{"text_format":"1","workbook":"xlsx","n_sheets":7,"sheets":["HOME","Instructions","Levels & Reps","Simulations","Calculations","True Parameters Estimator (BLL)","True Parameters Estimator (BLQ)"],"not_rendered":{"charts":4,"images":12,"macros":1,"external_links":0,"defined_names":257,"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":"HOME","index":0,"n_rows":13,"n_cols":16,"rows_kept":13,"cut":false,"hidden":false,"merged":[[2,8,2,12],[3,8,3,12]]}
[]
[null,"Maximum Ingredient Optimization Workbook"]
[null,null,null,null,null,null,null,null,"\"MIOW\""]
[null,null,null,null,null,null,null,null,"Verson 1.1"]
[]
[null,"A workbook to determine the maximum safe level of feed ingredients"]
[]
[]
[null,null,"Rashed A. Alhotan",null,null,null,null,null,"Dmitry V. Vedenov",null,null,null,null,null,null,"Gene M. Pesti"]
[null,null,"Department of Poultry Science",null,null,null,null,null,"Department of Agricultural Economics",null,null,null,null,null,null,"Department of Poultry Science"]
[null,null,"The University of Georgia",null,null,null,null,null,"Texas A&M University",null,null,null,null,null,null,"The University of Georgia"]
[null,null,"Athens, Georgia 30602",null,null,null,null,null,"College Station, TX 77843",null,null,null,null,null,null,"Athens, Georgia 30602"]
[null,null,"ralhota1@uga.edu",null,null,null,null,null,"vedenov@tamu.edu",null,null,null,null,null,null,"gpesti@uga.edu"]

{"sheet":"Instructions","index":1,"n_rows":16,"n_cols":2,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Instructions for feeding trial planning"]
[null,"1. Make changes in cells C5:C6 and C8:C9"]
[null,"2. Press \"Create Grid\" button"]
[null,"3. If you want to adjust levels, edit directly in corresponding cells"]
[null,"4. Select baseline model which will be used to generate random data"]
[null,"5. Enter \"true\" coefficients of the baseline mode"]
[null,"6. Provide guesses for coefficients for all remaining models (this is necessary to ensure convergence of Solver Routine)"]
[null,"6. Select simulation parameters (number of \"experiments\" and coefficient of variation for random draws)"]
[null,"7. Press \"Run Simulations\""]
[]
[null,"Note: If you end up with poor estimates for a particular model, try to provide more accurate initial guesses for the coefficients"]
[]
[null,"Estimation of the MSL for raw data"]
[]
[null,"Please follow instructions on \"True Parameters Estimator (BLL)\" and \"True Parameters Estimator (BLQ)\" worksheets"]

{"sheet":"Levels & Reps","index":2,"n_rows":27,"n_cols":10,"rows_kept":27,"cut":false,"hidden":false,"merged":[[1,7,1,13],[9,5,9,9],[11,3,26,3]]}
[]
[null,null,null,null,null,null,null,"Experimental Grid"]
[null,"1. Experiment Design"]
[]
[null,"Number of Levels (>1, < 25)",5]
[null,"Number of Reps (max = 20)",16]
[]
[null,"Minimum Ingredient Level",0]
[null,"Maximum Ingredient Level",21]
