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 T O P I C    R E V I E W coreyjkelly Posted - 07/11/2012 : 10:25:39 PM Origin Ver. and Service Release (Select Help-->About Origin): 8.6 (32-bit) Srl b97Operating System: XP Home SP3This is more of a statistics question than an Origin question, but since I'm performing the analysis in Origin, this seemed like a reasonable place to ask about it.I'm performing a linear fit on a set of values with associated standard errors. The value in which I'm ultimately interested is the slope of the fit line. I've sorted out how to perform the fit using the error values as weights, but I'm currently very confused about the error in the slope value. Is the standard error in the fit parameters related to the error in the initial data? My statistics knowledge is REALLY lacking, which is likely the source of my confusion.The specific problem is that the standard error value Origin is giving me seems much too small. The dataset I'm fitting only has three points, and they have relatively large errors (I'm working on better data..) and the upper and lower confidence bounds for the slope are large (as expected) but the standard error is small.I'm getting a slope value of 8000 with 95% UCL of 12000 and 95% LCL of 4000. The standard error is 300. Is the standard error a poor estimate of the uncertainty in the slope value in this case? 3   L A T E S T    R E P L I E S    (Newest First) Sam Fang Posted - 07/13/2012 : 04:20:23 AM You can use fitted parameter's standard error to estimate the error of the fitted slope.And you can use the adjusted r-square value to measure the goodness of fit.SamOriginLab Technical Services coreyjkelly Posted - 07/13/2012 : 02:33:52 AM Thanks for the clarification! As I said, I'm a bit helpless when it comes to stats. If possible, could you suggest a measure of error in the slope which does reflect the error in the initial data set? Thanks! Sam Fang Posted - 07/12/2012 : 10:49:33 PM 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_IntervalsSamOriginLab Technical Services

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