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[]
[null,"NUTRITIONAL"]
[null,null,"RESPONSE",null,null,null,null,null,null,"Verson 1.3"]
[null,null,null,"MODELS"]
[]
[null,"A workbook to fit data from nutritional experiments to several models"]
[]
[]
[]
[null,"Dmitry Vedenov",null,null,"Department of Agricultural Economics",null,null,null,null,null,null,null,null,"vedenov@tamu.edu"]
[null,null,null,null,"Texas A&M University"]
[null,null,null,null,"College Station, TX 77843"]
[]
[null,"Gene Pesti",null,null,"Department of Poultry Science",null,null,null,null,null,null,null,null,"gpesti@uga.edu"]
[null,null,null,null,"The University of Georgia"]
[null,null,null,null,"Athens, Georgia 30602"]

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[]
[null,"The Nutritional Response Models workbook consists of 21 individual worksheets:"]
[]
[null,null,"Worksheets",null,null,"Content"]
[null,null,"HOME ",null,null,"Title Page"]
[null,null,"Information",null,null,"This Page"]
[null,null,"Input & Summary",null,null,"Main Data Input Page and Summary of Model Fits"]
[null,null,"Broken Line",null,null,"Individual Model Pages"]
[null,null,"Broken Quadratic"]
[null,null,"Saturation Kinetics"]
[null,null,"Logistics, 3 Parameters"]
[null,null,"Logistics, 4 Parameters"]
[null,null,"Compartmental"]
[null,null,"RNB, Model 1"]
[null,null,"RNB, Model 2"]
[null,null,"Multiple Range Tests",null,null,"Warning"]
[null,null,"Test Data Generator",null,null,"Random Data Generator for each of the models"]
[null,null,"BLL Graph",null,null,"Black and White Graphs of the Individual Models for Printing.  If the Axes are Set the Same, they serve nicely for comparing the models.  "]
[null,null,"BLQ Graph"]
[null,null,"SK Graph"]
[null,null,"L3 Graph"]
[null,null,"L4 Graph"]
[null,null,"Com Graph"]
[null,null,"RNB1 Graph"]
[null,null,"RNB2 Graph"]
[]
[null,"Up to 100 response points can be entered into the Input & Summary worksheet, where the data is automatically "]
[null,null,"transferred to the other worksheets by pressing the \"Copy Data\" button."]
[]
[null,"After the data has been copied to all the worksheets, you must go to each worksheet to fit the corresponding model"]
[null,null,"Excel's Solver module is used to minimize the sum of squared errors for each model"]
[null,null,"Follow the instructions on each page. Solver is run automatically by pressing a corresponding button on each worksheet"]
[]
[null,"A comparison of model fits is shown on the \"Input & Summary\" worksheet"]
[]
[null,"Feel free to use and modify this workbook."]
[]
[null,"Please don't forget to reference this workbook in all future modifications."]
[]
[null,null,"REFERENCES"]
[]
[null,"Broken Line with Linear Ascending Segment (Broken Line) Model"]
[]
[null,"ROBBINS, K.R. (1986) A Method, SAS Program, and Examples for Fitting the Broken Line to Growth Data. University of Tennessee Research Report. 86-09. University of Tennessee Agricultural Experiment Station, Knoxville, TN USA."]
[]
[null,"Broken Line with Quadratic Ascending Segment (Broken Quadratic) Model"]
[]
[null,"Pesti, G. M.; Vedenov, D.; Cason, J. A.  & L. Billard (2009). A comparison of methods to estimate nutritional requirements from experimental data"]
[null,"BRITISH POULTRY SCIENCE  Volume: 50   Issue: 1   Pages: 16-32  "]
[]
[null,"MORGAN, P.H., MERCER, L.P. & FLODIN (1975) General model for nutritional responses in higher animals.  Proceedings of the National Academy of Sciences, USA 72: 4327-4331."]
[]
[null,"MERCER, L.P. (1982) The quantitative nutrient-response relationship.  Journal of Nutrition, 112: 560-566."]
[]
[null,"MERCER, L.P. (1992) The determination of nutritional requirements:  mathematical modeling of nutrient-response curves. Journal of Nutrition, 122: 706-708."]
[]
[null,"MERCER, L.P., FLODIN, N.W. & MORGAN, P.H. (1978) New methods for comparing the biological efficiency of alternative nutrient sources. Journal of Nutrition, 108: 1244-1249."]
[]
[null,"MICHAELIS, L & MENTEN, M (1913). Die Kinetik der Invertinwirkung, Biochemische Zeitschrift 49:333-369."]
[]
[null,"Logistics Model, 3 Parameter"]
[]
[null,"SAS. 1990. User’s Guide. Release 6.08. SAS Institute Inc., Cary, NC. "]
[]
[null,"Logistics Model, 4 Parameter"]
[]
[null,"GAHL, M.J., FINKE, M.D., CRENSHAW, T.D. & BENEVENGA, N.J. (1991) Use of a four parameter logistic equation to evaluate the response of growing rats to ten levels of each indispensable amino acid.  Journal of Nutrition 121:  1720-1729."]
[]
[null,"Compartmental Model"]
[]
[null,"SAS. 1990. User’s Guide. Release 6.08. SAS Institute Inc., Cary, NC. "]
[]
[null,"RNB, Model 1"]
[]
[null,"ROBBINS, K.R., NORTON, H.W. & BAKER, D.H. (1979) Estimation of nutrient requirements from growth data. Journal of Nutrition, 109: 1710-1714."]
[]
[]
[null,"RNB, Model 2"]
[]
[null,"ROBBINS, K.R., NORTON, H.W. & BAKER, D.H. (1979) Estimation of nutrient requirements from growth data. Journal of Nutrition, 109: 1710-1714."]
[]
[]
[null,"Multiple Range Tests"]
[]
[null,"BAKER, R.J. (1980) Multiple comparison tests. Canadian Journal of Plant Science, 60: 325-327. "]
[]
[null,"CARMER, S.G. & WALKER, W.M. (1982) Baby bear’s dilemma: a statistical tale. Agronomy Journal, 74: 122-124."]
[]
[null,"CHEW, V. (1976) Comparing treatment means: a compendium.  HortScience, 11: 348-357."]
[]
[null,"COUSENS, R. (1988) Misinterpretations of results in weed research through inappropriate use of statistics. Weed Research, 28: 281-289."]
[]
[null,"DAWKINS, H.C. (1983) Multiple comparisons misused: why so frequently in response-curve studies?  Biometrics, 39: 789-790."]
[]
[null,"DUNCAN, D.B. (1955) Multiple range and multiple F tests. Biometrics, 11: 1-42."]
[]
[null,"GATES, C.E. (1991) A user’s guide to misanalyzing planned experiments. HortScience, 26: 1262-1265."]
[]
[null,"GILL, J.L. (1973) Current status of multiple comparisons of means in designed experiments.  Journal of Dairy Science, 56: 973-977."]
[]
[null,"GILLIGAN, C.A. (1986) Use and misuse of the analysis of variance in plant pathology, in: INGRAM, D.S., & WILLIAMS, P.H. (Eds.) Advances in Plant Pathology, Vol. 5, pp. 225-261 (New York: Academic Press)."]
[]
[null,"HAYTER, A.J. (1984), A Proof of the Conjecture that the Tukey-Kramer Method is Conservative, The Annals of Statistics, 12, 61 - 75."]
[]
[null,"JSFA (1988) Recommendations of the Editorial Board on the use of statistics in papers submitted to JSFA Ð Guidelines to Authors (as formulated by A.W.A. Murray). Journal of the Science of Food and Agriculture, 42: unnumbered."]
[]
[null,"LITTLE, T.M. (1978) If Galileo published in HortScience.  HortScience, 13: 504-506."]
[]
[null,"LOWRY, S.R. (1992) Use and misuse of multiple comparisons in animal experiments. Journal of Animal Science, 70: 1971-1977."]
[]
[null,"MAINDONALD, J.H., & COX, N.R. (1984) Use of statistical evidence in some recent issues of DSIR agricultural journals. New Zealand Journal of Agricultural Research, 27: 597-610."]
[]
[null,"MIHAIL, J.D., & NIBLACK, T.L. (1991) Comparison of treatment means: a statistical fantasy.  Journal of Nematology, 23(4S): 557-563."]
[]
[null,"NELSON, L.A. & RAWLINGS, J.O. (1983) Ten common misuses of statistics in agronomic research and reporting.  Journal of Agronomic Education, 12: 100-105."]
[]
[null,"PEARCE, S.C. (1993) Data analysis in agricultural experimentation. III. Multiple comparisons. Experimental Agriculture, 29: 1-8."]
[]
[null,"PERRY, J.N. (1986) Multiple-comparison procedures: a dissenting view. Journal of Economic Entomology, 79: 1149-1155."]
[]
[null,"PETERSEN, R.G.  (1977) Use and misuse of multiple comparison procedures. Agronomy Journal, 69: 205-208."]
[]
[null,"SWALLOW, W.H. (1984) Those overworked and oft-misused mean separation procedures--Duncan’s, LSD, etc.  Plant Disease, 68: 919-921."]
[]
[null,"SCHEFFÉ, H. (1953), A Method for Judging All Contrasts in the Analysis of Variance, Biometrika, 40, 87 - 104."]
[]
[null,"WALLER, R.A. & DUNCAN, D.B. (1969), \"A Bayes Rule for the Symmetric Multiple Comparison Problem,\" Journal of the American Statistical Association, 64, 1484 - 1499."]
[]
[null,"WELSCH, R.E. (1977), Stepwise Multiple Comparison Procedures, Journal of the American Statistical Association, 72, 359."]
[]
[null,"General"]
[null,"ALMQUIST, H.J. (1952) Amino acid requirements of chickens and turkeys - a review. Poultry Science 31: 966-981 "]
[]
[null,"ALMQUIST, H.J. (1953) Interpretation of amino acid requirement data according to the law of diminishing returns.  Archives of Biochemistry and Biophysics, 44: 245-247."]
[]
[null,"ALMQUIST, H.J. (1954a) Proportional requirements of amino acids.  Archives of Biochemistry and Biophysics, 48: 482-483."]
[]
[null,"ALMQUIST, H.J. (1954b) A fallacy in the analysis of nutritional requirement data. Archives of Biochemistry and Biophysics, 50: 503."]
[]
[null,"BAKER, D.H. (1986) Problems and pitfalls in animal experiments designed to establish dietary requirements for essential nutrients. Journal of Nutrition, 116: 2339-2349."]
[]
[null,"BAKER, D.H. & HAN, Y.M. (1994) Ideal amino-acid profile for chicks during the first 3 weeks posthatching.  Poultry Science 73: 1441-1447."]
