{"text_format":"1","workbook":"xlsx","n_sheets":12,"sheets":["Info","Experimental data","Output","Input","Plots","Test of calibration function","Linear","2nd degree","3rd degree","Conc Raw","Conc Rounded","Standard deviations"],"not_rendered":{"charts":29,"images":0,"macros":1,"external_links":0,"defined_names":483,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Info","index":0,"n_rows":30,"n_cols":16,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Calibration_Quant_8.15.xlsm",null,null,null,null,null,null,null,null,"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, PLEN, University of Copenhagen, 2017 - 2025"]
[]
[null,"Write any information you like in the white area",null,null,null,null,"Text in the white area can be edited anytime"]
[]
[null,"Created:",null,"25-05-20   14:37:34",null,null,null,null,null,null,null,null,null,null,null,"Output file: Filename after saving results"]
[null,"Input file:"]
[null,"Calibration file:",null,null,null,null,null,null,null,null,null,null,null,null,null,"If you want to save the output under a new name,"]
[null,"X-values:",null,null,null,null,null,null,null,null,null,null,null,null,null,"delete the filename in D10 and"]
[null,"Include custom samples:",null,null,null,null,null,null,null,null,null,null,null,null,null,"you can change the filename when saving"]
[null,"Output file:"]
[null,"Input multiplier:",null,null,null,null,null,null,null,null,null,null,null,null,null,"If Output file is created, it will be updated"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"with all results when the workbook is closed"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
[]
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[null,"Go to sheet \"Experimental data\" to start calibrations:"]

{"sheet":"Experimental data","index":1,"n_rows":183,"n_cols":87,"rows_kept":183,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Info!$A$1","v":"Calibration_Quant_8.15.xlsm"},null,null,null,null,null,null,null,null,{"$f":"Info!$J$1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, PLEN, University of Copenhagen, 2017 - 2025"}]
[]
[null,null,null,null,null,null,null,null,null,"Execution key:"]
[]
[null,null,null,"24-03-02   15:32:24",null,null,null,null,null,"Table 0","Weighted?"]
[null,null,null,null,null,null,null,null,null,null,"Degree?"]
[null,"Save copies of graphs to sheet Plots?",null,null,null,"Yes","Yes/No","    Yes = big file",null,null,"Subtract blank"]
[null,null,null,null,null,null,null,null,null,null,"IS factor"]
["0) Go to sheet \"Input\"  and enter parameters in Table 1, Table 5 and Table 6",null,null,null,null,null,null,null,null,null,"Multiplier (not used)"]
[null,"These parameters in sheet \"Input\" will be used for all analyts (until changed)"]
[null,null,null,null,null,null,null,null,null,"Table 1","n(DL)"]
[null,null,null,null,null,null,null,null,null,"Data for ","s(DL)"]
["1) Copy-paste or enter experimental data for all analyts in the tables:",null,null,null,null,null,null,null,null,"detection","n(Blank)"]
[null,null,null,null,null,null,null,null,null,"limits","Mean(Bl)"]
[null,"Table 1 Row 12 - 16:",null,"n(DL)","* No of measurements for DL; may be blank",null,null,null,null,null,"s(Blank)"]
[null,null,null,"s(DL)","* Standard deviation for DL; may be blank"]
[null,null,null,"n(Blank)","* No of measurements of blank samples; may be blank",null,null,null,null,null,null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75]
[null,null,null,"Mean(Bl)","* Mean of blank samples; may be blank",null,null,null,null,"Table 2","No"]
[null,null,null,"s(Blank)","* Standard deviation of blank samples; may be blank",null,null,null,null,"Analyte",1]
[null,null,null,null,null,null,null,null,null,"Calibration",2]
[null,"Table 2 Row 18:",null,null,"* Analyte names",null,null,null,null,"Conc. X",3]
[null,null,null,null,null,null,null,null,null,null,4]
[null,"Table 2 starting in cell L19:",null,null,"* Up to 30 rows with calibration concentrations X",null,null,null,null,null,5]
[null,null,null,null,"  Concentrations must be in ascending order",null,null,null,null,null,6]
[null,null,null,null,null,null,null,null,null,null,7]
[null,"Table 3 starting in cell L51:",null,null,"* Up to 30 rows with calibration responses Y",null,null,null,null,null,8]
[null,null,null,null,null,null,null,null,null,null,9]
[null,"Table 4 starting in cell J85:",null,null,"* Up to 100 rows with responses Yo for unknown samples",null,null,null,null,null,10]
[null,null,null,null,"* Sample names in column L",null,null,null,null,null,11]
[null,null,null,null,"* V/m = Vol(IS blank, ml)/mass(sample, g) in column J",null,null,null,null,null,12]
[null,null,null,null,"* V/m = Vol(IS sample, ml)/mass(sample, g) in column K",null,null,null,null,null,13]
[null,null,null,null,"For liquid samples replace mass with volume",null,null,null,null,null,14]
[null,null,null,null,"Column J&K must either both be blank or have values",null,null,null,null,null,15]
["2) Fill in execution keys in Row 3:",null,null,null,null,null,null,null,null,null,16]
[null,null,null,null,null,null,null,null,null,null,17]
[null,null,null,null,"0: Skip this analyte",null,null,null,null,null,18]
[null,null,null,null,"1: To be analyzed ",null,null,null,null,null,19]
[null,null,null,null,null,null,null,null,null,null,20]
[null,"After analysis key is:",null,null,"2: analysed normally",null,null,null,null,null,21]
[null,null,null,null,"3: calibration responses Y are blank cells or all equal (0)",null,null,null,null,null,22]
[null,null,null,null,"4: analyte was skipped",null,null,null,null,null,23]
[null,null,null,null,null,null,null,null,null,null,24]
[null,null,null,null,"To reanalyze change key to 1 and run again",null,null,null,null,null,25]
["3a)",null,null,null,null,null,null,null,null,null,26]
[null,"Automatic analysis of analytes one-by-one:",null,null,null,null,null,null,null,null,27]
[null,null,null,null,null,null,null,null,null,null,28]
[null,null,"Enter parameters in Table 0:",null,null,null,null,null,null,null,29]
[null,null,"· Weighted?",null,"Blank: the statistically best method is used",null,null,null,null,null,30]
[null,null,null,null,"0 = Not weighted; 1 = Weighted ",null,null,null,null,null,null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75]
[null,null,"· Degree?",null,"Blank:      The statistically best degree",null,null,null,null,"Table 2","No","Sample",{"$f":"M$18","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"BX$18","v":0},0,0,0,0,0,0,0,0,0,0,0]
[null,null,null,null,null,"up to degree 3",null,null,null,"Calibration",1]
[null,null,null,null,"1, 2 or 3: The statistically best degree",null,null,null,null,"Response Y",2]
[null,null,null,null,null,"up to degree 1, 2 or 3",null,null,null,null,3]
[null,null,"· Subtract blank",null,"0 = No; 1 = Yes",null,null,null,null,null,4]
[null,null,"· IS factor",null,"Conc. of IS stock solution for X = ratios",null,null,null,null,null,5]
[null,null,null,null,"V(cal)/V(IS,cal) for X = concentrations",null,null,null,null,null,6]
[null,null,"· Multiplier",null,"Not used",null,null,null,null,null,7]
[null,null,null,null,null,null,null,null,null,null,8]
[null,null,null,null,null,null,null,null,null,null,9]
[null,null,"OBS: Statistics may not always be ok, CHECK the results!",null,null,null,null,null,null,null,10]
[null,null,null,null,null,null,null,null,null,null,11]
[null,null,"Press the button \"Run next analyte\"",null,null,null,null,null,null,null,12]
[null,null,null,null,null,null,null,null,null,null,13]
[null,null,"You will see the results in the sheet Test of calibrafion function",null,null,null,null,null,null,null,14]
[null,null,null,null,null,null,null,null,null,null,15]
[null,null,"Examine the results and go to the sheet with the best",null,null,null,null,null,null,null,16]
[null,null,"calibration function, and either:",null,null,null,null,null,null,null,17]
[null,null,"· Press: \"Save Results and run next analyte\"",null,null,null,null,null,null,null,18]
[null,null,"· Press \"Save Results\" and do something else like",null,null,null,null,null,null,null,19]
[null,null,"   testing another degree or weightening",null,null,null,null,null,null,null,20]
[null,null,null,null,null,null,null,null,null,null,21]
["3b)",null,null,null,null,null,null,null,null,null,22]
[null,"Automatic analysis of all analytes:",null,null,null,null,null,null,null,null,23]
[null,null,"Enter parameters in Table 0:",null,null,null,null,null,null,null,24]
[null,null,null,null,null,null,null,null,null,null,25]
[null,null,"Press the button \"Run all analytes\"",null,null,null,null,null,null,null,26]
[null,null,null,null,null,null,null,null,null,null,27]
[null,null,"You will see all results in sheet \"Output\"",null,null,null,null,null,null,null,28]
[null,null,"· Only data for the last analyte will be seen in the other sheets.",null,null,null,null,null,null,null,29]
[null,null,null,null,null,null,null,null,null,null,30]
[null,"It is highly recommended to analyse analytes one by one 3a)",null,null,null,null,null,null,null,null,null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75]
[null,null,null,null,null,null,null,"Table 5",null,"V/m blank","V/m sample","Sample",{"$f":"M$18","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"BX$18","v":0},0,0,0,0,0,0,0,0,0,0,0]
[null,null,null,null,null,null,null,"Unknown","No"]
[null,null,null,null,null,null,null,"Response Yo",1]
[null,null,null,null,null,null,null,null,2]
[null,null,null,null,null,null,null,null,3]
[null,null,null,null,null,null,null,null,4]
[null,null,null,null,null,null,null,null,5]
[null,null,null,null,null,null,null,null,6]
[null,null,null,null,null,null,null,null,7]
[null,null,null,null,null,null,null,null,8]
[null,null,null,null,null,null,null,null,9]
[null,null,null,null,null,null,null,null,10]
[null,null,null,null,null,null,null,null,11]
[null,null,null,null,null,null,null,null,12]
[null,null,null,null,null,null,null,null,13]
[null,null,null,null,null,null,null,null,14]
[null,null,null,null,null,null,null,null,15]
[null,null,null,null,null,null,null,null,16]
[null,null,null,null,null,null,null,null,17]
[null,null,null,null,null,null,null,null,18]
[null,null,null,null,null,null,null,null,19]
[null,null,null,null,null,null,null,null,20]
[null,null,null,null,null,null,null,null,21]
[null,null,null,null,null,null,null,null,22]
[null,null,null,null,null,null,null,null,23]
[null,null,null,null,null,null,null,null,24]
[null,null,null,null,null,null,null,null,25]
[null,null,null,null,null,null,null,null,26]
[null,null,null,null,null,null,null,null,27]
[null,null,null,null,null,null,null,null,28]
[null,null,null,null,null,null,null,null,29]
[null,null,null,null,null,null,null,null,30]
[null,null,null,null,null,null,null,null,31]
[null,null,null,null,null,null,null,null,32]
[null,null,null,null,null,null,null,null,33]
[null,null,null,null,null,null,null,null,34]
[null,null,null,null,null,null,null,null,35]
[null,null,null,null,null,null,null,null,36]
[null,null,null,null,null,null,null,null,37]
[null,null,null,null,null,null,null,null,38]
[null,null,null,null,null,null,null,null,39]
[null,null,null,null,null,null,null,null,40]
[null,null,null,null,null,null,null,null,41]
[null,null,null,null,null,null,null,null,42]
[null,null,null,null,null,null,null,null,43]
[null,null,null,null,null,null,null,null,44]
[null,null,null,null,null,null,null,null,45]
[null,null,null,null,null,null,null,null,46]
[null,null,null,null,null,null,null,null,47]
[null,null,null,null,null,null,null,null,48]
[null,null,null,null,null,null,null,null,49]
[null,null,null,null,null,null,null,null,50]
[null,null,null,null,null,null,null,null,51]
[null,null,null,null,null,null,null,null,52]
[null,null,null,null,null,null,null,null,53]
[null,null,null,null,null,null,null,null,54]
[null,null,null,null,null,null,null,null,55]
[null,null,null,null,null,null,null,null,56]
[null,null,null,null,null,null,null,null,57]
[null,null,null,null,null,null,null,null,58]
[null,null,null,null,null,null,null,null,59]
[null,null,null,null,null,null,null,null,60]
[null,null,null,null,null,null,null,null,61]
[null,null,null,null,null,null,null,null,62]
[null,null,null,null,null,null,null,null,63]
[null,null,null,null,null,null,null,null,64]
[null,null,null,null,null,null,null,null,65]
[null,null,null,null,null,null,null,null,66]
[null,null,null,null,null,null,null,null,67]
[null,null,null,null,null,null,null,null,68]
[null,null,null,null,null,null,null,null,69]
[null,null,null,null,null,null,null,null,70]
[null,null,null,null,null,null,null,null,71]
[null,null,null,null,null,null,null,null,72]
[null,null,null,null,null,null,null,null,73]
[null,null,null,null,null,null,null,null,74]
[null,null,null,null,null,null,null,null,75]
[null,null,null,null,null,null,null,null,76]
[null,null,null,null,null,null,null,null,77]
[null,null,null,null,null,null,null,null,78]
[null,null,null,null,null,null,null,null,79]
[null,null,null,null,null,null,null,null,80]
[null,null,null,null,null,null,null,null,81]
[null,null,null,null,null,null,null,null,82]
[null,null,null,null,null,null,null,null,83]
[null,null,null,null,null,null,null,null,84]
[null,null,null,null,null,null,null,null,85]
[null,null,null,null,null,null,null,null,86]
[null,null,null,null,null,null,null,null,87]
[null,null,null,null,null,null,null,null,88]
[null,null,null,null,null,null,null,null,89]
[null,null,null,null,null,null,null,null,90]
[null,null,null,null,null,null,null,null,91]
[null,null,null,null,null,null,null,null,92]
[null,null,null,null,null,null,null,null,93]
[null,null,null,null,null,null,null,null,94]
[null,null,null,null,null,null,null,null,95]
[null,null,null,null,null,null,null,null,96]
[null,null,null,null,null,null,null,null,97]
[null,null,null,null,null,null,null,null,98]
[null,null,null,null,null,null,null,null,99]
[null,null,null,null,null,null,null,null,100]

{"sheet":"Output","index":2,"n_rows":54,"n_cols":85,"rows_kept":54,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Info!$A$1","v":"Calibration_Quant_8.15.xlsm"},null,null,null,null,"Output of results",null,null,null,{"$f":"Info!$J$1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, PLEN, University of Copenhagen, 2017 - 2025"}]
[]
["For all runs:",null,"Row 3 to 12:"]
[null,null,"Can be used for comments or"]
["a(DL) %",1,"calculations"]
["b(LOD) %",5]
["s(LOQ)",10,"Color codes for results:"]
["CI(LOQ)%",20,"Not detected"]
["a(LOQ) %",5,"Below blank limit"]
["a(Blank) %",10]
["m",1,"Below Low limit: LOQ or Min(X) "]
["r",1,"Abowe highest calibration conc."]
