Appendix on Linear Regress in Excel

Appendix on Linear Regress in Excel - 1 Appendix on Linear...

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Unformatted text preview: 1 Appendix on Linear Regress in EXc¡l There are at least two ways to do regression fitting in EXc¡l, There's the manual way and the built-in automatic way. The reason not to be fully-reliant on the automatic way is that it's part of a "Data Analysis" add-in (that, confusingly, shows up under "Tools" on the menu in versions of EXc¡l prior to 2007, but is on the "Data" tab thereafter). Further, some Apple/Macintosh versions of EXc¡l lack the "Data Analysis" add-in completely. Let y I be the absorbances you measured and X I be the concentrations of the solutions. If a working curve is linear i.e. if Beer's Law holds, there's no interference, or the concentration of an interference is constant including in the blank, then y I  b  mX I   y I (10) where b = extrapolated blank when X I = 0, m = slope of the working curve, the change in absorbance per unit concentration,  y I = the measurement error in y I . The mean of  y I is presumed to be 0. We assume that the error in x i is negligible or else independent of concentration so that the contribution from errors in sample preparation can be lumped in with  y I . See Harris, Chapter 5, Section 1 (or analogous sections of Harvey), to see where the math comes from. It turns out that y I I  1 N   bN  m X I I  1 N  (11a) X I y I I  1 N   b X I I  1 N   m X I 2 I  1 N  (11b) where N is the number of independent data points. If you make replica measurements at a particular concentration, each measurement is independent, so if you make triplicate measurements on each of 5 solutions, N = 3*5 = 15. What happened to the errors,  y I ? They average to 0, as does the product X I  y I ....
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Appendix on Linear Regress in Excel - 1 Appendix on Linear...

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