[]
[null,"CURNOW, R.N. (1973) A smooth population response curve based on abrupt threshold and plateau model for individuals.  Biometrics, 29: 1-10."]
[]
[null,"FISHER, C., MORRIS, T.R. & JENNINGS, R.C. (1973) A model for the description and prediction of the response of laying hens to amino acid intake. British Poultry Science, 14:469-484."]
[]
[null,"FISHER, C. (1985) The prediction of responses to nutrients.  In: Proceedings of the Thirteenth International Congress of Nutrition, (Taylor, T.J. & Jenkins, N.K., eds.), Libbey, London, U.K."]
[]
[null,"LERMAN, P.M. & BIE, S.W. (1975). Problems in determining the best levels of essential nutrients in feedingstuffs.  Journal of Agricultural Science (Cambridge) 84:  459-468."]
[]
[null,"MAS-COLELL, A., WHINSTON, M., and GREEN, J.  Microeconomic Theory. Oxford University Press, 1995"]
[]
[null,"MILLER, R. G.J. (1981), Simultaneous Statistical Inference, New York: Springer-Verlag."]
[]
[null,"SHEARER, K.D. (2000) Experimental design, statistical analysis and modelling of dietary nutrient requirement studies for fish: a critical review. Aquaculture Nutrition, 6: 91-102."]
[]
[null,"STERLING KG, VEDENOV DV, PESTI GM, BAKALLI, R.I. (2005) Economically optimal dietary crude protein and lysine levels for starting broiler chicks Poultry Science 84: 29-36"]
[]
[null,"VARIAN, H. Microeconomic Analysis. 3rd ed. W.W. Norton Company, 1992"]
[]
[null,"WILSON, B.J. (1973) Growth curves: Their analysis and use.  pp. 89-115 Growth and Poultry Meat Production, K.N. Boorman & B.J. Wilson, eds. British Poultry Science Ltd, Edinburgh"]

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["Point","Input","Output",null,"INSTRUCTIONS"]
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[4,1.19,0.125,null,"2. Enter your data into columns B and C."]
[5,1.27,0.13100000000000001,null,null,"Column B, Input, should contain the nutrient levels fed."]
[6,1.35,0.13100000000000001,null,null,"Column C, Output, should contain the observed responses."]
[7,1.43,0.13200000000000001,null,"3. Press the button below to automatically copy data to all spreadsheets simultaneously."]
[8]
[9]
[10,null,null,null,"4. Go to each page and follow the instructions to solve for each of the models."]
[11,null,null,null,"5. Return to this page to compare the model fits. The best fit model is highlighted yellow."]
[12]
[13,null,null,null,"Model Fit Comparisons"]
[14,null,null,null,"Model",null,null,"Sum of Residuals",null,"R2","Qm","Critical Xi2"]
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[18,null,null,null,null,"Broken-Line (Quadratic Ascending)",null,{"$f":"'Broken Quadratic'!K8","v":3.2646401347689473E-6},null,{"$f":"'Broken Quadratic'!H16","v":0.99729300154662615},{"$f":"'Broken Quadratic'!F104","v":2.732890540450474E-5},{"$f":"_xlfn.CHISQ.INV.RT(0.05,COUNT($C$3:$C$101)-4)","v":5.9914645471079817}]
[19,null,null,null,null,"Saturation Kinetics",null,{"$f":"'Saturation Kinetics'!L8","v":3.0138518608492678E-6},null,{"$f":"'Saturation Kinetics'!H16","v":0.9975009520225131},{"$f":"'Saturation Kinetics'!F104","v":2.3542046656404908E-5},{"$f":"_xlfn.CHISQ.INV.RT(0.05,COUNT($C$3:$C$101)-5)","v":3.8414588206941236}]
[20,null,null,null,null,"Logistics, 3 Parameters",null,{"$f":"'Logistics, 3 Parameters'!K8","v":1.7626745634507473E-5},null,{"$f":"'Logistics, 3 Parameters'!H16","v":0.98538412468117142},{"$f":"'Logistics, 3 Parameters'!F104","v":1.6163418147699019E-4},{"$f":"_xlfn.CHISQ.INV.RT(0.05,COUNT($C$3:$C$101)-4)","v":5.9914645471079817}]
[21,null,null,null,null,"Logistics, 4 Parameters",null,{"$f":"'Logistics, 4 Parameters'!L8","v":1.1009394519604593E-5},null,{"$f":"'Logistics, 4 Parameters'!H16","v":0.99087114882288185},{"$f":"'Logistics, 3 Parameters'!F104","v":1.6163418147699019E-4},{"$f":"_xlfn.CHISQ.INV.RT(0.05,COUNT($C$3:$C$101)-5)","v":3.8414588206941236}]
[22,null,null,null,null,"RNB, Model 1",null,{"$f":"'RNB, Model 1'!L8","v":1.0921837321732548E-5},null,{"$f":"'RNB, Model 1'!H16","v":0.99094375014781722},{"$f":"'RNB, Model 1'!F104","v":9.0787560638607557E-5},{"$f":"_xlfn.CHISQ.INV.RT(0.05,COUNT($C$3:$C$101)-5)","v":3.8414588206941236}]
[23,null,null,null,null,"RNB, Model 2",null,{"$f":"'RNB, Model 2'!K8","v":1.1343420464536879E-5},null,{"$f":"'RNB, Model 2'!H16","v":0.99059417871928956},{"$f":"'RNB, Model 2'!F104","v":9.3264341711292339E-5},{"$f":"_xlfn.CHISQ.INV.RT(0.05,COUNT($C$3:$C$101)-4)","v":5.9914645471079817}]
[24,null,null,null,"Regression models with Qm>critical Xi2, indicating inadequate fits, are highlighted in red"]
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[null,"Fitting the Compartmental Model to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
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[null,null,null,{"$f":"SUM(D4:D103)","v":5.2597446860841446E-6},4.9023631428435771E-3,{"$f":"SUM(F4:F103)","v":0.83999474025531384},{"$f":"SUM(G4:G103)","v":3.4310681224434476E-5},null,null,null,null,null,null,null,null,null,null,null,null,null,98,{"$f":"$U$4+(U104-1)*($V$4-$U$4)/($W$4-1)","v":1.94},6.2927222689972639E-2]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,100,{"$f":"$U$4+(U106-1)*($V$4-$U$4)/($W$4-1)","v":1.98},5.2864333158583188E-2]
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{"sheet":"Broken Line","index":5,"n_rows":107,"n_cols":33,"rows_kept":107,"cut":false,"hidden":false,"merged":[[1,23,1,25],[2,26,2,28],[6,26,6,28],[17,7,17,12],[7,13,9,15],[15,7,15,9],[13,13,14,15],[1,1,1,3],[5,7,5,10],[1,7,1,10],[1,18,1,20],[19,11,19,12],[18,11,18,12],[18,7,19,7],[18,8,18,10],[19,8,19,10],[2,31,3,31],[2,32,3,32],[4,13,6,15],[4,18,4,20],[2,13,2,15],[2,30,3,30]]}
[null,"Fitting the Broken-Line (Ascending Linear) Model to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
["Point","Input","Output","Residuals","Expected","Qm",null,"Min Input",{"$f":"MIN(B4:B103)","v":0.95},"Min Output",{"$f":"MIN(C4:C103)","v":9.5000000000000001E-2},null,null,"Instructions",null,null,null,null,"Min Input","Max Input","# of Points",null,null,"Maximum(X0)","Rate Constant (X1)","Requirement(X2)","Q0",null,null,null,"Number of Observations, T","Number of Regressors, K","sigma"]
[1,0.95,9.5000000000000001E-2,{"$f":"IF(ISBLANK(B4),\"\",IF(B4<$J$8,C4-($H$8+$I$8*($J$8-B4)),C4-$H$8))","v":-1.2008049136470883E-3},{"$f":"IF(ISBLANK(B4),\"\",IF(B4<$J$8,($H$8+$I$8*($J$8-B4)),$H$8))","v":9.6200804913647089E-2},{"$f":"IF(ISBLANK(B4),\"\",D4^2/E4)","v":1.4988777296960412E-5},null,"Max Input",{"$f":"MAX(B4:B103)","v":1.43},"Max Output",{"$f":"MAX(C4:C103)","v":0.13200000000000001},null,null,"1. Copy data in cells B4:C103",null,null,null,null,{"$f":"FLOOR(I3,1)","v":0},{"$f":"CEILING(I4,1)","v":2},101,null,null,{"$f":"IF(ISBLANK(B4),\"\",1)","v":1},{"$f":"IF(ISBLANK(B4),\"\",($J$8-B4)*IF(B4<$J$8,1,0))","v":0.27555184444026648},{"$f":"IF(ISBLANK(B4),\"\",$I$8*IF(B4<$J$8,1,0))","v":-0.1274973570370517},{"$f":"SUMPRODUCT(X$4:X$103,X$4:X$103)","v":7},{"$f":"SUMPRODUCT(X$4:X$103,Y$4:Y$103)","v":0.62220737776106572},{"$f":"SUMPRODUCT(X$4:X$103,Z$4:Z$103)","v":-0.5099894281482068}]
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[3,1.1100000000000001,0.11899999999999999,2.3996179604246076E-3,0.11660038203957539,4.9383769206158964E-5,null,"Regression",null,null,null,null,null,null,null,null,null,null,"Point","Input","Output",null,null,1,0.11555184444026634,-0.1274973570370517,{"$f":"SUMPRODUCT(Z$4:Z$103,X$4:X$103)","v":-0.5099894281482068},{"$f":"SUMPRODUCT(Z$4:Z$103,Y$4:Y$103)","v":-7.9329796193490301E-2},{"$f":"SUMPRODUCT(Z$4:Z$103,Z$4:Z$103)","v":6.5022304205733752E-2}]
[4,1.19,0.125,-1.8001706025395081E-3,0.12680017060253951,2.5556859922572955E-5,null,"Max or Min","Rate Constant","Requirement","SSE",null,null,null,null,null,null,null,1,{"$f":"$S$4+(S7-1)*($T$4-$S$4)/($U$4-1)","v":0},{"$f":"IF(T7<$J$8,($H$8+$I$8*($J$8-T7)),$H$8)","v":-2.492168427155203E-2},null,null,1,3.5551844440266489E-2,-0.1274973570370517,"inv(Q0)"]
[5,1.27,0.13100000000000001,-3.329368064658722E-4,0.13133293680646588,8.4401460741747716E-7,null,0.13133293680646588,-0.1274973570370517,1.2255518444402664,{"$f":"SUMPRODUCT(D4:D103,D4:D103)","v":1.1466668313527139E-5},null,null,"3. Guess the Rate Constant values in cell I8 until the predicted line is close to the observed points",null,null,null,null,2,0.02,-2.2371737130810976E-2,null,null,1,0,0,{"$f":"MINVERSE(AA4:AC6)","v":0.33333333333333331},1.0150610510858574E-15,2.6144332798715513]