[null,null,null,null,null,"Levels"]
[null,null,null,null,null,1,2,3,4,5]
[null,null,null,"Replicates",1,0,5.25,10.5,15.75,21]
[null,null,null,null,2,0,5.25,10.5,15.75,21]
[null,null,null,null,3,0,5.25,10.5,15.75,21]
[null," ",null,null,4,0,5.25,10.5,15.75,21]
[null,null,null,null,5,0,5.25,10.5,15.75,21]
[null,null,null,null,6,0,5.25,10.5,15.75,21]
[null,null,null,null,7,0,5.25,10.5,15.75,21]
[null,null,null,null,8,0,5.25,10.5,15.75,21]
[null,null,null,null,9,0,5.25,10.5,15.75,21]
[null,null,null,null,10,0,5.25,10.5,15.75,21]
[null,null,null,null,11,0,5.25,10.5,15.75,21]
[null,null,null,null,12,0,5.25,10.5,15.75,21]
[null,null,null,null,13,0,5.25,10.5,15.75,21]
[null,null,null,null,14,0,5.25,10.5,15.75,21]
[null,null,null,null,15,0,5.25,10.5,15.75,21]
[null,null,null,null,16,0,5.25,10.5,15.75,21]

{"sheet":"Simulations","index":3,"n_rows":140,"n_cols":20,"rows_kept":140,"cut":false,"hidden":false,"merged":[[34,15,34,19],[34,9,34,13],[34,3,34,7],[33,3,33,19],[2,2,2,6],[2,10,2,14],[18,3,18,6],[33,2,35,2],[4,3,4,6],[16,2,16,6],[4,10,4,13],[5,10,5,13],[6,10,6,13]]}
[]
[]
[null,null,"2. Choose One Model to Simulate Experiments From",null,null,null,null,null,null,null,"4. Choose Simulation Parameters"]
[]
[null,null,"Model","True Parameters of the Response Function",null,null,null,null,null,null,"Selected (\"True\") Model",null,null,null,"BLQ"]
[null,null,null,"Max","Rate Constant","Ingredient Level",null,null,null,null,"Number of Experiments (Max = 1000)",null,null,null,100]
[null,null,null,56.1,-18.828384062673344,6,null,null,null,null,"Coefficient of variation",null,null,null,0.05]
[null,null,null,"Max","Rate Constant","Ingredient Level"]
[null,null,null,56.1,-1.74,6]
[null,null,null,"Const","Linear","Quadratic",null,null,null,null,null,null,null,null,null," "]
[null,null,null,2.1821000000000002,1.6000000000000001E-3,-3.0000000000000001E-5]
[]
[]
[]
[]
[]
[null,null,"3. Select up to Three Models to Fit to Simulated Experiments"]
[]
[null,null,"Model","Initial Guesses for the Parameters of Fitted Functions"]
[null,null,null,"Max","Rate Constant","Ingredient Level"]
[null,null,null,56.1,-18.828384062673344,7]
[null,null,null,"Max","Rate Constant","Ingredient Level"]
[null,null,null,56.1,-1.74,5]
[null,null,null,"Const","Linear","Quadratic"]
[null,null,null,2.0122,6.2399999999999997E-2,-2.3E-3]
[]
[]
[]
[]
[]
[]
[null,null,"5. Results"]
[]
[null,null,"Experiment #","Model Fits"]
[null,null,null,"Broken Line Model",null,null,null,null,null,"Broken Line Quadratic Model",null,null,null,null,null,"Quadratic (2nd Order Polynomial)"]
[null,null,null,"Max/Min","Rate Constant","Maximum Safe Level","R-Squared","SE of Requirement",null,"Max/Min","Rate Constant","Maximum Safe Level","R-Squared","SE of Requirement",null,"Const","Linear","Square","Max. Safe Level (Calculated)","R-Squared"]
