# PharmPK Discussion - R2 and Standard Error

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• On 2 Sep 2002 at 09:11:33, "Bonate, Peter" (pbonate.-a-.ilexonc.com) sent the message
`If I may add my two cents into this topic on R2 and SE of the slope.They go hand in hand.  R2 is equal to 1 - SSE/SStotal.  The standarderror of the slope is equal to sqrt(MSE/Sxx) where Sxx=sum((x -mean(x))^2)).   After a little algebra, the standard error of theslope can be written as sqrt((-(R2-1)/(n-2)*SStotal)/Sxx).  Hence,for high R2, SE(slope) will be small.  For small R2, SE(slope) willbe large.  So implicit in the calculation of the standard error isthe use of R2.pete bonate`
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• On 4 Sep 2002 at 12:37:35, "J.H.Proost" (J.H.Proost.-a-.farm.rug.nl) sent the message
`Dear Martin Schumacher and Pete Bonate,Thank you for your contributions, which provide a more completepicture of the topic.Martin Schumacher explained the rather large confidence interval ofthe estimated variance. I completely agree. However, in general, weare not interested in the confidence interval of the variance, but inthe confidence interval of the estimated parameter. The fact thatthese two are related does not matter. By using the t-distribution inthe calculation of the confidence interval of the estimatedparameter, we take into account the uncertainty in the estimatedvariance. That is exactly what the t-distribution is for. Or am Iwrong here?Pete Bonate explained the relationship between R2 and the standarderror of the slope. I completely agree (please note that MSE =SSE/(n-2) ). It is clear that SE(slope) is dependent of R2. However,it is also dependent on SStotal, Sxx and n. So, knowledge on R2 doesnot tell the whole story about SE(slope). I still do not see a keyrole for R2, in contrast to SE(slope). To say it more pathetically:"I can live without R2, but not without SE(slope)".Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The NetherlandsEmail: j.h.proost.-at-.farm.rug.nl`
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