[6,1.35,0.13100000000000001,-3.329368064658722E-4,0.13133293680646588,8.4401460741747716E-7,null,null,null,null,null,null,null,null,null,null,null,null,3,0.04,-1.9821789990069949E-2,null,null,1,0,0,0,31.250000000000021,38.126242392190832]
[7,1.43,0.13200000000000001,6.6706319353412868E-4,0.13133293680646588,3.3881318349232493E-6,null,{"$f":"IF(ISNUMBER(H13),H$8-NORMSINV(0.975)*H$13,\"N/A\")","v":0.12941702244388395},{"$f":"IF(ISNUMBER(I13),I$8-NORMSINV(0.975)*I$13,\"N/A\")","v":-0.14604811808465024},{"$f":"IF(ISNUMBER(J13),J$8-NORMSINV(0.975)*J$13,\"N/A\")","v":1.1954285789808865},"Lower 95% Confidence Levels",null,null,null,null,null,null,null,4,0.06,-1.7271842849328922E-2,null,null,1,0,0,2.6144332798715513,38.126242392190832,82.400653704563382]
[8,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),H$8+NORMSINV(0.975)*H$13,\"N/A\")","v":0.13324885116904781},{"$f":"IF(ISNUMBER(I14),I$8+NORMSINV(0.975)*I$13,\"N/A\")","v":-0.10894659598945317},{"$f":"IF(ISNUMBER(J14),J$8+NORMSINV(0.975)*J$13,\"N/A\")","v":1.2556751098996464},"Upper 95% Confidence Levels",null,null,"4. Press the button below to run solver with current settings",null,null,null,null,5,0.08,-1.4721895708587868E-2,null,null,"","",""]
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[10,null,null,"","","",null,{"$f":"IF(ISNUMBER(AA8),SQRT(AA8)*$AG$5,\"N/A\")","v":9.7752529010452106E-4},{"$f":"IF(ISNUMBER(AB9),SQRT(AB9)*$AG$5,\"N/A\")","v":9.4648479226784651E-3},{"$f":"IF(ISNUMBER(AC10),SQRT(AC10)*$AG$5,\"N/A\")","v":1.5369295403889207E-2},"Standard Errors",null,null,null,null,null,null,null,7,0.12,-9.6220014271057863E-3,null,null,"","",""]
[11,null,null,"","","",null,{"$f":"IF(ISNUMBER(H13),H8/H13,\"N/A\")","v":134.35246958410991},{"$f":"IF(ISNUMBER(I13),I8/I13,\"N/A\")","v":-13.470618659551702},{"$f":"IF(ISNUMBER(J13),J8/J13,\"N/A\")","v":79.740275154717892},"t-Statistics",null,null,"5. Solver will attempt to minimize SSE (red cell) by changing cells H8:J8",null,null,null,null,8,0.14000000000000001,-7.0720542863647595E-3,null,null,"","",""]
[12,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),2*TDIST(ABS(H14),$AE$5-$AF$5,1),\"N/A\")","v":1.8408069836035783E-8},{"$f":"IF(ISNUMBER(I14),2*TDIST(ABS(I14),$AE$5-$AF$5,1),\"N/A\")","v":1.7571605701579483E-4},{"$f":"IF(ISNUMBER(J14),2*TDIST(ABS(J14),$AE$5-$AF$5,1),\"N/A\")","v":1.4824673118422503E-7},"p-values",null,null,null,null,null,null,null,9,0.16,-4.5221071456237605E-3,null,null,{"$f":"IF(ISBLANK(B15),\"\",1)","v":""},"",""]
[13,null,null,"","","",null,{"$f":"1-K8/(SUMPRODUCT(C4:C103,C4:C103)-COUNT(C4:C103)*AVERAGE(C4:C103)^2)","v":0.9904919831562794},null,null,"Goodness of Fit (R2)",null,null,null,null,null,null,null,10,0.18,-1.9721600048827059E-3,null,null,{"$f":"IF(ISBLANK(B16),\"\",1)","v":""},"",""]
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[15,null,null,"","","",null,"Functional Form",null,null,null,null,null,null,null,null,null,null,12,0.22,3.1277342765993477E-3,null,null,{"$f":"IF(ISBLANK(B18),\"\",1)","v":""},"",""]
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[17,null,null,"","","",null,null,"Maximum + Rate Constant×(Requirement - x)",null,null,"if x £ Requirement",null,null,null,null,null,null,14,0.26,8.227628558081429E-3,null,null,"","",""]
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[24,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,21,0.4,2.6077258543268672E-2,null,null,"","",""]
[25,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,22,0.42,2.8627205684009685E-2,null,null,"","",""]
[26,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,23,0.44,3.1177152824750726E-2,null,null,"","",""]
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[28,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,25,0.48,3.6277047106232793E-2,null,null,"","",""]
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[31,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,28,0.54,4.3926888528455901E-2,null,null,"","",""]
[32,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,29,0.56000000000000005,4.6476835669196942E-2,null,null,"","",""]
[33,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,30,0.57999999999999996,4.9026782809937969E-2,null,null,{"$f":"IF(ISBLANK(B36),\"\",1)","v":""},"",""]
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[35,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,32,0.62,5.4126677091420036E-2,null,null,"","",""]
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[37,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,34,0.66,5.9226571372902104E-2,null,null,"","",""]
[38,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,35,0.68,6.1776518513643144E-2,null,null,"","",""]
[39,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,36,0.7,6.4326465654384171E-2,null,null,"","",""]
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{"sheet":"Broken Quadratic","index":6,"n_rows":107,"n_cols":33,"rows_kept":107,"cut":false,"hidden":false,"merged":[[2,31,3,31],[2,32,3,32],[4,13,6,15],[4,18,4,20],[2,13,2,15],[2,30,3,30],[15,7,15,9],[1,1,1,3],[5,7,5,10],[1,7,1,10],[19,11,19,12],[17,7,17,12],[18,7,19,7],[18,8,18,10],[18,11,18,12],[19,8,19,10],[14,13,15,15],[1,23,1,25],[2,26,2,28],[6,26,6,28],[1,18,1,20],[7,13,9,15]]}
[null,"Fitting the Broken-Line (Ascending Quadratic) Model to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
["Point","Input","Output","Residuals","Expected","Qm",null,"Min Input",{"$f":"MIN(B4:B103)","v":0.95},"Min Output",{"$f":"MIN(C4:C103)","v":9.5000000000000001E-2},null,null,"Instructions",null,null,null,null,"Min Input","Max Input","# of Points",null,null,"Maximum(X0)","Rate Constant (X1)","Requirement(X2)","Q0",null,null,null,"Number of Observations, T","Number of Regressors, K","sigma"]
[1,0.95,9.5000000000000001E-2,{"$f":"IF(ISBLANK(B4),\"\",IF(B4<$J$8,C4-($H$8+$I$8*($J$8-B4)^2),C4-$H$8))","v":3.9432649511052242E-4},{"$f":"IF(ISBLANK(B4),\"\",IF(B4<$J$8,($H$8+$I$8*($J$8-B4)^2),$H$8))","v":9.4605673504889479E-2},{"$f":"IF(ISBLANK(B4),\"\",D4^2/E4)","v":1.6435947125106881E-6},null,"Max Input",{"$f":"MAX(B4:B103)","v":1.43},"Max Output",{"$f":"MAX(C4:C103)","v":0.13200000000000001},null,null,"1. Copy data in cells B4:C103",null,null,null,null,{"$f":"FLOOR(I3,1)","v":0},{"$f":"CEILING(I4,1)","v":2},101,null,null,{"$f":"IF(ISBLANK(B4),\"\",1)","v":1},{"$f":"IF(ISBLANK(B4),\"\",($J$8-B4)^2*IF(B4<$J$8,1,0))","v":0.16127257937251277},{"$f":"IF(ISBLANK(B4),\"\",2*$I$8*($J$8-B4)*IF(B4<$J$8,1,0))","v":-0.18467223201237751},{"$f":"SUMPRODUCT(X$4:X$103,X$4:X$103)","v":7},{"$f":"SUMPRODUCT(X$4:X$103,Y$4:Y$103)","v":0.35582529928856105},{"$f":"SUMPRODUCT(X$4:X$103,Z$4:Z$103)","v":-0.55620685930134794}]
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[3,1.1100000000000001,0.11899999999999999,7.3291905604121188E-4,0.11826708094395878,4.5420106628224036E-6,null,"Regression",null,null,null,null,null,null,null,null,null,null,"Point","Input","Output",null,null,1,5.8364555779643973E-2,-0.11109536097598852,{"$f":"SUMPRODUCT(Z$4:Z$103,X$4:X$103)","v":-0.55620685930134794},{"$f":"SUMPRODUCT(Z$4:Z$103,Y$4:Y$103)","v":-5.3750468110125772E-2},{"$f":"SUMPRODUCT(Z$4:Z$103,Z$4:Z$103)","v":7.5245319010147735E-2}]
[4,1.19,0.125,-6.8317240131007817E-4,0.12568317240131008,3.7135005505869419E-6,null,"Max or Min","Rate Constant","Requirement","SSE",null,null,null,null,null,null,null,1,{"$f":"$S$4+(S7-1)*($T$4-$S$4)/($U$4-1)","v":0},{"$f":"IF(T7<$J$8,($H$8+$I$8*($J$8-T7)^2),$H$8)","v":-0.28834271600168482},null,null,1,2.6110543983209673E-2,-7.4306925457794132E-2,"inv(Q0)"]
[5,1.27,0.13100000000000001,8.4381098279417976E-4,0.13015618901720583,5.4704811201098971E-6,null,0.13168671029925563,-0.22992772198871539,1.3515875737277148,{"$f":"SUMPRODUCT(D4:D53,D4:D53)","v":3.2646401347689473E-6},null,null,"3. Guess the Rate Constant values in cell I8 until the predicted line is close to the observed points",null,null,null,null,2,0.02,{"$f":"IF(T8<$J$8,($H$8+$I$8*($J$8-T8)^2),$H$8)","v":-0.2760039890146615},null,null,1,6.6565321867752894E-3,-3.7518489939599629E-2,{"$f":"MINVERSE(AA4:AC6)","v":0.45804615263990633},7.7866939140135809,8.9481560280527503]
[6,1.35,0.13100000000000001,-6.8613079164600577E-4,0.13168613079164601,3.5749813622334779E-6,null,null,null,null,null,null,null,null,null,null,null,null,3,0.04,-0.26384920420522928,null,null,1,2.5203903409298691E-6,-7.3005442140513675E-4,7.78669391401358,542.07030643100484,444.77910022558007]