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[null,null,"Std. Dev.",{"$f":"IF(OR(ISBLANK(D$41),ISNA(D$41),D$41=\"N/A\"),\"N/A\",STDEV(D$41:D$1040))","v":6.0810905106027784},{"$f":"IF(OR(ISBLANK(E$41),ISNA(E$41),E$41=\"N/A\"),\"N/A\",STDEV(E$41:E$1040))","v":4.9090832035403027},1.1575492379212304,3.0924820794270718E-3,7.5987382661326089E-3,null,{"$f":"IF(OR(ISBLANK(J$41),ISNA(J$41),J$41=\"N/A\"),\"N/A\",STDEV(J$41:J$1040))","v":0.51378986572792862},4.2103284561909315E-2,0.11997696503319558,1.0034197566588174E-3,2.7093002758061771E-2,null,{"$f":"IF(OR(ISBLANK(P$41),ISNA(P$41),P$41=\"N/A\"),\"N/A\",STDEV(P$41:P$1040))","v":"N/A"},"N/A","N/A","N/A","N/A"]
[null,null,"Lower 95%",{"$f":"IF(OR(ISBLANK(D$41),ISNA(D$41),D$41=\"N/A\"),\"N/A\",D$37-_xlfn.CONFIDENCE.NORM(0.05,D$38,COUNTA(D$41:D$1040)))","v":48.636498360848108},{"$f":"IF(OR(ISBLANK(E$41),ISNA(E$41),E$41=\"N/A\"),\"N/A\",E$37-_xlfn.CONFIDENCE.NORM(0.05,E$38,COUNTA(E$41:E$1040)))","v":-39.834961358743953},10.917327646393472,0.98671328763052013,0.1674719826843023,null,{"$f":"IF(OR(ISBLANK(J$41),ISNA(J$41),J$41=\"N/A\"),\"N/A\",J$37-_xlfn.CONFIDENCE.NORM(0.05,J$38,COUNTA(J$41:J$1040)))","v":56.068686155387397},-1.7396460490427978,5.9473699408915719,0.99690091075492382,0.15742609803300528,null,{"$f":"IF(OR(ISBLANK(P$41),ISNA(P$41),P$41=\"N/A\"),\"N/A\",P$37-_xlfn.CONFIDENCE.NORM(0.05,P$38,COUNTA(P$41:P$1040)))","v":"N/A"},"N/A","N/A","N/A","N/A"]
[null,null,"Upper 95%",{"$f":"IF(OR(ISBLANK(D$41),ISNA(D$41),D$41=\"N/A\"),\"N/A\",D$37+_xlfn.CONFIDENCE.NORM(0.05,D$38,COUNTA(D$41:D$1040)))","v":51.020242038350048},{"$f":"IF(OR(ISBLANK(E$41),ISNA(E$41),E$41=\"N/A\"),\"N/A\",E$37+_xlfn.CONFIDENCE.NORM(0.05,E$38,COUNTA(E$41:E$1040)))","v":-37.91063610353406},11.371078609724952,0.98792551833022257,0.17045063335021554,null,{"$f":"IF(OR(ISBLANK(J$41),ISNA(J$41),J$41=\"N/A\"),\"N/A\",J$37+_xlfn.CONFIDENCE.NORM(0.05,J$38,COUNTA(J$41:J$1040)))","v":56.270088081877077},-1.723141864768361,5.9944000469794689,0.99729424407180933,0.16804635996077438,null,{"$f":"IF(OR(ISBLANK(P$41),ISNA(P$41),P$41=\"N/A\"),\"N/A\",P$37+_xlfn.CONFIDENCE.NORM(0.05,P$38,COUNTA(P$41:P$1040)))","v":"N/A"},"N/A","N/A","N/A","N/A"]
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[null,72,21,-321.46460548573788,{"$f":"IF($C$76>K8,I8+J8*(K8-$C$76)^2,I8)","v":-336.59870645893994},{"$f":"$D$76-$E$76","v":15.134100973202067},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$76>K8,(K8-$C$76)^2,0)","v":220.51749710738412},{"$f":"IF($C$76>K8,J8*2*(K8-$C$76),0)","v":52.85048607564611}]
[null,73,21,-334.67648090355686,{"$f":"IF($C$77>K8,I8+J8*(K8-$C$77)^2,I8)","v":-336.59870645893994},{"$f":"$D$77-$E$77","v":1.9222255553830792},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$77>K8,(K8-$C$77)^2,0)","v":220.51749710738412},{"$f":"IF($C$77>K8,J8*2*(K8-$C$77),0)","v":52.85048607564611}]