["a(CI) %",95,"na: Not applicable",null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,68,70,71,72,73,74,75,76,77,78,79,80]
["Headings",null,null,"No"]
[null,null,null,"Analyte"]
[null,null,null,"IS factor"]
[null,null,null,"Not used"]
[null,null,null,"Not used"]
[null,null,null,"Subtract blank"]
[null,null,null,"Blank stdev"]
[null,null,null,"Multiplier"]
[null,null,null,"Run comment"]
[null,null,null,"Run comment"]
[null,null,null,"Auto keys (W-degree)?"]
[]
["Calibration",null,null,"Type"]
[null,null,null,"a0"]
[null,null,null,"a1"]
[null,null,null,"a2"]
[null,null,null,"a3"]
[]
["Statistics",null,null,"R2"]
[null,null,null,"Force zero OK?"]
[null,null,null,"s(y/x)"]
[null,null,null,"P(a0)"]
[null,null,null,"P(a1)"]
[null,null,null,"P(a2)"]
[null,null,null,"P(a3)"]
[]
["Weights",null,null,"s0"]
[null,null,null,"s½"]
[null,null,null,"s1"]
[null,null,null,"n (calibration)"]
[]
["Detection Limits",null,null,"DL"]
[null,null,null,"LOD"]
[null,null,null,"(DL from calibration)"]
[null,null,null,"(LOD from calibration)"]
[null,null,null,"LOQ-s"]
[null,null,null,"LOQ-ci"]
[null,null,null,"Blank limit"]
[null,null,null,"Low limit"]
[]
["Samples:"]

{"sheet":"Input","index":3,"n_rows":62,"n_cols":30,"rows_kept":62,"cut":false,"hidden":false,"merged":[[3,29,10,36]]}
[{"$f":"Info!$A$1","v":"Calibration_Quant_8.15.xlsm"},null,null,"Input and estimation of weights",null,null,null,null,null,{"$f":"'Experimental data'!J1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, PLEN, University of Copenhagen, 2017 - 2025"},null,null,null,null,null,null,null,null,"This sheet is not protected, so take care only to change the white cells!",null,null,null,null,null,null,null,null,null,null,"Most formulas are standard mathematics. Regression calculated by matrix maths."]
["0) Start by saving the sheet under a new name: File->Save As",null,null,null,null,null,-4105]
["1a) Enter statistical parameters for all analytes here",null,null,null,null,null,"1b) User input for output Table 1&6",null,null,null,null,null,null,null,null,null,null,null,"Input X,Y and Yo must be in ascending order and without blank lines",null,null,null,null,null,null,null,null,null,null,"Detection limits are calculated according to:"]
["2) Enter values for the present analyte here (Calibration X,Y and unknown Yo's):",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Please start with a data set containing the max number of unknown samples and calibration points",null,null,null,null,null,null,null,null,null,null,"W. Funk, V. Dammann and G. Donnevert, Quality Assurance in Analytical Chemistry: Applications in Environmental, Food, and Materials Analysis, Biotechnology, and Medical Engineering, Second Edition. Wiley-VCH, Weinheim, 2007. See page 29-35 for detection limits. The detection limit DL is called the Decision limit XDL  and the limit of detection LOD is called the Minimum Detectable Value XMDV in Funk et al.."]
["      a) Enter X, Ymean and s(Y)  in column X, Y1  and s(Y)obs.     B23 = no of replicates"]
["or: b) Enter X and Y1-Y4 in column Y1-Y4. Leave s(Y)obs empty. B23 = 1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"A short explanation to Table 5:"]
["3) Enter manual values for s(Y) as function of X in Table 5, see explanation in column S and T",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"In the white cells under manual enter values for s(Y) that will be used"]
["4) Press the button Copy X, Y and unknowns… to copy all values to the the other sheets",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"for weighted regression."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The input is the standard derviation at the lowest concentration in the"]
["Table 1: All analytes",null,null,"Table 5","See column S for an explanation",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"calibration for an uncertainty that has:"]
["a(DL)%",1,null,"s(Y) vs X","C(i)","Estimated","Manual",null,null,null,null,null,null,null,null,null,null,null,null,null,"s0:  Constant contribution to s(Y)"]
["b(LOD)%",5,null,"s0",{"$f":"G12","v":1},{"$f":"Q38","v":0},1,null,null,null,null,null,null,null,null,null,null,null,null,null,"s½: Contribution proportional to Sqrt(X)"]
["s(LOQ)%",10,null,"s½",{"$f":"IF(Q33=0,G13,G13/SQRT(Q33))","v":1.0534653429656149},{"$f":"Q39*SQRT(Q33)","v":0},1,null,null,null,null,null,null,null,null,null,null,null,null,null,"s1:  Contribution proportional to X"]
["CI(LOQ)%",20,null,"s1",{"$f":"IF(Q33=0,G14,G14/Q33)","v":0},{"$f":"Q40*Q33","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,"C(i):","The function that will be used for weighted regression (calculated from Manual input)"]
["a(LOQ)%",5,null,{"$f":"IF(E12>0,\"\",IF(E12=0,\"s0 should be >0\",\"s0 must be 0 or positive\"))","v":""},null,null,null,"Analyte no:",1,null,null,null,null,null,null,null,null,null,null,"Estimated:","The function fitted to s(Y)obs if repeat measurements are available"]
["a(Blank)%",10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Manual:","The manual input for s(Y)"]
["m",1]
["r",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"OBS:","The absolute values are unimportant.The weights gets normalized to a sum of N anyway"]
["CI %",95,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The plot shows the observed, the fitted and the manual function for s(Y)"]
["Low limit",1,"0: None; 1: LOQ-s; 2:LOQ-CI; 3: Min(X) "]
["Unc. Key",1,"1: s; 2: RSD%, 3:CI",null,null,null,null,"Table 6",null,null,null,"Table 2 B",null,null,null,null,null,null,"If no repeat measurements are available:"]
["DL Limit",1,"0: None; 1: from s; 2: from calibration",null,null,null,null,"Counters for output",null,null,null,"Subtract blank ?",null,1,"0 = No; 1 = Yes",null,null,null,null,"For uncertainty proportional to Sqrt(X) use ",null,null,null,null,"(s0, s½, s1) = (a, 1, 0)"]
["Digits",0,"In adddition to significant digits",null,null,null,null,"Run #",1," Start with 1",null,"IS factor",null,50,null,null,null,null,null,"For uncertainty proportional to X use ",null,null,null,null,"(s0, s½, s1) = (a, 0, 1)"]
["Table 2 A",null,null,null,null,null,null,"Nmax",{"$f":"MAX(COUNTIF('Experimental data'!L16:L45,\"*\"),COUNT(A33:A62))","v":20},null,null,"Auto?","Auto/ 2",1,null,null,null,null,null,"For uncertainty proportional to Sqrt(X) and X use",null,null,null,null,"(s0, s½, s1) = (a, b, c)"]
["Analyte","Naphthalene","Name of analyte",null,null,null,null,"Smax",{"$f":"COUNT(N33:N132)","v":19},null,null,null,null,null,null,null,null,null,null,"A constant uncertainty  a of zero is unrealistic  ",null,null,null,null,"a must be positive"]
["n(DL)",7,"Data for detetion limits from repeat measurements",null,null,null,null,"Plots?",{"$f":"'Experimental data'!F7","v":"Yes"},null,null,null,null,null,null,null,null,null,null,"Default for approximately exponentally increasing conc. ",null,null,null,null,"(s0, s½, s1) = (1, 1, 0)"]
["s(DL)",7.1277083571266633E-4,"Manual input"]
["n(Blank)",3]
["Mean(Bl)",4.0211616435671282E-2]
["s(Blank)",1.9145155541080702E-2,null,null,null,null,null,null,null,null,null,"V/m is V/m for X = ratios and V*C(IS)/m for X = concentrations"]
["Table 3",null,null,null,null,null,null,null,null,null,"Table 4"]
["X","Y1","Y2","Y3","Y4","s(Y)obs","X","Y","s(Y)","s(Y) man","Name","V/m blank","V/m sample","Yo",null,null,"X","Y",null,"s(Y) obs","Q","sq(X)","X","s(Y) est"]
[0.9010720000000001,1.1662007826355481E-2,null,null,null,null,{"$f":"IF(A33<>\"\",A33,\"\")","v":0.9010720000000001},{"$f":"IF(A33<>\"\",AVERAGE(B33:E33),\"\")","v":1.1662007826355481E-2},{"$f":"IF(A33<>\"\",IF(COUNT(B33:E33)=1,F33,STDEV(B33:E33)),\"\")","v":0},{"$f":"IF(A33<>\"\",SQRT($E$12^2+$E$13^2*G33+($E$14*G33)^2),\"\")","v":1.4142135623730951},"OYSTERS 1",2.2727272727272728E-2,2.2727272727272728E-2,3.3731744417127604E-2,null,"Min",{"$f":"MIN(G33:G62)","v":0.9010720000000001},{"$f":"MIN(H33:H62)","v":9.6324618884912391E-3},null,{"$f":"IF(A33<>\"\",I33,0)","v":0},{"$f":"IF(A33<>\"\",1,0)","v":1},{"$f":"IF(A33<>\"\",SQRT(A33),0)","v":0.94924812351671262},{"$f":"IF(A33<>\"\",A33,0)","v":0.9010720000000001},{"$f":"IF(T33<>\"\",$Q$38+V33*$Q$39+W33*$Q$40,\"\")","v":0}]
[0.9010720000000001,1.0161285068880616E-2,null,null,null,null,0.9010720000000001,1.0161285068880616E-2,0,1.4142135623730951,"OYSTERS 2",2.6595744680851068E-2,2.6595744680851068E-2,3.325294251057731E-2,null,"Max ",{"$f":"MAX(G33:G62)","v":901.07200000000012},{"$f":"MAX(H33:H62)","v":8.6259330638741201},null,0,1,0.94924812351671262,0.9010720000000001,{"$f":"IF(A34<>\"\",$Q$38+V34*$Q$39+W34*$Q$40,\"\")","v":0}]
[0.9010720000000001,1.0237308080130344E-2,null,null,null,null,0.9010720000000001,1.0237308080130344E-2,0,1.4142135623730951,"OYSTERS 3",3.3003300330033007E-2,3.3003300330033007E-2,2.7161728105650762E-2,null,null,null,null,null,0,1,0.94924812351671262,0.9010720000000001,0]
[0.9010720000000001,9.6324618884912391E-3,null,null,null,null,0.9010720000000001,9.6324618884912391E-3,0,1.4142135623730951,"OYSTERS #12",4.5454545454545456E-2,4.5454545454545456E-2,3.0410018148445697E-2,null,"Regression s(Y) obs ",null,null,null,0,1,0.94924812351671262,0.9010720000000001,0]
[0.9010720000000001,9.7391542398750364E-3,null,null,null,null,0.9010720000000001,9.7391542398750364E-3,0,1.4142135623730951,"OYSTERS 14",2.4449877750611249E-2,2.4449877750611249E-2,3.3875899851998258E-2,null,"Term","Coeff",null,null,0,1,0.94924812351671262,0.9010720000000001,0]