[7,1.43,0.13200000000000001,3.1328970074437357E-4,0.13168671029925563,7.4533289175083867E-7,null,{"$f":"IF(ISNUMBER(H13),H$8-NORMSINV(0.975)*H$13,\"N/A\")","v":0.13048834183197966},{"$f":"IF(ISNUMBER(I13),I$8-NORMSINV(0.975)*I$13,\"N/A\")","v":-0.2711529970624143},{"$f":"IF(ISNUMBER(J13),J$8-NORMSINV(0.975)*J$13,\"N/A\")","v":1.3163004567832526},"Lower 95% Confidence Levels",null,null,null,null,null,null,null,4,0.06,-0.25187836157338794,null,null,1,0,0,8.9481560280527486,444.77910022558007,397.15574333065013]
[8,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),H$8+NORMSINV(0.975)*H$13,\"N/A\")","v":0.13288507876653161},{"$f":"IF(ISNUMBER(I14),I$8+NORMSINV(0.975)*I$13,\"N/A\")","v":-0.18870244691501648},{"$f":"IF(ISNUMBER(J14),J$8+NORMSINV(0.975)*J$13,\"N/A\")","v":1.3868746906721769},"Upper 95% Confidence Levels",null,null,"4. Press the button below to run solver with current settings",null,null,null,null,5,0.08,-0.24009146111913757,null,null,"","",""]
[9,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,6,0.1,-0.22848850284247821,null,null,"","",""]
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[null,"Fitting the Saturation Kinetics Model to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
["Point","Input","Output","Residuals","Expected","Qm",null,"Min Input",{"$f":"MIN(B4:B103)","v":0.95},"Min Output",{"$f":"MIN(C4:C103)","v":9.5000000000000001E-2},null,null,"Instructions",null,null,null,null,"Min Input","Max Input","# of Points",null,null,"Maximum(X0)","Rate Constant (X1)","Intercept(X2)","Kinetic Order (X3)","Q0",null,null,null,null,"Number of Observations, T","Number of Regressors, K","sigma"]
[1,0.95,9.5000000000000001E-2,{"$f":"IF(ISBLANK(B4),\"\",C4-($J$8*$I$8+$H$8*B4^$K$8)/($I$8+B4^$K$8))","v":5.4063725572761623E-7},{"$f":"IF(ISBLANK(B4),\"\",($J$8*$I$8+$H$8*B4^$K$8)/($I$8+B4^$K$8))","v":9.4999459362744273E-2},{"$f":"IF(ISBLANK(B4),\"\",D4^2/E4)","v":3.0767400597998992E-12},null,"Max Input",{"$f":"MAX(B4:B103)","v":1.43},"Max Output",{"$f":"MAX(C4:C103)","v":0.13200000000000001},null,null,"1. Copy data in cells B4:C103",null,null,null,null,{"$f":"FLOOR(I3,1)","v":0},{"$f":"CEILING(I4,1)","v":2},101,null,null,{"$f":"IF(ISBLANK(B4),\"\",$B4^$K$8/($I$8 + $B4^$K$8))","v":0.24500178620874019},{"$f":"IF(ISBLANK(B4),\"\",$J$8/($I$8 + $B4^$K$8) - ($I$8*$J$8 + $H$8*$B4^$K$8)/($I$8 + $B4^$K$8)^2)","v":-5.9218036363229976E-3},{"$f":"IF(ISBLANK(B4),\"\",$I$8/($I$8 + $B4^$K$8))","v":0.75499821379125986},{"$f":"IF(ISBLANK(B4),\"\",($H$8* LN($B4)*$B4^$K$8)/($I$8 + $B4^$K$8) -(LN($B4)*$B4^$K$8)*($I$8*$J$8 + $H$8*$B4^$K$8)/($I$8 + $B4^$K$8)^2)","v":-4.7569929020799262E-4},{"$f":"SUMPRODUCT(X$4:X$103,X$4:X$103)","v":4.349613299560148},{"$f":"SUMPRODUCT(X$4:X$103,Y$4:Y$103)","v":-1.6310589615629312E-2},{"$f":"SUMPRODUCT(X$4:X$103,Z$4:Z$103)","v":0.85589694778982228},{"$f":"SUMPRODUCT(X$4:X$103,AA$4:AA$103)","v":3.0220244910966016E-3}]
[{"$f":"A4+1","v":2},1.03,0.107,-5.087029950601174E-5,{"$f":"IF(ISBLANK(B5),\"\",($J$8*$I$8+$H$8*B5^$K$8)/($I$8+B5^$K$8))","v":0.10705087029950601},{"$f":"IF(ISBLANK(B5),\"\",D5^2/E5)","v":2.4173436092497418E-8},null,null,null,null,null,null,null,"2. View the data and estimate values for the Max and Intercept in cells H8 and J8",null,null,null,null,"Prediction",null,null,null,null,0.48537228247786723,-7.9966294656624651E-3,0.51462771752213288,3.7017894446126861E-4,{"$f":"SUMPRODUCT(Y$4:Y$103,X$4:X$103)","v":-1.6310589615629312E-2},{"$f":"SUMPRODUCT(Y$4:Y$103,Y$4:Y$103)","v":1.5997910964225782E-4},{"$f":"SUMPRODUCT(Y$4:Y$103,Z$4:Z$103)","v":-1.109002504465491E-2},{"$f":"SUMPRODUCT(Y$4:Y$103,AA$4:AA$103)","v":-1.2723298017884523E-5},null,{"$f":"COUNT(B4:B53)","v":7},4,{"$f":"SQRT(L8/(AG5-AH5))","v":1.0023059846921776E-3}]
[3,1.1100000000000001,0.11899999999999999,3.4705902345992523E-4,0.11865294097654007,1.0151452191039426E-6,null,"Regression",null,null,null,null,null,null,null,null,null,null,"Point","Input","Output",null,null,0.71678049692031065,-6.499024347345856E-3,0.28321950307968941,1.0621851026993302E-3,{"$f":"SUMPRODUCT(Z$4:Z$103,X$4:X$103)","v":0.85589694778982228},{"$f":"SUMPRODUCT(Z$4:Z$103,Y$4:Y$103)","v":-1.109002504465491E-2},{"$f":"SUMPRODUCT(Z$4:Z$103,Z$4:Z$103)","v":0.93859280486020824},{"$f":"SUMPRODUCT(Z$4:Z$103,AA$4:AA$103)","v":3.3172445358693666E-4}]
[4,1.19,0.125,-1.0221542694513475E-3,0.12602215426945135,8.2906006218851354E-6,null,"Max or Min","Rate Constant","Intercept","Kinetic Order","SSE",null,"3. Guess the Rate Constant and Kinetic Order values in cells I8 and K8 until the predicted line is close to the observed points",null,null,null,null,1,{"$f":"$S$4+(S7-1)*($T$4-$S$4)/($U$4-1)","v":0},{"$f":"($J$8*$I$8+$H$8*T7^$K$8)/($I$8+T7^$K$8)","v":8.2715850302269897E-2},null,null,0.86376257774263288,-3.7672950047389622E-3,0.13623742225736704,1.0263139391432849E-3,{"$f":"SUMPRODUCT(AA$4:AA$103,X$4:X$103)","v":3.0220244910966016E-3},{"$f":"SUMPRODUCT(AA$4:AA$103,Y$4:Y$103)","v":-1.2723298017884523E-5},{"$f":"SUMPRODUCT(AA$4:AA$103,Z$4:Z$103)","v":3.3172445358693666E-4},{"$f":"SUMPRODUCT(AA$4:AA$103,AA$4:AA$103)","v":3.2787801506302637E-6}]
[5,1.27,0.13100000000000001,1.2884557956467091E-3,0.1297115442043533,1.2798539617415783E-5,null,0.13285266461107992,1.5660942964543876,8.2715850302269883E-2,13.19597580380278,{"$f":"SUMPRODUCT(D4:D53,D4:D53)","v":3.0138518608492678E-6},null,null,null,null,null,null,2,0.02,{"$f":"($J$8*$I$8+$H$8*T8^$K$8)/($I$8+T8^$K$8)","v":8.2715850302269897E-2},null,null,0.93734902286811883,-1.8800439734837295E-3,6.2650977131881114E-2,7.0374370890269669E-4]
[6,1.35,0.13100000000000001,-3.9948385766114258E-4,0.13139948385766115,1.2145203911508622E-6,null,null,null,null,null,null,null,null,null,null,null,null,3,0.04,8.2715850302269897E-2,null,null,0.97101569428667478,-9.0100661333074035E-4,2.8984305713325168E-2,4.2346598182232964E-4,"inv(Q0)"]
[7,1.43,0.13200000000000001,-1.6219979962625586E-4,0.13216219979962626,1.9906429401663112E-7,null,{"$f":"IF(ISNUMBER(H13),H$8-1.96*H$13,\"N/A\")","v":0.13066000240419332},{"$f":"IF(ISNUMBER(I13),I$8-1.96*I$13,\"N/A\")","v":0.4106145160200203},{"$f":"IF(ISNUMBER(J13),J$8-1.96*J$13,\"N/A\")","v":6.9212552454293905E-2},{"$f":"IF(ISNUMBER(K13),K$8-1.96*K$13,\"N/A\")","v":8.4754094524384271},"Lower 95% Confidence Levels",null,"4. Press the button below to run solver with current settings",null,null,null,null,4,0.06,8.2715850302269897E-2,null,null,0.9862283868456253,-4.3481161939946998E-4,1.3771613154374779E-2,2.4356055786262099E-4,{"$f":"MINVERSE(AB4:AE7)","v":1.2457493592415296},-386.86414713129386,-4.9475509883807458,-2148.8629727777015]
[8,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),H$8+1.96*H$13,\"N/A\")","v":0.13504532681796652},{"$f":"IF(ISNUMBER(I14),I$8+1.96*I$13,\"N/A\")","v":2.7215740768887549},{"$f":"IF(ISNUMBER(J14),J$8+1.96*J$13,\"N/A\")","v":9.6219148150245862E-2},{"$f":"IF(ISNUMBER(K14),K$8+1.96*K$13,\"N/A\")","v":17.916542155167132},"Upper 95% Confidence Levels",null,null,null,null,null,null,5,0.08,8.2715850302269994E-2,null,null,"","","","",-386.86414713129312,345948.86550954869,3982.2824671534922,1296123.1834719926]
[9,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,6,0.1,8.2715850302271937E-2,null,null,"","","","",-4.9475509883807369,3982.2824671534931,47.246202239664036,15233.307499197426]
[10,null,null,"","","",null,{"$f":"IF(ISNUMBER(AB10),SQRT(AB10)*$AI$5,\"N/A\")","v":1.1187052075952012E-3},{"$f":"IF(ISNUMBER(AC11),SQRT(AC11)*$AI$5,\"N/A\")","v":0.58953050022161602},{"$f":"IF(ISNUMBER(AD12),SQRT(AD12)*$AI$5,\"N/A\")","v":6.8894376775387664E-3},{"$f":"IF(ISNUMBER(AE13),SQRT(AE13)*$AI$5,\"N/A\")","v":2.4084522200838538},"Standard Errors",null,null,null,null,null,null,7,0.12,8.2715850302292504E-2,null,null,"","","","",-2148.8629727776993,1296123.1834719933,15233.307499197432,5773981.9648524057]
[11,null,null,"","","",null,{"$f":"IF(ISNUMBER(H13),H8/H13,\"N/A\")","v":118.75573985810219},{"$f":"IF(ISNUMBER(I13),I8/I13,\"N/A\")","v":2.6565110640851697},{"$f":"IF(ISNUMBER(J13),J8/J13,\"N/A\")","v":12.006183113020032},{"$f":"IF(ISNUMBER(K13),K8/K13,\"N/A\")","v":5.4790274408447024},"t-Statistics",null,"5. Solver will attempt to minimize SSE (red cell) by changing cells H8:K8",null,null,null,null,8,0.14000000000000001,8.2715850302442731E-2,null,null,"","","",""]
[12,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),2*TDIST(ABS(H14),$AG$5-$AH$5,1),\"N/A\")","v":1.3164248363772986E-6},{"$f":"IF(ISNUMBER(I14),2*TDIST(ABS(I14),$AG$5-$AH$5,1),\"N/A\")","v":7.6566465927905308E-2},{"$f":"IF(ISNUMBER(J14),2*TDIST(ABS(J14),$AG$5-$AH$5,1),\"N/A\")","v":1.2431246496133993E-3},{"$f":"IF(ISNUMBER(K14),2*TDIST(ABS(K14),$AG$5-$AH$5,1),\"N/A\")","v":1.1955972058680176E-2},"p-values",null,null,null,null,null,null,9,0.16,8.2715850303276647E-2,null,null,"","","",""]