[null,74,21,-345.11333233556212,{"$f":"IF($C$78>K8,I8+J8*(K8-$C$78)^2,I8)","v":-336.59870645893994},{"$f":"$D$78-$E$78","v":-8.5146258766221763},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$78>K8,(K8-$C$78)^2,0)","v":220.51749710738412},{"$f":"IF($C$78>K8,J8*2*(K8-$C$78),0)","v":52.85048607564611}]
[null,75,21,-367.49872949690888,{"$f":"IF($C$79>K8,I8+J8*(K8-$C$79)^2,I8)","v":-336.59870645893994},{"$f":"$D$79-$E$79","v":-30.900023037968936},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$79>K8,(K8-$C$79)^2,0)","v":220.51749710738412},{"$f":"IF($C$79>K8,J8*2*(K8-$C$79),0)","v":52.85048607564611}]
[null,76,21,-347.53487901406237,{"$f":"IF($C$80>K8,I8+J8*(K8-$C$80)^2,I8)","v":-336.59870645893994},{"$f":"$D$80-$E$80","v":-10.936172555122425},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$80>K8,(K8-$C$80)^2,0)","v":220.51749710738412},{"$f":"IF($C$80>K8,J8*2*(K8-$C$80),0)","v":52.85048607564611}]
[null,77,21,-331.72072744691565,{"$f":"IF($C$81>K8,I8+J8*(K8-$C$81)^2,I8)","v":-336.59870645893994},{"$f":"$D$81-$E$81","v":4.8779790120242978},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$81>K8,(K8-$C$81)^2,0)","v":220.51749710738412},{"$f":"IF($C$81>K8,J8*2*(K8-$C$81),0)","v":52.85048607564611}]
[null,78,21,-327.80667579877934,{"$f":"IF($C$82>K8,I8+J8*(K8-$C$82)^2,I8)","v":-336.59870645893994},{"$f":"$D$82-$E$82","v":8.7920306601606057},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$82>K8,(K8-$C$82)^2,0)","v":220.51749710738412},{"$f":"IF($C$82>K8,J8*2*(K8-$C$82),0)","v":52.85048607564611}]
[null,79,21,-321.83894107299608,{"$f":"IF($C$83>K8,I8+J8*(K8-$C$83)^2,I8)","v":-336.59870645893994},{"$f":"$D$83-$E$83","v":14.759765385943865},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$83>K8,(K8-$C$83)^2,0)","v":220.51749710738412},{"$f":"IF($C$83>K8,J8*2*(K8-$C$83),0)","v":52.85048607564611}]
[null,80,21,-316.76179691827207,{"$f":"IF($C$84>K8,I8+J8*(K8-$C$84)^2,I8)","v":-336.59870645893994},{"$f":"$D$84-$E$84","v":19.836909540667875},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"IF($C$84>K8,(K8-$C$84)^2,0)","v":220.51749710738412},{"$f":"IF($C$84>K8,J8*2*(K8-$C$84),0)","v":52.85048607564611}]

{"sheet":"True Parameters Estimator (BLL)","index":5,"n_rows":107,"n_cols":33,"rows_kept":107,"cut":false,"hidden":false,"merged":[[7,13,9,15],[13,13,14,15],[15,7,15,9],[17,7,17,12],[18,7,19,7],[18,8,18,10],[18,11,18,12],[19,8,19,10],[19,11,19,12],[2,30,3,30],[2,31,3,31],[2,32,3,32],[4,13,6,15],[4,18,4,20],[5,7,5,10],[6,26,6,28],[1,1,1,3],[1,7,1,10],[1,18,1,20],[1,23,1,25],[2,13,2,15],[2,26,2,28]]}
[null,"Fitting the Broken-Line (descending Linear) Model to Ingredient Tolerance 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",{"$f":"MIN(B4:B103)","v":0},"Min Output",{"$f":"MIN(C4:C103)","v":2.089},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"]
