitted result are not related to the error in the initial data, and they are esitimated from current fitted parameters. They can be used to estimate the precision of the fitted parameters.
UCL and LCL can be calculated from Standard Error:
LCL=P-t(0.025,n-p)*s
UCL=P+t(0.025,n-p)*s
where P is the fitted parameter, s is the standard error for the parameter, n is number of points, p is number of parameters. t is the Student's t distribution.
The large difference between standard error and confiderce interval is due to the fact that you only used three points to fit.
t(0.025,3-2)=12.7;
which means confidence interval half width is 12.7 times as large as the standard error.
However if you use more points to fit, e.g. 100 points:
t(0.025,100-2)=1.98;
Now confidence interval half width is only twice as large as the standard error.
For more information, see the page:
http://www.originlab.com/www/helponline/Origin/en/UserGuide/Linear_Regression_Results.html#Confidence_Intervals
Sam
OriginLab Technical Services
Standard Error in Linear Fit Parameters
Posted - 07/11/2012 : 10:25:39 PM