[0.9010720000000001,9.8205394631890389E-3,null,null,null,null,0.9010720000000001,9.8205394631890389E-3,0,1.4142135623730951,"OYSTERS #32",2.7472527472527472E-2,2.7472527472527472E-2,3.6428271049170492E-2,null,"s0",{"$f":"MMULT(P43:R45,MMULT(TRANSPOSE(U33:W62),T33:W62))","v":0},null,null,0,1,0.94924812351671262,0.9010720000000001,0]
[0.9010720000000001,1.072667925395529E-2,null,null,null,null,0.9010720000000001,1.072667925395529E-2,0,1.4142135623730951,"OYSTERS #9",2.557544757033248E-2,2.557544757033248E-2,0.13914067163242283,null,"s½",0,null,null,0,1,0.94924812351671262,0.9010720000000001,0]
[2.2526800000000002,2.2504646776853415E-2,null,null,null,null,2.2526800000000002,2.2504646776853415E-2,0,1.8708286933869709,"OYSTERS #25",2.1141649048625793E-2,2.1141649048625793E-2,5.0705578532177019E-2,null,"s1",0,null,null,0,1,1.5008930674768273,2.2526800000000002,0]
[4.5053600000000005,4.2061733561014863E-2,null,null,null,null,4.5053600000000005,4.2061733561014863E-2,0,2.4494897427831783,"OYSTERS #37",2.6525198938992044E-2,2.6525198938992044E-2,6.7463745014414142E-2,null,null,null,null,null,0,1,2.122583331697486,4.5053600000000005,0]
[13.516080000000002,0.12563395943218281,null,null,null,null,13.516080000000002,0.12563395943218281,0,4,"OYSTERS NIST",0.1,0.1,2.9610590727573192E-2,null,"Covar matrix",null,null,null,0,1,3.6764221737988692,13.516080000000002,0]
[27.032160000000005,0.24812367017405088,null,null,null,null,27.032160000000005,0.24812367017405088,0,5.5677643628300224,"DIESEL WATER1",1E-4,1E-4,4.863988111618271,null,{"$f":"MINVERSE(MMULT(TRANSPOSE(U33:W62),U33:W62))","v":0.14497191568867329},-2.5223227085154822E-2,7.4489664501143618E-4,null,0,1,5.1992460991955367,27.032160000000005,0]
[54.064320000000009,0.4953509199560755,null,null,null,null,54.064320000000009,0.4953509199560755,0,7.8102496759066549,"DIESEL WATER2",1E-4,1E-4,4.9365373857585357,null,-2.5223227085154849E-2,7.7498372323292347E-3,-2.6547148490940758E-4,null,0,1,7.3528443475977383,54.064320000000009,0]
[54.064320000000009,0.49538120241604172,null,null,null,null,54.064320000000009,0.49538120241604172,0,7.8102496759066549,"DIESEL FILTER1",1E-4,1E-4,5.073637372908546E-2,null,7.4489664501143737E-4,-2.6547148490940769E-4,1.0195704454095561E-5,null,0,1,7.3528443475977383,54.064320000000009,0]
[54.064320000000009,0.49446121665617948,null,null,null,null,54.064320000000009,0.49446121665617948,0,7.8102496759066549,"DIESEL FILTER2",1E-4,1E-4,4.7124420493675781E-2,null,null,null,null,null,0,1,7.3528443475977383,54.064320000000009,0]
[54.064320000000009,0.49776557507615971,null,null,null,null,54.064320000000009,0.49776557507615971,0,7.8102496759066549,"DIESEL WATER LAB BLANK",1E-4,1E-4,1.5827593437605692E-2,null,null,null,null,null,0,1,7.3528443475977383,54.064320000000009,0]
[90.107200000000006,0.81604958595898047,null,null,null,null,90.107200000000006,0.81604958595898047,0,10.049875621120892,"Diesel ca 1mg/ml",20,20,null,null,null,null,null,null,0,1,9.4924812351671264,90.107200000000006,0]
[180.21440000000001,1.7050031547310485,null,null,null,null,180.21440000000001,1.7050031547310485,0,14.177446878757825,"Diesel ca 1mg/ml +IS+RS",20,20,2.7417624493379877,null,null,null,null,null,0,1,13.424395703345459,180.21440000000001,0]
[270.32160000000005,2.57065243864839,null,null,null,null,270.32160000000005,2.57065243864839,0,17.349351572897476,"OYSTERS PLE BLANK",0.02,2.2727272727272728E-2,2.7962821273538045E-2,null,null,null,null,null,0,1,16.441459789203634,270.32160000000005,0]
[450.53600000000006,4.3155524207614553,null,null,null,null,450.53600000000006,4.3155524207614553,0,22.383029285599392,"DIESEL FILTER BLANK",1E-4,2.6595744680851068E-2,3.0398252458123422E-2,null,null,null,null,null,0,1,21.22583331697486,450.53600000000006,0]
[901.07200000000012,8.6259330638741201,null,null,null,null,901.07200000000012,8.6259330638741201,0,31.63858403911275,"DIESEL FILTER PLE BLANK",1E-4,3.3003300330033007E-2,6.2273775575352373E-2,null,null,null,null,null,0,1,30.017861349536549,901.07200000000012,0]
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[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
[null,null,null,null,null,null,"","","","",null,null,null,null,null,null,null,null,null,0,0,0,0,""]
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{"sheet":"Plots","index":4,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Test of calibration function","index":5,"n_rows":125,"n_cols":58,"rows_kept":125,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Info!$A$1","v":"Calibration_Quant_8.15.xlsm"},null,null,"Test of calibration functions",null,null,null,null,null,{"$f":"'Experimental data'!J1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, PLEN, University of Copenhagen, 2017 - 2025"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"This sheet is not protected, so take care only to change the white cells!",null,null,null,null,null,null,null,null,null,null,null,null,"Sum",{"$f":"SUM(AB19:AB48)","v":4.1339061699852486},null,"Statistical param",null,null,"SSreg",null,null,1,"Covariance matrix",null,2,"Covariance matrix",null,null,3,"Covariance matrix"]
["1) Look at the \"Statistics\" cell F10:K19, to see which polynomial degree is recommended.",null,null,null,null,null,null,null,null,null,null,null,null,null,"You may need to change the formatting of numbers in the tables depending on the magnitude of X and Y",null,null,null,null,null,null,null,null,null,null,null,null,"Norm",{"$f":"AF3/AC2","v":4.8380391759282162},null,"N",{"$f":"COUNT(X)*Input!B18","v":20},1,{"$f":"SUM(Q*(MMULT(X_1,AC12:AC13)-$AF$6)^2)","v":83.205122508434442},null,null,null,{"$f":"MINVERSE(MMULT(TRANSPOSE(X_1),X_1))","v":6.2878425784747449E-2},-1.1912763675928224E-4,null,{"$f":"MINVERSE(MMULT(TRANSPOSE(X_2),X_2))","v":7.7410425506269337E-2},-5.1350533553694592E-4,4.9250170641268228E-7,null,{"$f":"MINVERSE(MMULT(TRANSPOSE(X_3),X_3))","v":9.4950402614330937E-2},-1.5101492512850836E-3,4.5405940549503998E-6,-3.312385082230969E-9]
["2) Look at the \"Accuracy (Error %)\" in cell L10:M19 to see, whether or not weighted regression is better or worse.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Xmax",{"$f":"MAX(X)","v":901.07200000000012},2,{"$f":"SUM(Q*(MMULT(X_2,AE12:AE14)-$AF$6)^2)","v":83.205724468011226},null,null,null,-1.1912763675928221E-4,1.1019509742144923E-6,null,-5.135053355369482E-4,1.180479795148362E-5,-1.3365792275061089E-8,null,-1.5101492512851161E-3,6.8435378976662733E-5,-2.4338357306809037E-7,1.8821395367177193E-10]
["3) IMPORTANT - look at the plots of the calibration functions and the predicted error in X below ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"weights",null,null,"Xmin",{"$f":"MIN(X)","v":0.9010720000000001},3,{"$f":"SUM(Q*(MMULT(X_3,AG12:AG15)-$AF$6)^2)","v":83.207762296157426}]
["    OBS: Look careful at the function between datapoints - too high an order may give wrong results here even when the  statistics is ok",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"w0",{"$f":"B22^2/$AC$3","v":0.20669530849926243},null,"Ymean",{"$f":"SUM(Y)/$AF$3","v":1.0263226511921715},4,{"$f":"SUM(Q*(MMULT(X_4,AI12:AI16)-$AF$6)^2)","v":83.208224853605856},null,null,"W 1","Covariance matrix",null,"W 2","Covariance matrix",null,null,"W 3","Covariance matrix"]
["4) Enter 1 or 0 in cell C26 to choose weighted or unweighted regression.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"w1",{"$f":"B23^2/$AC$3","v":0.22938822702210526},null,"Xmean",{"$f":"SUM(X)/$AF$3","v":108.10611320000002},"1W",{"$f":"SUM(W*(MMULT(X_1,AD12:AD13)-$AF$8)^2)","v":0.82058731383241179},null,null,null,{"$f":"MINVERSE(MMULT(MMULT(TRANSPOSE(X_1),W),X_1))","v":5.1310837851629224E-2},-3.7903566425387186E-4,null,{"$f":"MINVERSE(MMULT(MMULT(TRANSPOSE(X_2),W),X_2))","v":5.3222277510912075E-2},-1.116288456100698E-3,1.3632795179326655E-6,null,{"$f":"MINVERSE(MMULT(MMULT(TRANSPOSE(X_3),W),X_3))","v":5.5691892649316947E-2},-2.3614620860959532E-3,9.2622967448321034E-6,-7.4956541165939747E-9]
["6) Go to the sheet for the best calibration function (Linear, 2nd degree or 3rd degree) - 4th degree is not included",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"w2",{"$f":"B24^2/$AC$3","v":0},null,"YmeanW",{"$f":"SUM(W*Y)/$AF$3","v":3.3897094703631926E-2},"2W",{"$f":"SUM(W*(MMULT(X_2,AF12:AF14)-$AF$8)^2)","v":0.82071582834005707},null,null,null,-3.7903566425387028E-4,1.0960015733281521E-4,null,-1.1162884561007167E-3,3.9396261494231374E-4,-5.2582440977527299E-7,null,-2.361462086095778E-3,1.0217759712523597E-3,-4.5084886722594459E-6,3.7792896149728467E-9]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"XmeanW",{"$f":"SUM(W*X)/$AF$3","v":3.4583496363319894},"3W",{"$f":"SUM(W*(MMULT(X_3,AH12:AH15)-$AF$8)^2)","v":0.82081536566575797}]
["Calibration curve",null,null,null,null,"Polynomial fit",null,null,"Accuracy (Error %)",null,"Through",null,null,"Y = a0 + a1X + a2X^2 + a3X^3 + a4X^4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SStotal",{"$f":"SUM(Q*(Y-$AF$6)^2)","v":83.20858250133432}]
[null,null,"Poly","Degree","R2","P","Degree Ok?",null,"Mean Abs","Max","zero OK?","s(y/x)","a0","a1","a2","a3","a4","0 = sign.",null,null,null,null,null,null,null,null,null,null,null,null,"SStotalW ",{"$f":"SUM(W*(Y-$AF$8)^2)","v":0.82084956502241457}]