[1,0,2.278,{"$f":"IF(B4=\"\",\"\",IF(B4>$J$8,C4-($H$8+$I$8*(-$J$8+B4)),C4-$H$8))","v":-2.3324470446750567E-3},{"$f":"IF(B4=\"\",\"\",IF(B4<$J$8,($H$8+$I$8*(-$J$8+B4)),$H$8))","v":2.8090086195316202},{"$f":"IF(B4=\"\",\"\",D4^2/E4)","v":1.9367363910476481E-6},null,"Max Input",{"$f":"MAX(B4:B103)","v":28},"Max Output",{"$f":"MAX(C4:C103)","v":2.2919999999999998},null,null,"1. Input data in cells B4:C103",null,null,null,null,{"$f":"FLOOR(I3,1)","v":0},{"$f":"CEILING(I4,1)","v":28},101,null,null,{"$f":"IF(ISBLANK(B4),\"\",1)","v":1},{"$f":"IF(B4=\"\",\"\",($J$8-B4)*IF(B4>$J$8,1,0))","v":0},{"$f":"IF(B4=\"\",\"\",$I$8*IF(B4>$J$8,1,0))","v":0},{"$f":"SUMPRODUCT(X$4:X$103,X$4:X$103)","v":5},{"$f":"SUMPRODUCT(X$4:X$103,Y$4:Y$103)","v":-7.8812945908650249},{"$f":"SUMPRODUCT(X$4:X$103,Z$4:Z$103)","v":-5.1429262397886095E-2}]
[{"$f":"A4+1","v":2},7,2.2919999999999998,{"$f":"IF(B5=\"\",\"\",IF(B5>$J$8,C5-($H$8+$I$8*(-$J$8+B5)),C5-$H$8))","v":1.1667552955324734E-2},{"$f":"IF(B5=\"\",\"\",IF(B5<$J$8,($H$8+$I$8*(-$J$8+B5)),$H$8))","v":2.6290062011390192},{"$f":"IF(B5=\"\",\"\",D5^2/E5)","v":5.1780704019004487E-5},null,null,null,null,null,null,null,"2. View the data and estimate values for the Maximum and MSL in cells H8 and J8",null,null,null,null,"Prediction",null,null,null,null,1,{"$f":"IF(B5=\"\",\"\",($J$8-B5)*IF(B5>$J$8,1,0))","v":0},{"$f":"IF(B5=\"\",\"\",$I$8*IF(B5>$J$8,1,0))","v":0},{"$f":"SUMPRODUCT(Y$4:Y$103,X$4:X$103)","v":-7.8812945908650249},{"$f":"SUMPRODUCT(Y$4:Y$103,Y$4:Y$103)","v":55.557402213999154},{"$f":"SUMPRODUCT(Y$4:Y$103,Z$4:Z$103)","v":0.20266458377431884},null,{"$f":"COUNT(B4:B53)","v":5},3,{"$f":"SQRT(K8/(AE5-AF5))","v":1.069267674615776E-2}]
[3,14,2.2709999999999999,-9.3324470446751739E-3,2.4490037827464177,3.5563263909700793E-5,null,"Regression",null,null,null,null,null,null,null,null,null,null,"Point","Input","Output",null,null,1,0,0,{"$f":"SUMPRODUCT(Z$4:Z$103,X$4:X$103)","v":-5.1429262397886095E-2},{"$f":"SUMPRODUCT(Z$4:Z$103,Y$4:Y$103)","v":0.20266458377431884},{"$f":"SUMPRODUCT(Z$4:Z$103,Z$4:Z$103)","v":1.3224845153953103E-3}]
[4,21,2.2690000000000001,-1.3643538161467461E-6,2.2803324470446751,8.163113839153824E-13,null,"Max or Min","Rate Constant","MSL","SSE",null,null,null,null,null,null,null,1,{"$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$8)","v":2.2803324470446751},{"$f":"--TRIM(SUBSTITUTE(B4,CHAR(160),\"\"))","v":0},2.278,1,-0.44064729543251246,-2.5714631198943048E-2,"inv(Q0)"]
[5,28,2.089,1.0540387851420974E-6,2.2803324470446751,4.8720867960445357E-13,0,2.2803324470446751,-2.5714631198943048E-2,20.559352704567488,{"$f":"SUMPRODUCT(D4:D53,D4:D53)","v":2.2866667199564582E-4},null,null,"3. Guess the Rate Constant values in cell I8 until the predicted line is close to the observed points",null,null,null,null,2,0.28000000000000003,{"$f":"IF(T8>$J$8,($H$8+$I$8*(-$J$8+T8)),$H$8)","v":2.2803324470446751},7,2.2919999999999998,1,-7.4406472954325125,-2.5714631198943048E-2,{"$f":"MINVERSE(AA4:AC6)","v":0.33333333333333337},2.8173620763065578E-17,12.962788801226697]