[13,null,null,"","","",null,{"$f":"1-L8/(SUMPRODUCT(C4:C103,C4:C103)-COUNT(C4:C103)*AVERAGE(C4:C103)^2)","v":0.9975009520225131},null,null,null,"Goodness of Fit (R2)",null,null,null,null,null,null,10,0.18,8.2715850307033462E-2,null,null,"","","",""]
[14,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,11,0.2,8.2715850321401316E-2,null,null,"","","",""]
[15,null,null,"","","",null,"Functional Form",null,null,null,null,null,null,null,null,null,null,12,0.22,8.2715850369562041E-2,null,null,"","","",""]
[16,null,null,"","","",null," y =","Intercept×Rate Constant + Maximum×XKinetic Order",null,null,null,null,null,null,null,null,null,13,0.24,8.2715850514409314E-2,null,null,"","","",""]
[17,null,null,"","","",null,null,"Rate Constant + XKinetic Order",null,null,null,null,null,null,null,null,null,14,0.26,8.2715850912285963E-2,null,null,"","","",""]
[18,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,15,0.28000000000000003,8.2715851924265116E-2,null,null,"","","",""]
[19,null,null,"",{"$f":"IF(ISBLANK(B22),\"\",($J$8*$I$8+$H$8*B22^$K$8)/($I$8+B22^$K$8))","v":""},{"$f":"IF(ISBLANK(B22),\"\",D22^2/E22)","v":""},null,null,null,null,null,null,null,null,null,null,null,null,16,0.3,8.2715854333555064E-2,null,null,"","","",""]
[20,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,17,0.32,8.2715859749616136E-2,null,null,"","","",""]
[21,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,18,0.34,8.2715871327742732E-2,null,null,"","","",""]
[22,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,19,0.36,8.2715895003242876E-2,null,null,"","","",""]
[23,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,20,0.38,8.2715941539595356E-2,null,null,"","","",""]
[24,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,21,0.4,8.2716029829589435E-2,null,null,"","","",""]
[25,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,22,0.42,8.2716192079101206E-2,null,null,"","","",""]
[26,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,23,0.44,8.2716481758865298E-2,null,null,"","","",""]
[27,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,24,0.46,8.2716985547015745E-2,null,null,"","","",""]
[28,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,25,0.48,8.2717840923654362E-2,null,null,"","","",""]
[29,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,26,0.5,8.2719261640158762E-2,null,null,"","","",""]
[30,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,27,0.52,8.2721573994052999E-2,null,null,"","","",""]
[31,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,28,0.54,8.2725267718681494E-2,null,null,"","","",""]
[32,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,29,0.56000000000000005,8.2731066365363468E-2,null,null,"","","",""]
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[35,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,32,0.62,8.2774092772320368E-2,null,null,"","","",""]
[36,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,33,{"$f":"$S$4+(S39-1)*($T$4-$S$4)/($U$4-1)","v":0.64},8.2804347027742572E-2,null,null,"","","",""]
[37,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,34,0.66,8.2848557326288583E-2,null,null,"","","",""]
[38,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,35,0.68,8.2912378460097927E-2,null,null,"","","",""]
[39,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,36,0.7,8.3003429899773093E-2,null,null,"","","",""]
[40,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,37,0.72,8.3131840868758231E-2,null,null,"","","",""]
[41,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,38,0.74,8.3310880047154048E-2,null,null,"","","",""]
[42,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,39,0.76,8.3557641183741843E-2,null,null,"","","",""]
[43,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,40,0.78,8.3893719677666567E-2,null,null,"","","",""]
[44,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,41,0.8,8.4345759721334332E-2,null,null,"","","",""]
[45,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,42,0.82,8.494567467385046E-2,null,null,"","","",""]
[46,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,43,0.84,8.5730250532904992E-2,null,null,"","","",""]
[47,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,44,0.86,8.673975567540472E-2,null,null,"","","",""]
[48,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,45,0.88,8.8015148111121183E-2,null,null,"","","",""]
[49,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,46,0.9,8.9593574199492584E-2,null,null,"","","",""]
[50,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,47,0.92,9.1502184103647743E-2,null,null,"","","",""]
[51,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,48,0.94,9.375089924632625E-2,null,null,"","","",""]
[52,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,49,0.96,9.6325562262337946E-2,null,null,"","","",""]
[53,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,50,0.98,9.9183559078979799E-2,null,null,"","","",""]
[54,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,51,1,0.10225403110025726,null,null,"","","",""]
[55,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,52,1.02,0.10544381535411787,null,null,"","","",""]
[56,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,53,1.04,0.10864840860903076,null,null,"","","",""]
[57,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,54,1.06,0.11176535838762673,null,null,"","","",""]
[58,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,55,1.08,0.11470657856092219,null,null,"","","",""]
[59,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,56,1.1000000000000001,0.11740667691779633,null,null,"","","",""]
[60,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,57,1.1200000000000001,0.11982605448071124,null,null,"","","",""]
[61,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,58,1.1399999999999999,0.12194932303425229,null,null,"","","",""]
[62,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,59,1.1599999999999999,0.12378068747775617,null,null,"","","",""]
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[null,"Fitting the Three-Parameter Logistics Model to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
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[null,"Fitting the Four-Parameter Logistics Model to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
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[5,1.27,0.13100000000000001,2.1628083986039437E-3,0.12883719160139606,46.372127227791566,0,0.13631287685234869,-5.8645794762242698,0.19309650352156971,5.4050063511972892,{"$f":"SUMPRODUCT(D4:D53,D4:D53)","v":1.1009394519604593E-5},null,null,null,null,null,null,2,6.9500000000000006E-2,{"$f":"($H$8+($I$8*(1+$J$8)-$H$8)*EXP(-$K$8*$T8))/(1+$J$8*EXP(-$K$8*$T8))","v":-4.2054149636157572},null,null,0.99875423773480621,1.2457622651937577E-3,-6.2579785476888214E-3,9.4922060624259182E-3]
[6,1.35,0.13100000000000001,-4.6119188415727486E-4,{"$f":"IF(ISBLANK(B9),\"\",IF(B9<$J$8,($H$8+$I$8*($J$8-B9)^2),$H$8))","v":0.13631287685234869},{"$f":"IF(ISBLANK(B9),\"\",D9^2/E9)","v":1.5603658210729957E-6},null,null,null,null,null,null,null,null,null,null,null,null,3,8.8999999999999996E-2,-3.8174095265504522,null,null,0.99919150608230733,8.0849391769275466E-4,-4.063177116096898E-3,6.5489176653536121E-3,"inv(Q0)"]
[7,1.43,0.13200000000000001,-1.1642340963886888E-3,0.13631287685234869,9.9436022662933939E-6,null,{"$f":"IF(ISNUMBER(H13),H$8-1.96*H$13,\"N/A\")","v":0.12336869753367982},{"$f":"IF(ISNUMBER(I13),I$8-1.96*I$13,\"N/A\")","v":-1861.7407609842835},{"$f":"IF(ISNUMBER(J13),J$8-1.96*J$13,\"N/A\")","v":-382.79503685142959},{"$f":"IF(ISNUMBER(K13),K$8-1.96*K$13,\"N/A\")","v":-5.0904809349473732},"Lower 95% Confidence Levels",null,"4. Press the button below to run solver with current settings",null,null,null,null,4,0.1085,-3.460269270537248,null,null,0.99947530424298547,5.2469575701448933E-4,-2.6376664982060236E-3,4.5021767868667437E-3,{"$f":"MINVERSE(AB4:AE7)","v":11.884877740907832},-1536424.1812712376,-317831.89721490128,-9253.4123490877646]
[8,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),H$8+1.96*H$13,\"N/A\")","v":0.14925705617101756},{"$f":"IF(ISNUMBER(I14),I$8+1.96*I$13,\"N/A\")","v":1850.0116020318351},{"$f":"IF(ISNUMBER(J14),J$8+1.96*J$13,\"N/A\")","v":383.18122985847276},{"$f":"IF(ISNUMBER(K14),K$8+1.96*K$13,\"N/A\")","v":15.900493637341953},"Upper 95% Confidence Levels",null,null,null,null,null,null,5,0.128,-3.1322062568823092,null,null,"","","","",-1536424.181280615,244311366697.06125,50416531708.713219,1356569031.0892649]