["Unweighted",null,"Linear",1,{"$f":"AH3/AF$10","v":0.99995841783628725},{"$f":"TDIST(SQRT((E12)*($AF$3-D12-1)/(1-E12)),$AF$3-D12-1,2)","v":6.8936132497259168E-41},{"$f":"IF(R12=0,IF(R13=0,\"A better fit is possible\",\"Ok\"),\"No correlation\")","v":"Ok"},null,{"$f":"F113","v":46.739129792464041},{"$f":"F114","v":137.55875499648616},{"$f":"IF(AN13>0.05,\"Yes\",\"No\")","v":"No"},{"$f":"SQRT(($AF$10-AH3)/($AF$3-2))","v":1.386440867007899E-2},{"$f":"AC12","v":-8.8348224009493492E-3},{"$f":"AC13","v":9.5753833243273096E-3},null,null,null,{"$f":"IF(F12<0.05,0,1)","v":0},null,null,null,null,null,null,null,null,null,"a0",{"$f":"MMULT(MINVERSE(MMULT(TRANSPOSE(X_1),X_1)),MMULT(TRANSPOSE(X_1),Y))","v":-8.8348224009493492E-3},{"$f":"MMULT(MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(X_1),W),X_1)),MMULT(TRANSPOSE(X_1),W)),Y)","v":1.0998858050337706E-3},{"$f":"MMULT(MINVERSE(MMULT(TRANSPOSE(X_2),X_2)),MMULT(TRANSPOSE(X_2),Y))","v":-5.8771752940458555E-3},{"$f":"MMULT(MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(X_2),W),X_2)),MMULT(TRANSPOSE(X_2),W)),Y)","v":1.5955144227566319E-3},{"$f":"MMULT(MINVERSE(MMULT(TRANSPOSE(X_3),X_3)),MMULT(TRANSPOSE(X_3),Y))","v":1.0140812796777254E-4},{"$f":"MMULT(MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(X_3),W),X_3)),MMULT(TRANSPOSE(X_3),W)),Y)","v":2.0913156798894588E-3},{"$f":"MMULT(MINVERSE(MMULT(TRANSPOSE(X_4),X_4)),MMULT(TRANSPOSE(X_4),Y))","v":2.7057943637487369E-3},null,null,null,"s Intercept","P Intercept",null,null,"s Intercept","P Intercept",null,null,"s Intercept","P Intercept"]
[null,null,"2nd",2,{"$f":"AH4/AF$10","v":0.99996565218109501},{"$f":"TDIST(SQRT((E13-E12)*($AF$3-D13-1)/(1-E13)),$AF$3-D13-1,2)","v":7.5618004292213589E-2},{"$f":"IF(R13>0,\"Too high\",IF(SUM(R12:R12)>0,\"OK??\",IF(R14=0,\"A better fit is possible\",\"Ok\")))","v":"Too high"},null,{"$f":"H113","v":34.233640396393312},{"$f":"H114","v":104.99501484366283},{"$f":"IF(AR13>0.05,\"Yes\",\"No\")","v":"Yes"},{"$f":"SQRT(($AF$10-AH4)/($AF$3-3))","v":1.2966094525368446E-2},{"$f":"AE12","v":-5.8771752940458555E-3},{"$f":"AE13","v":9.4951170098371979E-3},{"$f":"AE14","v":1.002371507728445E-7},null,null,1,null,null,null,null,null,null,null,null,null,"a1",9.5753833243273096E-3,9.4834855776420382E-3,9.4951170098371979E-3,9.292318893221024E-3,9.1554062591194807E-3,9.0423371688018589E-3,8.8813333039752251E-3,null,null,1,{"$f":"SQRT(AL3)*$L12","v":3.4765796311468124E-3},{"$f":"TDIST(ABS($M12/AM13),$AF$3-2,2)","v":2.0471116274201673E-2},null,2,{"$f":"SQRT(AO3)*$L13","v":3.6075213557866023E-3},{"$f":"TDIST(ABS($M13/AQ13),$AF$3-3,2)","v":0.12167073771423136},null,3,{"$f":"SQRT(AS3)*$L14","v":2.206224316739701E-3},{"$f":"TDIST(ABS($M14/AU13),$AF$3-4,2)","v":0.96390730979967887}]
[null,null,"3rd",3,{"$f":"AH5/AF$10","v":0.99999014278152276},{"$f":"TDIST(SQRT((E14-E13)*($AF$3-D14-1)/(1-E14)),$AF$3-D14-1,2)","v":1.0474157561761137E-5},{"$f":"IF(R14>0,\"Too high\",IF(SUM(R12:R13)>0,\"Ok??\",\"Ok\"))","v":"Ok??"},null,{"$f":"J113","v":9.094931460817989},{"$f":"J114","v":40.1076836376944},{"$f":"IF(AV13>0.05,\"Yes\",\"No\")","v":"Yes"},{"$f":"SQRT(($AF$10-AH5)/($AF$3-4))","v":7.1598061116088197E-3},{"$f":"AG12","v":1.0140812796777254E-4},{"$f":"AG13","v":9.1554062591194807E-3},{"$f":"AG14","v":1.4800484042848047E-6},{"$f":"AG15","v":-1.1290419829695323E-9},null,0,null,null,null,null,null,null,null,null,null,"a2",null,null,1.002371507728445E-7,3.5349289723193715E-7,1.4800484042848047E-6,1.9393038235379949E-6,4.0865078009821865E-6,null,null,"W 1",{"$f":"SQRT(AL7)*$L16","v":8.6462349823587554E-4},{"$f":"TDIST(ABS($M16/AM14),$AF$3-2,2)","v":0.21952771590704198},null,"W 2",{"$f":"SQRT(AO7)*$L17","v":6.4706444909568429E-4},{"$f":"TDIST(ABS($M17/AQ14),$AF$3-3,2)","v":2.4609632303770567E-2},null,"W 3",{"$f":"SQRT(AS7)*L18","v":3.4502055188743704E-4},{"$f":"TDIST(ABS($M18/AU14),$AF$3-4,2)","v":1.6496234215527082E-5}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a3",null,null,null,null,-1.1290419829695323E-9,-1.5048315323872479E-9,-7.6505091292037447E-9]
["Weigted",null,"Linear",1,{"$f":"AH7/AF$11","v":0.99968051248221634},{"$f":"TDIST(SQRT((E16)*($AF$3-D16-1)/(1-E16)),$AF$3-D16-1,2)","v":6.4331330912626952E-33},{"$f":"IF(R16=0,IF(R17=0,\"A better fit is possible\",\"Ok\"),\"No correlation\")","v":"A better fit is possible"},null,{"$f":"G113","v":4.2257895543762585},{"$f":"G114","v":23.601487626892911},{"$f":"IF(AN14>0.05,\"Yes\",\"No\")","v":"Yes"},{"$f":"SQRT(($AF$11-AH7)/($AF$3-2))","v":3.8170028236445062E-3},{"$f":"AD12","v":1.0998858050337706E-3},{"$f":"AD13","v":9.4834855776420382E-3},null,null,null,0,null,null,null,null,null,null,null,null,null,"a4",null,null,null,null,null,null,4.3986473428842064E-12]
[null,null,"2nd",2,{"$f":"AH8/AF$11","v":0.99983707528388122},{"$f":"TDIST(SQRT((E17-E16)*($AF$3-D17-1)/(1-E17)),$AF$3-D17-1,2)","v":8.4693949045139814E-4},{"$f":"IF(R17>0,\"Too high\",IF(SUM(R16:R16)>0,\"Ok??\",IF(R18=0,\"A better fit is possible\",\"Ok\")))","v":"A better fit is possible"},null,{"$f":"I113","v":3.2179726423031467},{"$f":"I114","v":20.220138221860953},{"$f":"IF(AR14>0.05,\"Yes\",\"No\")","v":"No"},{"$f":"SQRT(($AF$11-AH8)/($AF$3-3))","v":2.8047929813246808E-3},{"$f":"AF12","v":1.5955144227566319E-3},{"$f":"AF13","v":9.292318893221024E-3},{"$f":"AF14","v":3.5349289723193715E-7},null,null,0]
[null,null,"3rd",3,{"$f":"AH9/AF$11","v":0.99995833663302769},{"$f":"TDIST(SQRT((E18-E17)*($AF$3-D18-1)/(1-E18)),$AF$3-D18-1,2)","v":4.086998702438208E-6},{"$f":"IF(R18>0,\"Too high\",IF(SUM(R16:R17)>0,\"Ok??\",\"Ok\"))","v":"Ok"},null,{"$f":"K113","v":2.5544498509376345},{"$f":"K114","v":17.437514687138687},{"$f":"IF(AV14>0.05,\"Yes\",\"No\")","v":"No"},{"$f":"SQRT(($AF$11-AH9)/($AF$3-4))","v":1.4620054004817679E-3},{"$f":"AH12","v":2.0913156798894588E-3},{"$f":"AH13","v":9.0423371688018589E-3},{"$f":"AH14","v":1.9393038235379949E-6},{"$f":"AH15","v":-1.5048315323872479E-9},null,0,null,null,null,null,null,null,null,null,null,"NN weights","Weight diagonal matrix"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(A30<>\"\",1/($B$22^2+A30*$B$23^2+(A30*$B$24)^2),\"\")","v":0.5},0,{"$f":"IF($A30<>\"\",$C30,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[null,"C(i)","Used",null,"Recommended:",null,"2nd degree","Weighted","Recommendation is limited to the chosen max degree",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,0,0,{"$f":"IF($A31<>\"\",$C31,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["s0",{"$f":"Input!$E$12","v":1},{"$f":"IF($C$26,B22,1)","v":1},null,null,null,null,null,"A higher degree may be better",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,0,0,0,{"$f":"IF($A32<>\"\",$C32,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["s½",{"$f":"Input!$E$13","v":1.0534653429656149},{"$f":"IF($C$26,B23,0)","v":1.0534653429656149},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,0,0,0,0,{"$f":"IF($A33<>\"\",$C33,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["s1",{"$f":"Input!$E$14","v":0},{"$f":"IF($C$26,B24,0)","v":0},null,"Linear regression",null,null,null,null,null,null,null,"Polynomial regression",null,null,null,null,null,null,null,"Polynomial regression",null,null,null,null,null,null,0.5,0,0,0,0,0,{"$f":"IF($A34<>\"\",$C34,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[null,"Use weighted regression?",null,null,"Y = a0 + a1×X",null,null,null,null,null,null,null,"Y = a0 + a1×X +a2×X2",null,null,null,null,null,null,null,"Y = a0 + a1×X + a2×X2 + a3×X3",null,null,null,null,null,null,0.5,0,0,0,0,0,0,{"$f":"IF($A35<>\"\",$C35,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["1 = Yes 0 = No",null,1,null,"Degree = 1",null,null,null,null,null,null,null,"Degree = 2",null,null,null,null,null,null,null,"Degree = 3",null,null,null,null,null,null,0.2857142857142857,0,0,0,0,0,0,0,{"$f":"IF($A36<>\"\",$C36,0)","v":1.3822969074080618},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16666666666666663,0,0,0,0,0,0,0,0,{"$f":"IF($A37<>\"\",$C37,0)","v":0.80633986265470248},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["X","Y","W",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.2499999999999986E-2,0,0,0,0,0,0,0,0,0,{"$f":"IF($A38<>\"\",$C38,0)","v":0.30237744849551346},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,1.1662007826355481E-2,{"$f":"IF(A29<>\"\",AB19*$AC$3,\"\")","v":2.4190195879641081},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.2258064516129024E-2,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A39<>\"\",$C39,0)","v":0.15606577986865211},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,1.0161285068880616E-2,{"$f":"IF(A30<>\"\",AB20*$AC$3,\"\")","v":2.4190195879641081},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6393442622950817E-2,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A40<>\"\",$C40,0)","v":7.9312117638167465E-2},{"$f":"$E42","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,1.0237308080130344E-2,2.4190195879641081,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6393442622950817E-2,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A41<>\"\",$C41,0)","v":7.9312117638167465E-2},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,9.6324618884912391E-3,2.4190195879641081,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6393442622950817E-2,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A42<>\"\",$C42,0)","v":7.9312117638167465E-2},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,9.7391542398750364E-3,2.4190195879641081,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6393442622950817E-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A43<>\"\",$C43,0)","v":7.9312117638167465E-2},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,9.8205394631890389E-3,2.4190195879641081,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.9009900990098994E-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A44<>\"\",$C44,0)","v":4.7901377979487278E-2},0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0.9010720000000001,1.072667925395529E-2,2.4190195879641081,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.9751243781094518E-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A45<>\"\",$C45,0)","v":2.4069846646409033E-2},0,0,0,0,0,0,0,0,0,0,0,0,0]
