Residual sum of squares

[mojo]

I validate the HPLC method for the linearity. I look at the correlation coefficient and y-axis intercpet. They are good. I also look at the residual sum of squares. How do I tell if they is good too? Is there a common acceptance criteria for the RSS? The method is for the assay. Please help.

[project44]

Hello,
The Residual Sum of Squares is the so-called the random error of your measurements. It describes the variance which can not be described by your least squares model. To ensure that the regression model you have selected is the best one (or the acceptable one) you should make two F-tests:
1) Check the ratio F=MS(regression)/MS(residual). The F value must be as large as possible (larger than the F(critical)), indicating that the total variation of your measurements can not be explained by the random variation (the MS(residual)), because the reason for this variation is the existance of a ''trend'' called (REGRESSION).
2) Check the ratio F=MS(Lack of fit)/MS(Pure error). For this check you need replicated measurements in each concentration level. If the regression model is the accepted one, then this ratio must be as small as possible (smaller than the F(critical)). This means that the lack of fit of your model is not significant and is comparable with the random errors (MSpure error).
SSresidual=SSpure error (if no lack of fit is present)
SSresidual=SSpure error + SSlack of fit (if lack of fit is present)
You should perform the 2) test first, and then the 1). If 2) is accepted then you can proceed to the 1) test. If not, then the model you have chosen (y=b0+b1X) is not the best one and you should remodel your measurements, possibly with a second degree regression model).