[9,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,6,0.14750000000000002,-2.8314151508771337,null,null,"","","","",-317831.89721681917,50416531708.709106,10404382568.947128,280251094.58825552]
[10,null,null,"","","",null,{"$f":"IF(ISNUMBER(AB10),SQRT(AB10)*$AI$5,\"N/A\")","v":6.6041731217698334E-3},{"$f":"IF(ISNUMBER(AC11),SQRT(AC11)*$AI$5,\"N/A\")","v":946.87560281023434},{"$f":"IF(ISNUMBER(AD12),SQRT(AD12)*$AI$5,\"N/A\")","v":195.40210885456693},{"$f":"IF(ISNUMBER(AE13),SQRT(AE13)*$AI$5,\"N/A\")","v":5.3548404521146233},"Standard Errors",null,null,null,null,null,null,7,0.16699999999999998,-2.5561005103470134,null,null,"","","","",-9253.4123491164428,1356569031.0855138,280251094.58750427,7813594.8938542539]
[11,null,null,"","","",null,{"$f":"IF(ISNUMBER(H13),H8/H13,\"N/A\")","v":20.640415437174152},{"$f":"IF(ISNUMBER(I13),I8/I13,\"N/A\")","v":-6.1936113453750106E-3},{"$f":"IF(ISNUMBER(J13),J8/J13,\"N/A\")","v":9.8820071417594977E-4},{"$f":"IF(ISNUMBER(K13),K8/K13,\"N/A\")","v":1.0093683275031762},"t-Statistics",null,"5. Solver will attempt to minimize SSE (red cell) by changing cells H8:K8",null,null,null,null,8,0.1865,-2.3044990635884042,null,null,"","","",""]
[12,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),2*TDIST(ABS(H14),$AG$5-$AH$5,1),\"N/A\")","v":2.4868964768589197E-4},{"$f":"IF(ISNUMBER(I14),2*TDIST(ABS(I14),$AG$5-$AH$5,1),\"N/A\")","v":0.99544708294284723},{"$f":"IF(ISNUMBER(J14),2*TDIST(ABS(J14),$AG$5-$AH$5,1),\"N/A\")","v":0.99927356868004003},{"$f":"IF(ISNUMBER(K14),2*TDIST(ABS(K14),$AG$5-$AH$5,1),\"N/A\")","v":0.387146563569015},"p-values",null,null,null,null,null,null,9,0.20600000000000002,-2.0748973938151987,null,null,"","","",""]
[13,null,null,"","","",null,{"$f":"1-L8/(SUMPRODUCT(C4:C103,C4:C103)-COUNT(C4:C103)*AVERAGE(C4:C103)^2)","v":0.99087114882288185},null,null,null,"Goodness of Fit (R2)",null,null,null,null,null,null,10,0.22550000000000003,-1.8656455105248033,null,null,"","","",""]
[14,null,null,"","","",null,null,null,null,null,null,null,"Note: The four-parameter logistics model reduces to the three-parameter version on the previous worksheet by restricting Shape = Maximum/Intercept – 1 ",null,null,null,null,11,0.245,-1.6751668148683885,null,null,"","","",""]
[15,null,null,"","","",null,"Functional Form",null,null,null,null,null,null,null,null,null,null,12,0.26450000000000001,-1.501964964961171,null,null,"","","",""]
[16,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,13,0.28399999999999997,-1.3446281259418384,null,null,"","","",""]
[17,null,null,"","","",null,"y =","Maximum + [Intercept×(1 + Shape) – Maximum]e–Scale×X",null,null,null,null,null,null,null,null,null,14,0.30349999999999999,-1.2018310551290492,null,null,"","","",""]
[18,null,null,"","","",null,null,"1 + Shape×e–Scale×X",null,null,null,null,null,null,null,null,null,15,0.32300000000000001,-1.0723354302075854,null,null,"","","",""]
[19,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,16,0.34249999999999997,-0.95498878218052752,null,null,"","","",""]
[20,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,17,0.36199999999999999,-0.84872234794250445,null,null,"","","",""]
[21,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,18,0.38149999999999995,-0.75254811194311821,null,null,"","","",""]
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[28,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,25,0.51800000000000002,-0.2941004615454394,null,null,"","","",""]
[29,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,26,0.53749999999999998,-0.25149508285987016,null,null,"","","",""]
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[null,null,null,null,{"$f":"SUM(E4:E103)","v":0.84799890218365925},{"$f":"SUM(F4:F103)","v":46.372183173669079},null,null,null,null,null,null,null,null,null,null,null,null,98,{"$f":"$S$4+(S104-1)*($T$4-$S$4)/($U$4-1)","v":1.9415},0.13611450454762727,null,null,"","","",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,99,{"$f":"$S$4+(S105-1)*($T$4-$S$4)/($U$4-1)","v":1.9610000000000001},0.13613434830754312,null,null,"","","",""]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,101,{"$f":"$S$4+(S107-1)*($T$4-$S$4)/($U$4-1)","v":2},0.1361682793306242,null,null,"","","",""]

{"sheet":"RNB, Model 1","index":10,"n_rows":107,"n_cols":35,"rows_kept":107,"cut":false,"hidden":false,"merged":[[13,13,14,15],[7,13,8,16],[2,32,3,32],[2,33,3,33],[2,13,2,15],[2,27,2,29],[8,27,8,29],[4,13,6,16],[1,1,1,3],[1,7,1,10],[5,7,5,11],[2,34,3,34],[4,18,4,20],[1,18,1,20],[1,23,1,25],[15,7,15,10],[17,7,17,11],[18,9,18,10],[19,9,19,10],[18,7,19,8]]}
[null,"Fitting the RNB Model 1 to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
["Point","Input","Output","Residuals","Expected","Qm",null,"Min Input",{"$f":"MIN(B4:B103)","v":0.95},"Min Output",{"$f":"MIN(C4:C103)","v":9.5000000000000001E-2},null,null,"Instructions",null,null,null,null,"Min Input","Max Input","# of Points",null,null,"Lower Asymptote(X0)","Range(X1)","r(X2)","s(X3)","Q0",null,null,null,null,"Number of Observations, T","Number of Regressors, K","sigma"]
[1,0.95,9.5000000000000001E-2,{"$f":"IF(ISBLANK(B4),\"\",C4-($H$8+$I$8/(1+EXP($J$8+$K$8*B4))))","v":6.2851712175751584E-4},{"$f":"IF(ISBLANK(B4),\"\",($H$8+$I$8/(1+EXP($J$8+$K$8*B4))))","v":9.4371482878242485E-2},{"$f":"IF(ISBLANK(B4),\"\",D4^2/E4)","v":4.1859443159542402E-6},null,"Max Input",{"$f":"MAX(B4:B103)","v":1.43},"Max Output",{"$f":"MAX(C4:C103)","v":0.13200000000000001},null,null,"1. Copy data in cells B4:C103",null,null,null,null,0.1,{"$f":"CEILING(I4,1)","v":2},101,null,null,{"$f":"IF(ISBLANK(B4),\"\",1)","v":1},{"$f":"IF(ISBLANK($B4),\"\",1/(1+EXP($J$8+$K$8*$B4)))","v":0.98251730111771063},{"$f":"IF(ISBLANK($B4),\"\",-$I$8*EXP($J$8+$K$8*$B4)/(1+EXP($J$8+$K$8*$B4))^2)","v":-4.1400951682892581E-2},{"$f":"IF(ISBLANK($B4),\"\",-$I$8*B4*EXP($J$8+$K$8*$B4)/(1+EXP($J$8+$K$8*$B4))^2)","v":-3.9330904098747954E-2},{"$f":"SUMPRODUCT(X$4:X$103,X$4:X$103)","v":7},{"$f":"SUMPRODUCT(X$4:X$103,Y$4:Y$103)","v":6.9520356772329563},{"$f":"SUMPRODUCT(X$4:X$103,Z$4:Z$103)","v":-0.11432016472974352},{"$f":"SUMPRODUCT(X$4:X$103,AA$4:AA$103)","v":-0.12250221598421797}]
[{"$f":"A4+1","v":2},1.03,0.107,{"$f":"IF(ISBLANK(B5),\"\",C5-($H$8+$I$8/(1+EXP($J$8+$K$8*B5))))","v":-1.8916019808738888E-3},{"$f":"IF(ISBLANK(B5),\"\",($H$8+$I$8/(1+EXP($J$8+$K$8*B5))))","v":0.10889160198087389},{"$f":"IF(ISBLANK(B5),\"\",D5^2/E5)","v":3.2859816450073901E-5},null,null,null,null,null,null,null,"2. View the data and estimate values for the lower asymptote and the range in cells H8 and I8",null,null,null,null,"Prediction",null,null,null,null,{"$f":"IF(ISBLANK(B5),\"\",1)","v":1},{"$f":"IF(ISBLANK($B5),\"\",1/(1+EXP($J$8+$K$8*$B5)))","v":0.98854162813307289},{"$f":"IF(ISBLANK($B5),\"\",-$I$8*EXP($J$8+$K$8*$B5)/(1+EXP($J$8+$K$8*$B5))^2)","v":-2.7301060374497164E-2},{"$f":"IF(ISBLANK($B5),\"\",-$I$8*B5*EXP($J$8+$K$8*$B5)/(1+EXP($J$8+$K$8*$B5))^2)","v":-2.8120092185732078E-2},{"$f":"SUMPRODUCT(Y$4:Y$103,X$4:X$103)","v":6.9520356772329563},{"$f":"SUMPRODUCT(Y$4:Y$103,Y$4:Y$103)","v":6.9046047951641407},{"$f":"SUMPRODUCT(Y$4:Y$103,Z$4:Z$103)","v":-0.11305234918864182},{"$f":"SUMPRODUCT(Y$4:Y$103,AA$4:AA$103)","v":-0.12122333245522755},null,{"$f":"COUNT(B4:B53)","v":7},4,{"$f":"SQRT(L8/(AG5-AH5))","v":1.9080388991258841E-3}]
[3,1.1100000000000001,0.11899999999999999,5.5357297433267227E-4,0.11844642702566732,2.5871868456202166E-6,null,"Regression",null,null,null,null,null,null,null,null,null,null,"Point","Input","Output",null,null,1,0.99250587871790286,-1.7927323085905691E-2,-1.989932862535532E-2,{"$f":"SUMPRODUCT(Z$4:Z$103,X$4:X$103)","v":-0.11432016472974352},{"$f":"SUMPRODUCT(Z$4:Z$103,Y$4:Y$103)","v":-0.11305234918864182},{"$f":"SUMPRODUCT(Z$4:Z$103,Z$4:Z$103)","v":3.0132503863793173E-3},{"$f":"SUMPRODUCT(Z$4:Z$103,AA$4:AA$103)","v":3.0407215035104392E-3}]
[4,1.19,0.125,2.8806130704017718E-4,0.12471193869295982,6.6536786680856518E-7,null,"Lower Asymptote","Range","r","s","SSE",null,null,null,null,null,null,1,{"$f":"$S$4+(S7-1)*($T$4-$S$4)/($U$4-1)","v":0.1},{"$f":"$H$8+$I$8/(1+EXP($J$8+$K$8*T7))","v":-1.3778943352190769},null,null,1,0.99510540913053547,-1.1739433039141059E-2,-1.3969925316577859E-2,{"$f":"SUMPRODUCT(AA$4:AA$103,X$4:X$103)","v":-0.12250221598421797},{"$f":"SUMPRODUCT(AA$4:AA$103,Y$4:Y$103)","v":-0.12122333245522755},{"$f":"SUMPRODUCT(AA$4:AA$103,Z$4:Z$103)","v":3.0407215035104392E-3},{"$f":"SUMPRODUCT(AA$4:AA$103,AA$4:AA$103)","v":3.0913543118320759E-3}]