[2.2526800000000002,2.2504646776853415E-2,1.3822969074080618,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.3222591362126238E-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A46<>\"\",$C46,0)","v":1.6073219853582111E-2},0,0,0,0,0,0,0,0,0,0,0,0]
[4.5053600000000005,4.2061733561014863E-2,0.80633986265470248,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.996007984031936E-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A47<>\"\",$C47,0)","v":9.6567648222120068E-3},0,0,0,0,0,0,0,0,0,0,0]
[13.516080000000002,0.12563395943218281,0.30237744849551346,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.9900099900099878E-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"IF($A48<>\"\",$C48,0)","v":4.8332059699582571E-3},0,0,0,0,0,0,0,0,0,0]
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[null,0,{"$f":"IF($A67<>\"\",$I$12*SQRT(($X$14+B67*$X$15+B67^2*$X$16)/$D$16+MMULT(MMULT($Z97:$AA97,COV),TRANSPOSE($Z97:$AA97)))/$C$10,\"\")","v":""},"",{"$f":"IF(A67=\"\",\"\",IF(Input!M81>0,(B67*Input!M81-$M$7*Input!L81)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,54.064320000000009,0.49446121665617948,null,7.9312117638167465E-2,1.3553538955517919E-2,null,1,-1.5,null,1,3.5838286129109553,null,1,3.0894091010337532,null,2.57065243864839,1,270.32160000000005,null,1,113.43824386561947,1.0768898354576764,{"$f":"$I$12*SQRT(($X$14+AH67*$X$15+AH67^2*$X$16)/$D$16+MMULT(MMULT($AG67:$AH67,COV),TRANSPOSE($AG67:$AH67)))","v":2.005426188826849E-2},1.0347573946558473,1.1190222762595055,3.9124188393813659,1.8622389429226496]
[null,0,{"$f":"IF($A68<>\"\",$I$12*SQRT(($X$14+B68*$X$15+B68^2*$X$16)/$D$16+MMULT(MMULT($Z98:$AA98,COV),TRANSPOSE($Z98:$AA98)))/$C$10,\"\")","v":""},"",{"$f":"IF(A68=\"\",\"\",IF(Input!M82>0,(B68*Input!M82-$M$7*Input!L82)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,54.064320000000009,0.49776557507615971,null,7.9312117638167465E-2,1.3553538955517919E-2,null,1,null,null,1,null,null,1,6.4505702327992367,null,4.3155524207614553,1,450.53600000000006,null,1,160.23577845625937,1.5206935798172143,{"$f":"$I$12*SQRT(($X$14+AH68*$X$15+AH68^2*$X$16)/$D$16+MMULT(MMULT($AG68:$AH68,COV),TRANSPOSE($AG68:$AH68)))","v":2.4052199463124181E-2},1.470161783848863,1.5712253757855656,3.3229439933865645,1.5816598282748868]
[null,0,{"$f":"IF($A69<>\"\",$I$12*SQRT(($X$14+B69*$X$15+B69^2*$X$16)/$D$16+MMULT(MMULT($Z99:$AA99,COV),TRANSPOSE($Z99:$AA99)))/$C$10,\"\")","v":""},"",{"$f":"IF(A69=\"\",\"\",IF(Input!M83>0,(B69*Input!M83-$M$7*Input!L83)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,90.107200000000006,0.81604958595898047,null,4.7901377979487278E-2,1.7440080199889348E-2,null,1,null,null,1,null,null,0,0,null,8.6259330638741201,1,901.07200000000012,null,1,226.33905306132024,2.1475830311692201,{"$f":"$I$12*SQRT(($X$14+AH69*$X$15+AH69^2*$X$16)/$D$16+MMULT(MMULT($AG69:$AH69,COV),TRANSPOSE($AG69:$AH69)))","v":2.8974215942226423E-2},2.0867104622974932,2.208455600040947,2.8344687021756529,1.3491546320540555]
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[null,0,{"$f":"IF($A74<>\"\",$I$12*SQRT(($X$14+B74*$X$15+B74^2*$X$16)/$D$16+MMULT(MMULT($Z104:$AA104,COV),TRANSPOSE($Z104:$AA104)))/$C$10,\"\")","v":""},"",{"$f":"IF(A74=\"\",\"\",IF(Input!M88>0,(B74*Input!M88-$M$7*Input!L88)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,0,0,null,0,0,0]
[null,0,{"$f":"IF($A75<>\"\",$I$12*SQRT(($X$14+B75*$X$15+B75^2*$X$16)/$D$16+MMULT(MMULT($Z105:$AA105,COV),TRANSPOSE($Z105:$AA105)))/$C$10,\"\")","v":""},"",{"$f":"IF(A75=\"\",\"\",IF(Input!M89>0,(B75*Input!M89-$M$7*Input!L89)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,0,0,null,0,0,0,null,"Values for plot of DL",null,null,"Values for limits "]
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[null,0,{"$f":"IF($A79<>\"\",$I$12*SQRT(($X$14+B79*$X$15+B79^2*$X$16)/$D$16+MMULT(MMULT($Z109:$AA109,COV),TRANSPOSE($Z109:$AA109)))/$C$10,\"\")","v":""},"",{"$f":"IF(A79=\"\",\"\",IF(Input!M93>0,(B79*Input!M93-$M$7*Input!L93)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,{"$f":"IF(A49<>\"\",1,0)","v":0},{"$f":"IF(B49<>\"\",$B49^1,0)","v":0},null,0,0,0,null,0,{"$f":"$C$9+AG80*$C$10","v":4.2443708421512853E-3},null,{"$f":"IF(K23<>\"\",1,0)","v":1},{"$f":"IF(K23<>\"\",$K23^1,0)","v":0.52181287339718552}]
[null,0,{"$f":"IF($A80<>\"\",$I$12*SQRT(($X$14+B80*$X$15+B80^2*$X$16)/$D$16+MMULT(MMULT($Z110:$AA110,COV),TRANSPOSE($Z110:$AA110)))/$C$10,\"\")","v":""},"",{"$f":"IF(A80=\"\",\"\",IF(Input!M94>0,(B80*Input!M94-$M$7*Input!L94)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,0,0,null,null,null,null,null,{"$f":"IF($K$19<>\"na\",$K$19,$K$23)","v":0.33157482144865086},{"$f":"$C$9+AG80*$C$10","v":4.2443708421512853E-3},null,{"$f":"IF(K24<>\"\",1,0)","v":1},{"$f":"IF(K24<>\"\",$K24^1,0)","v":0.73583638396770967}]
[null,0,{"$f":"IF($A81<>\"\",$I$12*SQRT(($X$14+B81*$X$15+B81^2*$X$16)/$D$16+MMULT(MMULT($Z111:$AA111,COV),TRANSPOSE($Z111:$AA111)))/$C$10,\"\")","v":""},"",{"$f":"IF(A81=\"\",\"\",IF(Input!M95>0,(B81*Input!M95-$M$7*Input!L95)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,0,0,null,null,null,null,null,null,null,null,1,{"$f":"J28","v":4.1241936111387227}]
[null,0,{"$f":"IF($A82<>\"\",$I$12*SQRT(($X$14+B82*$X$15+B82^2*$X$16)/$D$16+MMULT(MMULT($Z112:$AA112,COV),TRANSPOSE($Z112:$AA112)))/$C$10,\"\")","v":""},"",{"$f":"IF(A82=\"\",\"\",IF(Input!M96>0,(B82*Input!M96-$M$7*Input!L96)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,0,0]
[null,0,{"$f":"IF($A83<>\"\",$I$12*SQRT(($X$14+B83*$X$15+B83^2*$X$16)/$D$16+MMULT(MMULT($Z113:$AA113,COV),TRANSPOSE($Z113:$AA113)))/$C$10,\"\")","v":""},"",{"$f":"IF(A83=\"\",\"\",IF(Input!M97>0,(B83*Input!M97-$M$7*Input!L97)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,"","",null,1,null,null,1,null,null,0,0]
[null,0,{"$f":"IF($A84<>\"\",$I$12*SQRT(($X$14+B84*$X$15+B84^2*$X$16)/$D$16+MMULT(MMULT($Z114:$AA114,COV),TRANSPOSE($Z114:$AA114)))/$C$10,\"\")","v":""},"",{"$f":"IF(A84=\"\",\"\",IF(Input!M98>0,(B84*Input!M98-$M$7*Input!L98)*Input!$N$23,\"na\"))","v":""},null,null,null,null,"CI from",0,null,null,null,null,null,null,null,null,1,null,null,1,null,null,0,0]
[null,0,{"$f":"IF($A85<>\"\",$I$12*SQRT(($X$14+B85*$X$15+B85^2*$X$16)/$D$16+MMULT(MMULT($Z115:$AA115,COV),TRANSPOSE($Z115:$AA115)))/$C$10,\"\")","v":""},"",{"$f":"IF(A85=\"\",\"\",IF(Input!M99>0,(B85*Input!M99-$M$7*Input!L99)*Input!$N$23,\"na\"))","v":""},null,null,null,null,"0: sXo;     1: Low/High",null,null,null,null,null,null,null,null,null,1,null,null,1,null,null,0,0]
[null,0,{"$f":"IF($A86<>\"\",$I$12*SQRT(($X$14+B86*$X$15+B86^2*$X$16)/$D$16+MMULT(MMULT($Z116:$AA116,COV),TRANSPOSE($Z116:$AA116)))/$C$10,\"\")","v":""},"",{"$f":"IF(A86=\"\",\"\",IF(Input!M100>0,(B86*Input!M100-$M$7*Input!L100)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,null,1,null,null,0,0]
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[null,0,{"$f":"IF($A88<>\"\",$I$12*SQRT(($X$14+B88*$X$15+B88^2*$X$16)/$D$16+MMULT(MMULT($Z118:$AA118,COV),TRANSPOSE($Z118:$AA118)))/$C$10,\"\")","v":""},"",{"$f":"IF(A88=\"\",\"\",IF(Input!M102>0,(B88*Input!M102-$M$7*Input!L102)*Input!$N$23,\"na\"))","v":""},null,"dY-Low","dY-High","CI Low","CI High",null,"sXm",null,null,null,null,null,null,null,1,null,null,1,null,null,0,0]
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{"sheet":"2nd degree","index":7,"n_rows":188,"n_cols":56,"rows_kept":188,"cut":false,"hidden":false,"merged":[]}
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[null,null,null,null,null,null,{"$f":"Input!I15","v":1},{"$f":"Input!B25","v":"Naphthalene"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Statistical param ",null,null,"Covariance matrix"]
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["a0",null,{"$f":"MMULT(MMULT(COV,MMULT(TRANSPOSE(X_1),W)),Y)","v":1.5955144227566319E-3},{"$f":"SQRT(Z3)*$I$12","v":6.4706444909568429E-4},{"$f":"IF('Test of calibration function'!C26=1,'Test of calibration function'!AR14,'Test of calibration function'!AR13)","v":2.4609632303770567E-2},"s0",{"$f":"'Test of calibration function'!$C$22","v":1},"N",{"$f":"COUNT(X)*Input!B18","v":20},null,null,null,null,"This sheet is not protected, so take care only to change the white cells!",null,null,null,null,null,null,null,null,null,null,null,"LOQ data","D","Q","X","X2",null,null,null,null,null,null,null,null,null,"DL",{"$f":"K19","v":0.30009674612425435}]
["a1",null,9.292318893221024E-3,{"$f":"SQRT(AA4)*$I$12","v":5.5670909657330968E-5},{"$f":"TDIST(ABS(C10/D10),$I$9-$I$10,2)","v":9.0071365261131466E-29},"s½",{"$f":"'Test of calibration function'!$C$23","v":1.0534653429656149},"k",3,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sum",{"$f":"SUM(Z16:Z45)","v":4.1339061699852486},null,{"$f":"IF(AC10>0,100*$I$12*SQRT(($X$14+AC10*$X$15+AC10^2*$X$16)/$D$16+MMULT(MMULT($AB10:$AD10,COV),TRANSPOSE($AB10:$AD10)))/(($C$10+2*$C$11*$AC$10)*AC10),2*I15)","v":9.9999958809711487},{"$f":"(Z10-I15)/I15","v":-4.1190288513348605E-7},1,{"$f":"K15","v":2.8962819655932543},{"$f":"AC10^2","v":8.3884492242207251},null,null,null,null,null,null,null,null,null,"LOD",{"$f":"K20","v":0.49216467595458002}]
["a2",null,3.5349289723193715E-7,{"$f":"SQRT(AB5)*$I$12","v":8.745918490215737E-8},{"$f":"TDIST(ABS(C11/D11),$I$9-$I$10,2)","v":8.4693949044811084E-4},"s1",{"$f":"'Test of calibration function'!$C$24","v":0},"R2",{"$f":"X6/X5","v":0.99983707528388122},0,null,null,null,"White cells means that you may enter start values manually",null,null,null,null,null,null,null,null,"Norm",{"$f":"I9/X10","v":4.8380391759282162},null,{"$f":"IF(AC11>0,100*TINV(J16/100,I9-I10)*$I$12*SQRT(($X$14+AC11*$X$15+AC11^2*$X$16)/$D$16+MMULT(MMULT($AB11:$AD11,COV),TRANSPOSE($AB11:$AD11)))/(($C$10+2*$C$11*$AC$11)*AC11),2*I16)","v":20.000012706385537},{"$f":"(Z11-I16)/I16","v":6.3531927683158076E-7},1,{"$f":"K16","v":3.1505491301895931},{"$f":"AC11^2","v":9.9259598217384024},null,null,null,null,null,null,null,null,null,"DL-cal",{"$f":"K23","v":0.39500510885821088}]
[null,null,null,null,null,null,null,"s(y/x)",{"$f":"SQRT(X7/(I9-I10))","v":2.8047929813246808E-3},null,null,null,null,"\"Please update\" may mean that the target values are impossible",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"LOD-ca,",{"$f":"K24","v":0.55764863727252112}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Please look in Statistics for X in W37:X66 and enter a new:",null,null,null,null,null,null,null,null,"weights",null,null,"Update ok?",{"$f":"IF(AND(L15=\"Ok\", L16=\"Ok\"), \"Yes\",\"No\")","v":"Yes"},null,null,null,null,null,null,null,null,null,null,null,null,"Blank limit",{"$f":"IF(G28=0,\"na\",K28)","v":8.0382210435085018}]
["Unknown samples (Predict Xo from Yo)",null,null,null,null,null,"LOQ",null,"Target ±","a %","LOQx",null,null,"1) Reasonalbe start value in K15:K16 - then press Update LOQ again",null,null,null,null,null,null,null,null,"w0",{"$f":"G9^2/$X$11","v":0.20669530849926243},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"sBlank",{"$f":"IF(M7>0,$I$12*SQRT(($X$14+J28*$X$15+J28^2*$X$16)/$G$28+MMULT(MMULT(AL81:AN81,COV),TRANSPOSE(AL81:AN81)))/$C$10,0)","v":0.19960814902490673}]
["Confidence",null,"a %","m","t",null,"LOQ from ±s %",null,{"$f":"Input!$B$13","v":10},null,2.8962819655932543,{"$f":"IF(ABS($AA$10)>0.001,\"Please update\",\"Ok\")","v":"Ok"},null,"2) Reasonable target value for LOQ - go to sheet Input and enter new values",null,null,null,null,null,null,null,null,"w1",{"$f":"G10^2/$X$11","v":0.22938822702210526},null,"NN weights","Weight diagonal matrix"]
["interval",null,{"$f":"Input!$B$19","v":95},{"$f":"Input!$B$17","v":1},{"$f":"TINV((100-C16)/100,I9-I10)","v":2.109815577833317},null,"LOQ from ±CI %",null,{"$f":"Input!$B$14","v":20},{"$f":"Input!$B$15","v":5},3.1505491301895931,{"$f":"IF(ABS($AA$11)>0.001,\"Please update\",\"Ok\")","v":"Ok"},null,null,null,null,null,null,null,null,null,null,"w2",{"$f":"G11^2/$X$11","v":0},null,{"$f":"IF(N54<>\"\",1/($G$9^2+N54*$G$10^2+(N54*$G$11)^2),\"\")","v":0.5},{"$f":"IF($N54<>\"\",$Q54,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,0,{"$f":"IF($N55<>\"\",$Q55,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["Yo","Xo","sXo","RSD %","Xm",null,"DL From repeat exp",null,"n","s","DL/LOD",null,null,"Plot of line",null,"Prediction intervals",null,null,null,null,"Accuracy",null,"Statistics for X",null,null,0.5,0,0,{"$f":"IF($N56<>\"\",$Q56,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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[3.0410018148445697E-2,3.1005291391985765,{"$f":"IF($A22<>\"\",$I$12*SQRT(($X$14+B22*$X$15+B22^2*$X$16)/$D$16+MMULT(MMULT($AE52:$AG52,COV),TRANSPOSE($AE52:$AG52)))/($C$10+2*B22*$C$11),\"\")","v":0.29690158449581155},9.5758359675521234,{"$f":"IF(A22=\"\",\"\",IF(Input!M36>0,(B22*Input!M36-$M$7*Input!L36)*Input!$N$23,\"na\"))","v":-2.3966259819753963},null,"DL From calibration*",null,"X(DL)","a or b  %","DL/LOD","Calculated from s",null,0.9010720000000001,9.9688498042619679E-3,{"$f":"IF($N55<>\"\",$I$12*SQRT(($X$14+N22*$X$15+N22^2*$X$16)/$D$16+MMULT(MMULT($AA51:$AC51,COV),TRANSPOSE($AA51:$AC51))),\"\")","v":1.9124544185112273E-3},5.9339236801908227E-3,1.4003775928333113E-2,39.708817307254613,18.820989722729099,{"$f":"IF($N55<>0,-100*(O22-'Test of calibration function'!$B30)/(($C$10+2*N22*$C$11)*N22),\"\")","v":2.2981125202586323},null,{"$f":"IF(N22<>\"\",100*P22/(($C$10+N22*$C$11*2)*N22),\"\")","v":22.839033439709258},{"$f":"IF(N22<>\"\",W22*$E$16,\"\")","v":48.18614853375464},null,0.5,0,0,0,0,0,0,{"$f":"IF($N60<>\"\",$Q60,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[3.3875899851998258E-2,3.4734193945310388,{"$f":"IF($A23<>\"\",$I$12*SQRT(($X$14+B23*$X$15+B23^2*$X$16)/$D$16+MMULT(MMULT($AE53:$AG53,COV),TRANSPOSE($AE53:$AG53)))/($C$10+2*B23*$C$11),\"\")","v":0.30975157238877987},8.9177705656993016,{"$f":"IF(A23=\"\",\"\",IF(Input!M37>0,(B23*Input!M37-$M$7*Input!L37)*Input!$N$23,\"na\"))","v":-0.83328261214756993},null,"DL",null,null,{"$f":"Input!$B$11","v":1},{"$f":"(-$C$10+SIGN($C$10)*SQRT($C$10^2-4*$C$11*(-P20*TINV(J23/50,I9-I10))))/(2*$C$11)","v":0.39500510885821088},"at X = 0",null,0.9010720000000001,9.9688498042619679E-3,{"$f":"IF($N56<>\"\",$I$12*SQRT(($X$14+N23*$X$15+N23^2*$X$16)/$D$16+MMULT(MMULT($AA52:$AC52,COV),TRANSPOSE($AA52:$AC52))),\"\")","v":1.9124544185112273E-3},5.9339236801908227E-3,1.4003775928333113E-2,39.413936676405768,18.681223653150795,{"$f":"IF($N56<>0,-100*(O23-'Test of calibration function'!$B31)/(($C$10+2*N23*$C$11)*N23),\"\")","v":3.2059993066383963},null,22.839033439709258,48.18614853375464,null,0.2857142857142857,0,0,0,0,0,0,0,{"$f":"IF($N61<>\"\",$Q61,0)","v":1.3822969074080618},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[3.6428271049170492E-2,3.7480193353785918,{"$f":"IF($A24<>\"\",$I$12*SQRT(($X$14+B24*$X$15+B24^2*$X$16)/$D$16+MMULT(MMULT($AE54:$AG54,COV),TRANSPOSE($AE54:$AG54)))/($C$10+2*B24*$C$11),\"\")","v":0.31889244076790618},8.5082923067603247,{"$f":"IF(A24=\"\",\"\",IF(Input!M38>0,(B24*Input!M38-$M$7*Input!L38)*Input!$N$23,\"na\"))","v":-0.5591005987488441},null,"LOD",null,null,{"$f":"Input!$B$12","v":5},{"$f":"K23+(-$C$10+SIGN($C$10)*SQRT($C$10^2-4*$C$11*(-SQRT((I12*X14)^2/D16+D9^2)*TINV(J24/50,I9-I10))))/(2*$C$11)","v":0.55764863727252112},null,null,0.9010720000000001,9.9688498042619679E-3,{"$f":"IF($N57<>\"\",$I$12*SQRT(($X$14+N24*$X$15+N24^2*$X$16)/$D$16+MMULT(MMULT($AA53:$AC53,COV),TRANSPOSE($AA53:$AC53))),\"\")","v":1.9124544185112273E-3},5.9339236801908227E-3,1.4003775928333113E-2,41.888835593442948,19.854264056795355,{"$f":"IF($N57<>0,-100*(O24-'Test of calibration function'!$B32)/(($C$10+2*N24*$C$11)*N24),\"\")","v":-4.0172329246845653},null,22.839033439709258,48.18614853375464,null,0.16666666666666663,0,0,0,0,0,0,0,0,{"$f":"IF($N62<>\"\",$Q62,0)","v":0.80633986265470248},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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[null,0,{"$f":"IF($A86<>\"\",$I$12*SQRT(($X$14+B86*$X$15+B86^2*$X$16)/$D$16+MMULT(MMULT($AE116:$AG116,COV),TRANSPOSE($AE116:$AG116)))/($C$10+2*B86*$C$11),\"\")","v":""},"",{"$f":"IF(A86=\"\",\"\",IF(Input!M100>0,(B86*Input!M100-$M$7*Input!L100)*Input!$N$23,\"na\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,"",1,null,"",null,null,null,null,null,0,0,0]
[null,0,{"$f":"IF($A87<>\"\",$I$12*SQRT(($X$14+B87*$X$15+B87^2*$X$16)/$D$16+MMULT(MMULT($AE117:$AG117,COV),TRANSPOSE($AE117:$AG117)))/($C$10+2*B87*$C$11),\"\")","v":""},"",{"$f":"IF(A87=\"\",\"\",IF(Input!M101>0,(B87*Input!M101-$M$7*Input!L101)*Input!$N$23,\"na\"))","v":""},null,"Limits for confidence interval:",null,null,null,null,null,null,null,null,null,null,null,null,1,null,"",1,null,"",null,null,null,null,null,0,0,0]
[null,0,{"$f":"IF($A88<>\"\",$I$12*SQRT(($X$14+B88*$X$15+B88^2*$X$16)/$D$16+MMULT(MMULT($AE118:$AG118,COV),TRANSPOSE($AE118:$AG118)))/($C$10+2*B88*$C$11),\"\")","v":""},"",{"$f":"IF(A88=\"\",\"\",IF(Input!M102>0,(B88*Input!M102-$M$7*Input!L102)*Input!$N$23,\"na\"))","v":""},null,"dY-Low","dY-High","CI Low","CI High",null,"sXm",null,null,null,null,null,null,null,1,null,"",1,null,"",null,null,null,null,null,0,0,0]
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[null,null,null,null,null,null,{"$f":"IF(A115=\"\",\"\",($C$9+U153*($C$10+U153*$C$11)+$I$12*SQRT(($X$14+U153*$X$15+U153^2*$X$16)/$D$16+MMULT(MMULT($T153:$V153,COV),TRANSPOSE($T153:$V153)))*E$16-A115)^2)","v":""},{"$f":"IF(A115=\"\",\"\",($C$9+X153*($C$10+X153*$C$11)-$I$12*SQRT(($X$14+X153*$X$15+X153^2*$X$16)/$D$16+MMULT(MMULT($W153:$Y153,COV),TRANSPOSE($W153:$Y153)))*E$16-A115)^2)","v":""},"","","",{"$f":"IF(A115=\"\",\"\",IF(Input!M129>0,Input!$N$23*SQRT((Input!M129*C115)^2+(Input!L129*$AO$14)^2),\"na\"))","v":""}]
[null,null,null,null,null,null,{"$f":"IF(A116=\"\",\"\",($C$9+U154*($C$10+U154*$C$11)+$I$12*SQRT(($X$14+U154*$X$15+U154^2*$X$16)/$D$16+MMULT(MMULT($T154:$V154,COV),TRANSPOSE($T154:$V154)))*E$16-A116)^2)","v":""},{"$f":"IF(A116=\"\",\"\",($C$9+X154*($C$10+X154*$C$11)-$I$12*SQRT(($X$14+X154*$X$15+X154^2*$X$16)/$D$16+MMULT(MMULT($W154:$Y154,COV),TRANSPOSE($W154:$Y154)))*E$16-A116)^2)","v":""},"","","",{"$f":"IF(A116=\"\",\"\",IF(Input!M130>0,Input!$N$23*SQRT((Input!M130*C116)^2+(Input!L130*$AO$14)^2),\"na\"))","v":""}]