[5,1.27,0.13100000000000001,2.1889110952935109E-3,0.12881108890470649,3.7196578523170702E-5,null,-2.2737383817166963,2.4102474957957276,1.0607654445393464,-5.3575490955771823,{"$f":"SUMPRODUCT(D4:D53,D4:D53)","v":1.0921837321732548E-5},null,"3. Guess r and s values in cells G8 and I8 until the predicted line is close to the observed points",null,null,null,null,2,0.11900000000000001,{"$f":"$H$8+$I$8/(1+EXP($J$8+$K$8*T8))","v":-1.3198897256264366},null,null,1,0.99680612667879442,-7.6734386570942465E-3,-9.7452670945096936E-3]
[6,1.35,0.13100000000000001,-4.8889364062243423E-4,0.13148889364062244,1.8177732371398972E-6,null,null,null,null,null,null,null,null,null,null,null,null,3,0.13800000000000001,-1.260641876720406,null,null,1,0.99791713488047784,-5.0097639963651861E-3,-6.7631813950930026E-3,"inv(Q0)"]
[7,1.43,0.13200000000000001,-1.2364765933404742E-3,0.13323647659334048,1.1474893399840038E-5,null,{"$f":"IF(ISNUMBER(H13),H$8-1.96*H$13,\"N/A\")","v":-306.44792444476553},{"$f":"IF(ISNUMBER(I13),I$8-1.96*I$13,\"N/A\")","v":-301.77595729905863},{"$f":"IF(ISNUMBER(J13),J$8-1.96*J$13,\"N/A\")","v":-136.8295455029276},{"$f":"IF(ISNUMBER(K13),K$8-1.96*K$13,\"N/A\")","v":-15.793254889087301},"Lower 95% Confidence Levels",null,"4. Press the button below to run solver with current settings",null,null,null,null,4,0.157,-1.2004260125798658,null,null,1,0.9986421985744619,-3.2681938938475949E-3,-4.6735172682020607E-3,{"$f":"MINVERSE(AB4:AE7)","v":6615430598.4987669},-6615691990.6299191,2998709318.8690305,-223061297.64526817]
[8,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),H$8+1.96*H$13,\"N/A\")","v":301.9004476813322},{"$f":"IF(ISNUMBER(I14),I$8+1.96*I$13,\"N/A\")","v":306.59645229065006},{"$f":"IF(ISNUMBER(J14),J$8+1.96*J$13,\"N/A\")","v":138.95107639200631},{"$f":"IF(ISNUMBER(K14),K$8+1.96*K$13,\"N/A\")","v":5.0781566979329362},"Upper 95% Confidence Levels",null,null,null,null,null,null,5,0.17599999999999999,-1.1395365524750494,null,null,"","","","",-6615691990.6299849,6615953395.373661,-2998828438.0225196,223070823.24785894]
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[10,null,null,"","","",null,{"$f":"IF(ISNUMBER(AB10),SQRT(AB10)*$AI$5,\"N/A\")","v":155.19091125665759},{"$f":"IF(ISNUMBER(AC11),SQRT(AC11)*$AI$5,\"N/A\")","v":155.19704326268078},{"$f":"IF(ISNUMBER(AD12),SQRT(AD12)*$AI$5,\"N/A\")","v":70.35219946299334},{"$f":"IF(ISNUMBER(AE13),SQRT(AE13)*$AI$5,\"N/A\")","v":5.3243396905663873},"Standard Errors",null,null,null,null,null,null,7,0.214,-1.0169765534919222,null,null,"","","","",-223061297.6700002,223070823.27258971,-101352703.01032157,7786764.8927891897]
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[12,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),2*TDIST(ABS(H14),$AG$5-$AH$5,1),\"N/A\")","v":0.98923031539152073},{"$f":"IF(ISNUMBER(I14),2*TDIST(ABS(I14),$AG$5-$AH$5,1),\"N/A\")","v":0.98858425096747893},{"$f":"IF(ISNUMBER(J14),2*TDIST(ABS(J14),$AG$5-$AH$5,1),\"N/A\")","v":0.98891669625752976},{"$f":"IF(ISNUMBER(K14),2*TDIST(ABS(K14),$AG$5-$AH$5,1),\"N/A\")","v":0.38843115872084949},"p-values",null,null,null,null,null,null,9,0.252,-0.89547741154201632,null,null,"","","",""]
[13,null,null,"","","",null,{"$f":"1-L8/(SUMPRODUCT(C4:C103,C4:C103)-COUNT(C4:C103)*AVERAGE(C4:C103)^2)","v":0.99094375014781722},null,null,null,"Goodness of Fit (R2)",null,null,null,null,null,null,10,0.27100000000000002,-0.83589371494477249,null,null,"","","",""]
[14,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,11,0.29000000000000004,-0.7774688815170121,null,null,"","","",""]
[15,null,null,"","","",null,"Functional Form",null,null,null,null,null,null,null,null,null,null,12,0.309,-0.72046218527831685,null,null,"","","",""]
[16,null,null,"","","",null," y =Lower Asymptote +",null,"Range",null,null,null,null,null,null,null,null,13,0.32799999999999996,-0.66510621442503481,null,null,"","","",""]
[17,null,null,"","","",null,null,null,"1 + er + s×X",null,null,null,null,null,null,null,null,14,0.34699999999999998,-0.61160376648674708,null,null,"","","",""]
[18,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,15,0.36599999999999999,-0.56012581987148757,null,null,"","","",""]
[19,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,16,0.38500000000000001,-0.51081057162037591,null,null,"","","",""]
[20,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,17,0.40400000000000003,-0.46376347645127258,null,null,"","","",""]
[21,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,18,0.42299999999999993,-0.419058178330175,null,null,"","","",""]
[22,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,19,0.44199999999999995,-0.37673819486922211,null,null,"","","",""]
[23,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,20,0.46099999999999997,-0.3368191972508523,null,null,"","","",""]
[24,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,21,0.48,-0.29929172323002118,null,null,"","","",""]
[25,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,22,0.499,-0.2641241662116034,null,null,"","","",""]
[26,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,23,0.51800000000000002,-0.23126589701187195,null,null,"","","",""]
[27,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,24,0.53699999999999992,-0.20065039407656515,null,null,"","","",""]
[28,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,25,0.55599999999999994,-0.17219828014871918,null,null,"","","",""]
[29,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,26,0.57499999999999996,-0.14582018649729411,null,null,"","","",""]
[30,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,27,0.59399999999999997,-0.12141938812735686,null,null,"","","",""]
[31,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,28,0.61299999999999999,-9.8894173679890951E-2,null,null,"","","",""]
[32,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,29,0.6319999999999999,-7.8139931245088778E-2,null,null,"","","",""]
[33,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,30,0.65099999999999991,-5.9050945707376901E-2,null,null,"","","",""]
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[35,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,32,0.68899999999999995,-2.544919673081969E-2,null,null,"","","",""]
[36,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,33,{"$f":"$S$4+(S39-1)*($T$4-$S$4)/($U$4-1)","v":0.70799999999999996},-1.0731816910632741E-2,null,null,"","","",""]
[37,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,34,0.72699999999999998,2.7277533739917814E-3,null,null,"","","",""]
[38,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,35,0.74599999999999989,1.5023009312352009E-2,null,null,"","","",""]
[39,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,36,0.76500000000000001,2.6242996810966535E-2,null,null,"","","",""]
[40,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,37,0.78399999999999992,3.647204128914483E-2,null,null,"","","",""]
[41,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,38,0.80299999999999994,4.5789597826001227E-2,null,null,"","","",""]
[42,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,39,0.82199999999999995,5.4270201128255202E-2,null,null,"","","",""]
[43,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,40,0.84099999999999997,6.1983496020740159E-2,null,null,"","","",""]
[44,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,41,0.86,6.899433147341627E-2,null,null,"","","",""]
[45,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,42,0.87899999999999989,7.5362903454970542E-2,null,null,"","","",""]
[46,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,43,0.89799999999999991,8.1144934064865115E-2,null,null,"","","",""]
[47,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,44,0.91700000000000004,8.6391876392872824E-2,null,null,"","","",""]
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[null,"Fitting the RNB Model 2 to Nutritional Response Data"]
[null,"Data",null,null,null,null,null,"Sample Statistics",null,null,null,null,null,null,null,null,null,null,"Plotting Parameters",null,null,null,null,"Error Analysis"]
["Point","Input","Output","Residuals","Expected","Qm",null,"Min Input",{"$f":"MIN(B4:B103)","v":0.95},"Min Output",{"$f":"MIN(C4:C103)","v":9.5000000000000001E-2},null,null,"Instructions",null,null,null,null,"Min Input","Max Input","# of Points",null,null,"Intercept(X0)","Maximum(X1)","c(X2)","Q0",null,null,null,"Number of Observations, T","Number of Regressors, K","sigma"]
[1,0.95,9.5000000000000001E-2,{"$f":"IF(ISBLANK(B4),\"\",C4-($H$8+$I$8*(1-EXP(B4*$J$8))))","v":4.7566630056053438E-4},{"$f":"IF(ISBLANK(B4),\"\",($H$8+$I$8*(1-EXP(B4*$J$8))))","v":9.4524333699439467E-2},{"$f":"IF(ISBLANK(B4),\"\",D4^2/E4)","v":2.3936527308236014E-6},null,"Max Input",{"$f":"MAX(B4:B103)","v":1.43},"Max Output",{"$f":"MAX(C4:C103)","v":0.13200000000000001},null,null,"1. Copy data in cells B4:C103",null,null,null,null,0.05,{"$f":"CEILING(I4,1)","v":2},101,null,null,{"$f":"IF(ISBLANK($B4),\"\",1)","v":1},{"$f":"IF(ISBLANK($B4),\"\",(1-EXP($J$8*$B4)))","v":0.99238068181265471},{"$f":"IF(ISBLANK($B4),\"\",-B4*$I$8*EXP($J$8*$B4))","v":-4.0438396290148948E-2},{"$f":"SUMPRODUCT(X$4:X$103,X$4:X$103)","v":7},{"$f":"SUMPRODUCT(X$4:X$103,Y$4:Y$103)","v":6.9786546458518197},{"$f":"SUMPRODUCT(X$4:X$103,Z$4:Z$103)","v":-0.12807832607071765}]
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[3,1.1100000000000001,0.11899999999999999,6.3042293910187119E-4,0.11836957706089812,3.3575610559237904E-6,null,"Regression",null,null,null,null,null,null,null,null,null,null,"Point","Input","Output",null,null,1,0.99664890922617366,-2.0780853428849101E-2,{"$f":"SUMPRODUCT(Z$4:Z$103,X$4:X$103)","v":-0.12807832607071765},{"$f":"SUMPRODUCT(Z$4:Z$103,Y$4:Y$103)","v":-0.12749483975041864},{"$f":"SUMPRODUCT(Z$4:Z$103,Z$4:Z$103)","v":3.3213636185354003E-3}]
[4,1.19,0.125,3.2475432346057431E-4,0.12467524567653943,8.4592069607753033E-7,null,"Intercept","Range","c","SSE",null,null,"3. Guess values of Maximum and c in cells I8 and J8 until the predicted line is close to the observed points",null,null,null,null,1,{"$f":"$S$4+(S7-1)*($T$4-$S$4)/($U$4-1)","v":0.05},{"$f":"$H$8+$I$8*(1-EXP(T7*$J$8))","v":-4.1848228148044164},null,null,1,0.99777760509385127,-1.4774826942279405E-2,"inv(Q0)"]
[5,1.27,0.13100000000000001,2.1429261495666818E-3,0.12885707385043332,3.5637410855898014E-5,null,-5.4495942364786067,5.5866853031150452,-5.1337562000139032,{"$f":"SUMPRODUCT(D4:D53,D4:D53)","v":1.1343420464536879E-5},null,null,null,null,null,null,null,2,6.9500000000000006E-2,{"$f":"$H$8+$I$8*(1-EXP(T8*$J$8))","v":-3.7731150441304599},null,null,1,0.99852613985945948,-1.0457170838226131E-2,{"$f":"MINVERSE(AA4:AC6)","v":6608935.0100483326},-6605232.8971714331,1303146.5250996316]
[6,1.35,0.13100000000000001,-6.3040177835493871E-4,0.13163040177835494,3.0191080235570474E-6,null,null,null,null,null,null,null,null,null,null,null,null,3,8.8999999999999996E-2,-3.4006267704393567,null,null,1,0.99902255728364742,-7.3718975584132042E-3,-6605232.8971714331,6601533.3427459439,-1302397.9405247457]
[7,1.43,0.13200000000000001,-1.4696327261495279E-3,0.13346963272614953,1.6182110534470203E-5,null,{"$f":"IF(ISNUMBER(H13),H$8-1.96*H$13,\"N/A\")","v":-13.93482839161906},{"$f":"IF(ISNUMBER(I13),I$8-1.96*I$13,\"N/A\")","v":-2.8937960079955918},{"$f":"IF(ISNUMBER(J13),J$8-1.96*J$13,\"N/A\")","v":-6.8101723975883983},"Lower 95% Confidence Levels",null,null,"4. Press the button below to run solver with current settings",null,null,null,null,4,0.1085,-3.0636219239914695,null,null,1,0.99935177413550225,-5.1786504917131146E-3,1303146.5250996316,-1302397.9405247457,257968.9969427032]
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[10,null,null,"","","",null,{"$f":"IF(ISNUMBER(AA8),SQRT(AA8)*$AG$5,\"N/A\")","v":4.3292010995614563},{"$f":"IF(ISNUMBER(AB9),SQRT(AB9)*$AG$5,\"N/A\")","v":4.3267761791380801},{"$f":"IF(ISNUMBER(AC10),SQRT(AC10)*$AG$5,\"N/A\")","v":0.85531438651759961},"Standard Errors",null,null,null,null,null,null,null,7,0.16699999999999998,-2.2332855603404234,null,null,"","",""]
[11,null,null,"","","",null,{"$f":"IF(ISNUMBER(H13),H8/H13,\"N/A\")","v":-1.2587990511761269},{"$f":"IF(ISNUMBER(I13),I8/I13,\"N/A\")","v":1.2911888833195773},{"$f":"IF(ISNUMBER(J13),J8/J13,\"N/A\")","v":-6.0021861913441192},"t-Statistics",null,null,"5. Solver will attempt to minimize SSE (red cell) by changing cells H8:J8",null,null,null,null,8,0.1865,-2.0074822464564948,null,null,"","",""]
[12,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),2*TDIST(ABS(H14),$AE$5-$AF$5,1),\"N/A\")","v":0.27656009247022989},{"$f":"IF(ISNUMBER(I14),2*TDIST(ABS(I14),$AE$5-$AF$5,1),\"N/A\")","v":0.26620358754882756},{"$f":"IF(ISNUMBER(J14),2*TDIST(ABS(J14),$AE$5-$AF$5,1),\"N/A\")","v":3.8773562869718519E-3},"p-values",null,null,null,null,null,null,null,9,0.20600000000000002,-1.8031890740330785,null,null,"","",""]
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[null,null,null,null,{"$f":"SUM(E4:E103)","v":0.84038769014564352},{"$f":"SUM(F4:F103)","v":9.3264341711292339E-5},null,null,null,null,null,null,null,null,null,null,null,null,98,{"$f":"$S$4+(S104-1)*($T$4-$S$4)/($U$4-1)","v":1.9415},0.13682897111108439]
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{"sheet":"Multiple Range Tests","index":12,"n_rows":9,"n_cols":12,"rows_kept":9,"cut":false,"hidden":false,"merged":[[2,11,2,13]]}
[]
[null,null,"Multiple"]
[null,null,null,null,null,"Range",null,null,null,null,null,"Instructions:  If there are ordered pairs of data, and the values of x are continuous, then some form of regression best describes the data.  And all points are assumed to have different \"y values\" (responses) as long as the slope is not equal to zero."]
[null,null,null,null,null,null,null,"Tests"]
[null,null,null,"Should NEVER be Used"]
[]
[null,null,null,null,null,"To Determine Nutritional Requirements:"]
[]
[null,null,null,null,"(The Devil Made Me Do It!)"]

{"sheet":"Test Data Generator","index":13,"n_rows":112,"n_cols":16,"rows_kept":112,"cut":false,"hidden":false,"merged":[[1,0,1,12],[2,12,2,15],[10,0,11,0],[2,4,2,8],[3,4,3,9],[10,1,11,1],[3,11,4,11],[7,4,8,9],[6,4,6,9],[4,4,5,9],[10,8,11,8],[10,9,11,9],[10,2,11,2],[10,6,11,6],[10,4,11,4],[10,3,11,3],[10,5,11,5],[17,11,18,11],[13,11,14,11],[15,11,16,11],[5,11,6,11],[7,11,8,11],[9,11,10,11],[10,7,11,7],[11,11,12,11]]}
[null,null,"Random Data Generator"]
["This spreadsheet generates 100 random inputs points in the selected range and then generates outputs by adding random noise around each model. Model parameters can be adjsuted to produce required data. Data can be copied to other spreadsheets for testing the goodness of fit"]
[null,null,null,null,"Instructions",null,null,null,null,null,null,"Model","Parameters"]
[null,"Min","Max",null,"1. Adjust values in cells B4 and C4 for a desired range of inputs",null,null,null,null,null,null,"Broken Line","Max","Rate Constant","Requirement"]
["Range",0,1.25,null,"2. Adjust model parameter in the Table K3:017 to generate corrresponding outputs",null,null,null,null,null,null,null,250,-175,0.75]
[null,null,null,null,null,null,null,null,null,null,null,"Broken Line Quadratic","Max","Rate Constant","Requirement"]
[null,null,null,null,"3. Generated data are ploted on separate graphs for each model",null,null,null,null,null,null,null,250,-250,0.75]
[null,null,null,null,"Note: Data are regenerated every time the spreadsheet changes, e.g. due to saving, changing cells, etc. To force data regeneration, Press F9",null,null,null,null,null,null,"Saturation Kinetics","Max","Rate Constant","Intercept","Kinetic Order"]
[null,null,null,null,null,null,null,null,null,null,null,null,250,0.05,75,8]
[null,null,null,null,null,null,null,null,null,null,null,"Logistics, 3 parameters","Max","Intercept","Scale"]
["Observation","Input","Broken Line","Broken Line Quadratic","Saturation Kinetics","Logistics, 3 Parameters","Logistics, 4 Parameters","Compartmental Model","RNB, Model 1","RNB, Model 2",null,null,250,20,5]
[null,null,null,null,null,null,null,null,null,null,null,"Logistics, 4 parameters","Max","Intercept","Shape","Scale"]
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[2,{"$f":"$B$5+($C$5-$B$5)*RAND()","v":1.0992741153612535},{"$f":"IF($B14<$O$5,$M$5+$N$5*($O$5-$B14),$M$5)+(RAND()-0.5)*0.1*$M$5","v":258.47905608290972},{"$f":"IF($B14<$O$7,$M$7+$N$7*($O$7-$B14)^2,$M$7)+(RAND()-0.5)*0.1*$M$7","v":246.19631852115114},{"$f":"($O$9*$N$9+$M$9*$B14^$P$9)/($N$9+$B14^$P$9)+(RAND()-0.5)*0.1*$M$9","v":234.2515627570962},{"$f":"$M$11*$N$11*EXP($O$11*B14)/($M$11+$N$11*(EXP($O$11*B14)-1))+(RAND()-0.5)*0.1*$M$11","v":228.45058781373271},{"$f":"($M$13+($N$13*(1+$O$13)-$M$13)*EXP(-$P$13*$B14))/(1+$O$13*EXP(-$P$13*$B14))+(RAND()-0.5)*0.1*$M$13","v":239.9246265141158},{"$f":"$M$15*EXP(-$N$15*B14)*(1-EXP(-$O$15*(B14-$P$15)))+(RAND()-0.5)*0.1*$M$15","v":63.901340946041699},{"$f":"$M$17+$N$17/(1+EXP($O$17+$P$17*B14))+(RAND()-0.5)*0.05*($M$17+$N$17)","v":254.084128729252},{"$f":"$M$19+$N$19*(1-EXP($O$19*B14))+(RAND()-0.5)*0.1*($M$19+$N$19)","v":250.18627795528178},null,"Compartmental Model","a","b","c","d"]
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