[null,null,null,null,null,null,{"$f":"IF(A117=\"\",\"\",($C$9+U155*($C$10+U155*$C$11)+$I$12*SQRT(($X$14+U155*$X$15+U155^2*$X$16)/$D$16+MMULT(MMULT($T155:$V155,COV),TRANSPOSE($T155:$V155)))*E$16-A117)^2)","v":""},{"$f":"IF(A117=\"\",\"\",($C$9+X155*($C$10+X155*$C$11)-$I$12*SQRT(($X$14+X155*$X$15+X155^2*$X$16)/$D$16+MMULT(MMULT($W155:$Y155,COV),TRANSPOSE($W155:$Y155)))*E$16-A117)^2)","v":""},"","","",{"$f":"IF(A117=\"\",\"\",IF(Input!M131>0,Input!$N$23*SQRT((Input!M131*C117)^2+(Input!L131*$AO$14)^2),\"na\"))","v":""}]
[null,null,null,null,null,null,{"$f":"IF(A118=\"\",\"\",($C$9+U156*($C$10+U156*$C$11)+$I$12*SQRT(($X$14+U156*$X$15+U156^2*$X$16)/$D$16+MMULT(MMULT($T156:$V156,COV),TRANSPOSE($T156:$V156)))*E$16-A118)^2)","v":""},{"$f":"IF(A118=\"\",\"\",($C$9+X156*($C$10+X156*$C$11)-$I$12*SQRT(($X$14+X156*$X$15+X156^2*$X$16)/$D$16+MMULT(MMULT($W156:$Y156,COV),TRANSPOSE($W156:$Y156)))*E$16-A118)^2)","v":""},"","","",{"$f":"IF(A118=\"\",\"\",IF(Input!M132>0,Input!$N$23*SQRT((Input!M132*C118)^2+(Input!L132*$AO$14)^2),\"na\"))","v":""}]

{"sheet":"3rd degree","index":8,"n_rows":188,"n_cols":56,"rows_kept":188,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Info!$A$1","v":"Calibration_Quant_8.15.xlsm"},null,null,"3rd degree polynomial regression",null,null,null,null,null,null,null,null,null,{"$f":"'Experimental data'!$J$1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, PLEN, University of Copenhagen, 2017 - 2025"}]
[null,null,null,null,null,null,{"$f":"Input!I15","v":1},{"$f":"Input!B25","v":"Naphthalene"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Statistical param ",null,null,"Covariance matrix"]
[null,null,null,null,null,null,null,null,null,null,null,2,null,null,null,null,null,null,null,null,null,null,"Ymean",{"$f":"SUM(W*Y)/I9","v":3.3897094703631926E-2},null,{"$f":"MINVERSE(MMULT(MMULT(TRANSPOSE(X_1),W),X_1))","v":5.5691892649316947E-2},-2.3614620860959532E-3,9.2622967448321034E-6,-7.4956541165939747E-9]
[null,null,null,null,null,null,{"$f":"IF(G6=0,\"Remember to save the results\",\"\")","v":"Remember to save the results"},null,null,null,"Comments to output",null,null,null,null,null,null,null,null,null,null,null,"Xmean",{"$f":"SUM(W*X)/I9","v":3.4583496363319894},null,-2.361462086095778E-3,1.0217759712523597E-3,-4.5084886722594459E-6,3.7792896149728467E-9]
[null,null,null,null,null,null,{"$f":"IF(G6=0,\"\",\"Results are saved\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SStotal",{"$f":"SUM(W*(Y-$X$3)^2)","v":0.82084956502241457},null,9.2622967448297131E-6,-4.5084886722594908E-6,2.6237176950840893E-8,-2.3974707667252756E-11]
[null,null,null,null,null,null,{"$f":"'Test of calibration function'!C117","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SSreg",{"$f":"SUM(W*(MMULT(X_1,C9:C12)-X3)^2)","v":0.82081536566575797},null,-7.4956541165945868E-9,3.7792896149729153E-9,-2.3974707667252872E-11,2.2750439840576188E-14,null,null,null,"DL/LOD ","Target","D","Q","X","X2","X3","Detection limits to output:"]
[{"$f":"IF('Test of calibration function'!$C$26=0,\"Simple 3rd degr.\",\"Weighted 3rd degr.\")","v":"Weighted 3rd degr."},null," Y = a0 + a1X + a2X^2 + a3X^3",null,null,"Weigthts",null,"Statistics",null,null,"Subtract blank =",null,{"$f":"IF(Input!N22=1,IF(H28=0,0,J28),0)","v":0},null,null,null,null,null,null,null,null,null,"SSres",{"$f":"X5-X6","v":3.4199356656605673E-5},null,null,null,null,null,null,null,null,{"$f":"MMULT(AJ7:AM7,$C$9:$C$12)-$C$9","v":2.4620367220524429E-2},{"$f":"SQRT((J19*TINV(J23/50,I19-1))^2+(D9*TINV(J23/50,I9-I10))^2)","v":2.4108352309694047E-3},{"$f":"(AG7-AH7)/AH7","v":9.2123807153027624},1,{"$f":"K19","v":2.7212032289915391},{"$f":"AK7^2","v":7.4049470134739792},{"$f":"AK7^3","v":20.150365723576645},"LOQ-s",{"$f":"IF(L15=\"Ok\",K15,\"na\")","v":"na"}]
[{"$f":"IF('Test of calibration function'!$C$26=0,\"3\",\"W 3\")&IF(J11=0,\"\",\" ZERO\")","v":"W 3"},null,"Coeff","s","P",null,null,null,null,null,"Please check the predicted Xo",null,null,null,"This sheet is not protected, so take care only to change the white cells!",null,null,null,null,null,null,null,"Xmax",{"$f":"MAX(X)","v":901.07200000000012},null,null,null,null,null,null,null,null,{"$f":"MMULT(AJ8:AM8,$C$9:$C$12)-$C$9","v":2.9572064148753859E-2},{"$f":"AH7+SQRT((J19*TINV(J24/50,I19-1))^2+(D9*TINV(J24/50,I9-I10))^2)","v":3.9211949503598353E-3},{"$f":"(AG8-AH8)/AH8","v":6.5415949788571783},1,{"$f":"K20","v":3.2681156690035658},{"$f":"AK8^2","v":10.680580025986623},{"$f":"AK8^3","v":34.905370936973398},"LOQ-ci",{"$f":"IF(L16=\"Ok\",K16,\"na\")","v":"na"}]
["a0",null,{"$f":"MMULT(MMULT(COV,MMULT(TRANSPOSE(X_1),W)),Y)","v":2.0913156798894588E-3},{"$f":"SQRT(Z3)*$I$12","v":3.4502055188743704E-4},{"$f":"IF('Test of calibration function'!C26=1,'Test of calibration function'!AV14,'Test of calibration function'!AV13)","v":1.6496234215527082E-5},"s0",{"$f":"'Test of calibration function'!$C$22","v":1},"N",{"$f":"COUNT(X)*Input!B18","v":20},null,"carefully. If they looks wrong",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"LOQ data","D","Q","X","X2","X3",null,null,null,null,null,null,null,null,"DL",{"$f":"IF(I19=0,\"na\",IF(L19=\"Ok\",K19,\"na\"))","v":"na"}]
["a1",null,9.0423371688018589E-3,{"$f":"SQRT(AA4)*$I$12","v":4.6733339854974737E-5},{"$f":"TDIST(ABS(C10/D10),$I$9-$I$10,2)","v":2.1786846145954799E-28},"s½",{"$f":"'Test of calibration function'!$C$23","v":1.0534653429656149},"k",4,null,"enter resonable starting values ",null,null,null,"· Many calculations are performed by Solver using macros:",null,null,null,null,null,null,null,"Sum",{"$f":"SUM(Z16:Z45)","v":4.1339061699852486},null,{"$f":"IF(AC10>0,100*$I$12*SQRT(($X$14+AC10*$X$15+AC10^2*$X$16)/$D$16+MMULT(MMULT($AB10:$AE10,COV),TRANSPOSE($AB10:$AE10)))/(($C$10+AC10*(2*$C$11+$AC10*3*$C$12))*AC10),2*I15)","v":9.3962432902186013},{"$f":"(Z10-I15)/I15","v":-6.0375670978139874E-2},1,{"$f":"K15","v":1.2763886444648465},{"$f":"AC10^2","v":1.6291679717188081},{"$f":"AC10^3","v":2.0794514990277126},null,null,null,null,null,null,null,null,"LOD",{"$f":"IF(I19=0,\"na\",IF(L20=\"Ok\",K20,\"na\"))","v":"na"}]
["a2",null,1.9393038235379949E-6,{"$f":"SQRT(AB5)*$I$12","v":2.3681408480655788E-7},{"$f":"TDIST(ABS(C11/D11),$I$9-$I$10,2)","v":4.0898235399831776E-7},"s",{"$f":"'Test of calibration function'!$C$24","v":0},"R2",{"$f":"X6/X5","v":0.99995833663302769},0,"in B19:B118 and Update Xo ",null,null,null,"· Here Accuracy may be improved by repeating the updates",null,null,null,null,null,null,null,"Norm",{"$f":"I9/X10","v":4.8380391759282162},null,{"$f":"IF(AC11>0,100*TINV(J16/100,I9-I10)*$I$12*SQRT(($X$14+AC11*$X$15+AC11^2*$X$16)/$D$16+MMULT(MMULT($AB11:$AE11,COV),TRANSPOSE($AB11:$AE11)))/(($C$10+$AC$11*(2*$C$11+$AC11*3*$C$12))*AC11),2*I16)","v":2.6449240077378282},{"$f":"(Z11-I16)/I16","v":-0.86775379961310861},1,{"$f":"K16","v":42.377891086185265},{"$f":"AC11^2","v":1795.8856529125806},{"$f":"AC11^3","v":76105.846602372054},null,{"$f":"MMULT(AJ11:AM11,$C$9:$C$12)-$C$9","v":3.0252134790764482E-2},{"$f":"P20*TINV(J23/50,I9-I10)","v":1.9347578260033545E-3},{"$f":"(AG11-AH11)/AH11","v":14.636135119430719},1,{"$f":"K23","v":3.3432191962335707},{"$f":"AK11^2","v":11.177114594064642},{"$f":"AK11^3","v":37.367544069379306},"DL-cal",{"$f":"IF(L23=\"Ok\",K23,\"na\")","v":"na"}]
["a3",null,-1.5048315323872479E-9,{"$f":"SQRT(AC6)*$I$12","v":2.2051791398355206E-10},{"$f":"TDIST(ABS(C12/D12),$I$9-$I$10,2)","v":4.0869986957016322E-6},null,null,"s(y/x)",{"$f":"SQRT(X7/(I9-I10))","v":1.4620054004817679E-3},null,null,null,null,null,"· White cells means that you may enter start values manually",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(AJ12:AM12,$C$9:$C$12)-$C$9","v":3.5284179582721863E-2},{"$f":"AH11+SQRT((I12*X14)^2/D16+D9^2)*TINV(J24/50,I9-I10)","v":2.7355034679897743E-3},{"$f":"(AG12-AH12)/AH12","v":11.898605319133802},1,{"$f":"K24","v":3.8988580685636332},{"$f":"AK12^2","v":15.201094238803744},{"$f":"AK12^3","v":59.266908923956137},"LOD-ca,",{"$f":"IF(ABS(AI12)>0.001,\"na\",K24)","v":"na"}]
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["Unknown samples (Predict Xo from Yo)",null,null,null,null,null,"LOQ",null,"Target ±","a %","LOQx",null,null,null,"Please look in Statistics for X in W37:X66 and enter a new:",null,null,null,null,null,null,null,"w0",{"$f":"G9^2/$X$11","v":0.20669530849926243},null,null,null,null,null,null,null,null,{"$f":"MMULT(AJ14:AM14,$C$9:$C$12)","v":2.0913156798894588E-3},{"$f":"IF(G28=0,0,H28)","v":4.0211616435671282E-2},{"$f":"((AG14-AH14)/AG14)^2","v":332.25647218878777},1,{"$f":"J28","v":0},{"$f":"AK14^2","v":0},{"$f":"AK14^3","v":0},"sBlank",{"$f":"IF(M7>0,$I$12*SQRT(($X$14+J28*$X$15+J28^2*$X$16)/$G$28+MMULT(MMULT(AQ81:AT81,COV),TRANSPOSE(AQ81:AT81)))/$C$10,0)","v":0}]
["Confidence",null,"a %","m","t",null,"LOQ from ±s %",null,{"$f":"Input!$B$13","v":10},null,1.2763886444648465,{"$f":"IF(ABS($AA$10)>0.001,\"Please update\",\"Ok\")","v":"Please update"},null,null,"1) Reasonalbe start value in K15:K16 - then press Update LOQ again",null,null,null,null,null,null,null,"w1",{"$f":"G10^2/$X$11","v":0.22938822702210526},null,"NN weights","Weight diagonal matrix"]
["interval",null,{"$f":"Input!$B$19","v":95},{"$f":"Input!$B$17","v":1},{"$f":"TINV((100-C16)/100,I9-I10)","v":2.119905299221255},null,"LOQ from ±CI %",null,{"$f":"Input!$B$14","v":20},{"$f":"Input!$B$15","v":5},42.377891086185265,{"$f":"IF(ABS($AA$11)>0.001,\"Please update\",\"Ok\")","v":"Please update"},null,null,"2) Reasonable target value for LOQ - go to sheet Input and enter new values",null,null,null,null,null,null,null,"w2",{"$f":"G11^2/$X$11","v":0},null,{"$f":"IF(N54<>\"\",1/($G$9^2+N54*$G$10^2+(N54*$G$11)^2),\"\")","v":0.5},{"$f":"IF($N54<>\"\",$Q54,0)","v":2.4190195879641081},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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[null,null,{"$f":"IF($A72<>\"\",$I$12*SQRT(($X$14+B72*$X$15+B72^2*$X$16)/$D$16+MMULT(MMULT($AF102:$AI102,COV),TRANSPOSE($AF102:$AI102)))/($C$10+B72*(2*$C$11+B72*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A72=\"\",\"\",IF(Input!M86>0,(B72*Input!M86-$M$7*Input!L86)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,450.53600000000006,4.3155524207614553,null,9.6567648222120068E-3,1.4877609296106098E-2,null,null,null,null,null,null,null,0,0,0,0,0,null,0,0,0,0,0,0,0,null,1,637.9101238265846,406929.32608044852,259584336.78864753,6.168818641376177,{"$f":"$I$12*SQRT(($X$14+AO72*$X$15+AO72^2*$X$16)/$D$16+MMULT(MMULT($AN72:$AQ72,COV),TRANSPOSE($AN72:$AQ72)))","v":2.4752390023007845E-2},6.1163459185980109,6.221291364154343,0.85061218085120638,0.40125008469183876]
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[null,null,{"$f":"IF($A74<>\"\",$I$12*SQRT(($X$14+B74*$X$15+B74^2*$X$16)/$D$16+MMULT(MMULT($AF104:$AI104,COV),TRANSPOSE($AF104:$AI104)))/($C$10+B74*(2*$C$11+B74*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A74=\"\",\"\",IF(Input!M88>0,(B74*Input!M88-$M$7*Input!L88)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,null,null,null,null,null,null,0,0,0,0,0,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A75<>\"\",$I$12*SQRT(($X$14+B75*$X$15+B75^2*$X$16)/$D$16+MMULT(MMULT($AF105:$AI105,COV),TRANSPOSE($AF105:$AI105)))/($C$10+B75*(2*$C$11+B75*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A75=\"\",\"\",IF(Input!M89>0,(B75*Input!M89-$M$7*Input!L89)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,null,null,null,null,null,null,0,0,0,0,0,null,0,0,0,0,0,0,0,null,"Values for plot of DL",null,null,"Values for limits "]
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[null,null,{"$f":"IF($A78<>\"\",$I$12*SQRT(($X$14+B78*$X$15+B78^2*$X$16)/$D$16+MMULT(MMULT($AF108:$AI108,COV),TRANSPOSE($AF108:$AI108)))/($C$10+B78*(2*$C$11+B78*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A78=\"\",\"\",IF(Input!M92>0,(B78*Input!M92-$M$7*Input!L92)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,null,null,null,null,null,null,0,0,0,0,0,null,{"$f":"IF(A48<>\"\",1,0)","v":0},{"$f":"IF(B48<>\"\",$B48^1,0)","v":0},{"$f":"AG78^2","v":0},{"$f":"AG78^3","v":0},0,{"$f":"AJ78-A48","v":0},0,null,{"$f":"IF($K$19<>\"na\",$K$19,$K$23)","v":2.7212032289915391},{"$f":"$C$9+AN78*$C$10","v":2.6697352781263291E-2},null,{"$f":"IF(K20<>\"\",1,0)","v":1},{"$f":"IF(K20<>\"na\",$K20^1,0)","v":3.2681156690035658},{"$f":"AR78^2","v":10.680580025986623},{"$f":"AR78^3","v":34.905370936973398}]
[null,null,{"$f":"IF($A79<>\"\",$I$12*SQRT(($X$14+B79*$X$15+B79^2*$X$16)/$D$16+MMULT(MMULT($AF109:$AI109,COV),TRANSPOSE($AF109:$AI109)))/($C$10+B79*(2*$C$11+B79*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A79=\"\",\"\",IF(Input!M93>0,(B79*Input!M93-$M$7*Input!L93)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,null,null,null,null,null,null,0,0,0,0,0,null,{"$f":"IF(A49<>\"\",1,0)","v":0},{"$f":"IF(B49<>\"\",$B49^1,0)","v":0},{"$f":"AG79^2","v":0},{"$f":"AG79^3","v":0},0,{"$f":"AJ79-A49","v":0},0,null,0,{"$f":"$C$9+AN80*$C$10","v":2.6697352781263291E-2},null,{"$f":"IF(K23<>\"\",1,0)","v":1},{"$f":"IF(K23<>\"na\",$K23^1,0)","v":3.3432191962335707},{"$f":"AR79^2","v":11.177114594064642},{"$f":"AR79^3","v":37.367544069379306}]
[null,null,{"$f":"IF($A80<>\"\",$I$12*SQRT(($X$14+B80*$X$15+B80^2*$X$16)/$D$16+MMULT(MMULT($AF110:$AI110,COV),TRANSPOSE($AF110:$AI110)))/($C$10+B80*(2*$C$11+B80*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A80=\"\",\"\",IF(Input!M94>0,(B80*Input!M94-$M$7*Input!L94)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(A50<>\"\",1,0)","v":0},{"$f":"IF(B50<>\"\",$B50^1,0)","v":0},{"$f":"AG80^2","v":0},{"$f":"AG80^3","v":0},0,{"$f":"AJ80-A50","v":0},0,null,{"$f":"IF($K$19<>\"na\",$K$19,$K$23)","v":2.7212032289915391},{"$f":"$C$9+AN80*$C$10","v":2.6697352781263291E-2},null,{"$f":"IF(K24<>\"\",1,0)","v":1},{"$f":"IF(K24<>\"na\",$K24^1,0)","v":3.8988580685636332},{"$f":"AR80^2","v":15.201094238803744},{"$f":"AR80^3","v":59.266908923956137}]
[null,null,{"$f":"IF($A81<>\"\",$I$12*SQRT(($X$14+B81*$X$15+B81^2*$X$16)/$D$16+MMULT(MMULT($AF111:$AI111,COV),TRANSPOSE($AF111:$AI111)))/($C$10+B81*(2*$C$11+B81*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A81=\"\",\"\",IF(Input!M95>0,(B81*Input!M95-$M$7*Input!L95)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,"Values for CI Low",null,null,null,"Values for CI High",null,null,null,null,null,null,null,{"$f":"IF(A51<>\"\",1,0)","v":0},{"$f":"IF(B51<>\"\",$B51^1,0)","v":0},{"$f":"AG81^2","v":0},{"$f":"AG81^3","v":0},0,{"$f":"AJ81-A51","v":0},0,null,null,null,null,1,{"$f":"IF(J28<>\"na\",$J28^1,0)","v":0},{"$f":"AR81^2","v":0},{"$f":"AR81^3","v":0}]
[null,null,{"$f":"IF($A82<>\"\",$I$12*SQRT(($X$14+B82*$X$15+B82^2*$X$16)/$D$16+MMULT(MMULT($AF112:$AI112,COV),TRANSPOSE($AF112:$AI112)))/($C$10+B82*(2*$C$11+B82*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A82=\"\",\"\",IF(Input!M96>0,(B82*Input!M96-$M$7*Input!L96)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"","",null,"Q","X","X2","X3","Q","X","X2","X3",null,null,null,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A83<>\"\",$I$12*SQRT(($X$14+B83*$X$15+B83^2*$X$16)/$D$16+MMULT(MMULT($AF113:$AI113,COV),TRANSPOSE($AF113:$AI113)))/($C$10+B83*(2*$C$11+B83*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A83=\"\",\"\",IF(Input!M97>0,(B83*Input!M97-$M$7*Input!L97)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,"",{"$f":"IF(N83<>\"\",$I$12/SQRT(Q83),\"\")","v":""},null,1,-41.785328321726759,{"$f":"IF($A19=\"\",\"\",U83^2)","v":1746.0136629545004},{"$f":"IF($A19=\"\",\"\",U83*V83)","v":-72957.754160774566},1,-4.1809084318298133,{"$f":"IF($A19=\"\",\"\",Y83^2)","v":17.479995315345629},{"$f":"IF($A19=\"\",\"\",Y83*Z83)","v":-73.08225980227418},null,null,null,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A84<>\"\",$I$12*SQRT(($X$14+B84*$X$15+B84^2*$X$16)/$D$16+MMULT(MMULT($AF114:$AI114,COV),TRANSPOSE($AF114:$AI114)))/($C$10+B84*(2*$C$11+B84*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A84=\"\",\"\",IF(Input!M98>0,(B84*Input!M98-$M$7*Input!L98)*Input!$N$23,\"na\"))","v":""},{"$f":"IF(A84<>\"\",IF(ABS(AK114)>0.005*A84,IF(B84<=0,\"Min\",IF(B84>=$X$8,\"Max\",\"Update\")),\"Ok\"),\"\")","v":""},null,null,null,"CI from",0,null,null,null,null,null,null,null,null,1,-14.936833845028726,{"$f":"IF($A20=\"\",\"\",U84^2)","v":223.10900531399565},{"$f":"IF($A20=\"\",\"\",U84*V84)","v":-3332.5421417047842},1,-55.186155969275397,{"$f":"IF($A20=\"\",\"\",Y84^2)","v":3045.5118106651908},{"$f":"IF($A20=\"\",\"\",Y84*Z84)","v":-168070.08978963955},null,null,null,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A85<>\"\",$I$12*SQRT(($X$14+B85*$X$15+B85^2*$X$16)/$D$16+MMULT(MMULT($AF115:$AI115,COV),TRANSPOSE($AF115:$AI115)))/($C$10+B85*(2*$C$11+B85*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A85=\"\",\"\",IF(Input!M99>0,(B85*Input!M99-$M$7*Input!L99)*Input!$N$23,\"na\"))","v":""},"",null,null,null,"0: ±CI;     1: Low/High",null,null,null,null,null,null,null,null,null,1,-24.000000000000004,576.00000000000023,-13824.000000000007,1,-15.208919460962218,231.31123117003528,-3517.9938852810801,null,null,null,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A86<>\"\",$I$12*SQRT(($X$14+B86*$X$15+B86^2*$X$16)/$D$16+MMULT(MMULT($AF116:$AI116,COV),TRANSPOSE($AF116:$AI116)))/($C$10+B86*(2*$C$11+B86*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A86=\"\",\"\",IF(Input!M100>0,(B86*Input!M100-$M$7*Input!L100)*Input!$N$23,\"na\"))","v":""},"",null,null,null,null,null,null,null,null,null,null,null,null,null,1,-39.426144086097715,1554.4208374977377,-61284.819909618491,1,-2.1528376215746534,4.6347098248672109,-9.9777776760558048,null,null,null,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A87<>\"\",$I$12*SQRT(($X$14+B87*$X$15+B87^2*$X$16)/$D$16+MMULT(MMULT($AF117:$AI117,COV),TRANSPOSE($AF117:$AI117)))/($C$10+B87*(2*$C$11+B87*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A87=\"\",\"\",IF(Input!M101>0,(B87*Input!M101-$M$7*Input!L101)*Input!$N$23,\"na\"))","v":""},"","Limits for confidence interval:",null,null,null,null,null,null,null,null,null,null,null,null,1,-24.000000000000004,576.00000000000023,-13824.000000000007,1,-45.515281842672927,2071.640881217952,-94291.318585438392,null,null,null,null,0,0,0,0,0,0,0]
[null,null,{"$f":"IF($A88<>\"\",$I$12*SQRT(($X$14+B88*$X$15+B88^2*$X$16)/$D$16+MMULT(MMULT($AF118:$AI118,COV),TRANSPOSE($AF118:$AI118)))/($C$10+B88*(2*$C$11+B88*3*$C$12)),\"\")","v":""},"",{"$f":"IF(A88=\"\",\"\",IF(Input!M102>0,(B88*Input!M102-$M$7*Input!L102)*Input!$N$23,\"na\"))","v":""},"","dY-Low","dY-High","CI Low","CI High",null,"sXm",null,null,null,null,null,null,null,1,-52.062548700602527,2710.5089772026099,-141116.00562903122,1,-5.8971345115561533,34.776195447386634,-205.07990235340571,null,null,null,null,0,0,0,0,0,0,0]
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{"sheet":"Conc Rounded","index":10,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Standard deviations","index":11,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}