[6,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,3,0.56000000000000005,2.2803324470446751,14,2.2709999999999999,"","","",0,4.0816326530612242E-2,-6.2549116690796085]
[7,null,null,"","","",null,{"$f":"IF(ISNUMBER(H13),H$8-NORMSINV(0.975)*H$13,\"N/A\")","v":2.2682327665796351},{"$f":"IF(ISNUMBER(I13),I$8-NORMSINV(0.975)*I$13,\"N/A\")","v":-2.9948637368953021E-2},{"$f":"IF(ISNUMBER(J13),J$8-NORMSINV(0.975)*J$13,\"N/A\")","v":19.572181105397672},"Lower 95% Confidence Levels",null,null,null,null,null,null,null,4,0.84,2.2803324470446751,21,2.2690000000000001,"","","",12.96278880122669,-6.2549116690796094,2218.7902409947728]
[8,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),H$8+NORMSINV(0.975)*H$13,\"N/A\")","v":2.292432127509715},{"$f":"IF(ISNUMBER(I14),I$8+NORMSINV(0.975)*I$13,\"N/A\")","v":-2.1480625028933074E-2},{"$f":"IF(ISNUMBER(J14),J$8+NORMSINV(0.975)*J$13,\"N/A\")","v":21.546524303737304},"Upper 95% Confidence Levels",null,null,"4. Press the button below to run solver with current settings",null,null,null,null,5,1.1200000000000001,2.2803324470446751,28,2.089,"","",""]
[9,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,6,1.4,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[10,null,null,"","","",null,{"$f":"IF(ISNUMBER(AA8),SQRT(AA8)*$AG$5,\"N/A\")","v":6.1734197977518354E-3},{"$f":"IF(ISNUMBER(AB9),SQRT(AB9)*$AG$5,\"N/A\")","v":2.160246924641103E-3},{"$f":"IF(ISNUMBER(AC10),SQRT(AC10)*$AG$5,\"N/A\")","v":0.50366823419027118},"Standard Errors",null,null,null,null,null,null,null,7,1.68,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[11,null,null,"","","",null,{"$f":"IF(ISNUMBER(H13),H8/H13,\"N/A\")","v":369.37913211006645},{"$f":"IF(ISNUMBER(I13),I8/I13,\"N/A\")","v":-11.903561072406202},{"$f":"IF(ISNUMBER(J13),J8/J13,\"N/A\")","v":40.819236372172647},"t-Statistics",null,null,"5. Solver will attempt to minimize SSE (red cell) by changing cells H8:J8",null,null,null,null,8,1.96,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[12,null,null,"","","",null,{"$f":"IF(ISNUMBER(H14),2*TDIST(ABS(H14),$AE$5-$AF$5,1),\"N/A\")","v":7.3290977226659244E-6},{"$f":"IF(ISNUMBER(I14),2*TDIST(ABS(I14),$AE$5-$AF$5,1),\"N/A\")","v":6.9835809075283351E-3},{"$f":"IF(ISNUMBER(J14),2*TDIST(ABS(J14),$AE$5-$AF$5,1),\"N/A\")","v":5.9962466803687917E-4},"p-values",null,null,null,null,null,null,null,9,2.2400000000000002,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$f":"IF(ISBLANK(B15),\"\",1)","v":""},"",""]
[13,null,null,"","","",null,{"$f":"1-K8/(SUMPRODUCT(C4:C103,C4:C103)-COUNT(C4:C103)*AVERAGE(C4:C103)^2)","v":0.99204659793829708},null,null,"Goodness of Fit (R2)",null,null,null,null,null,null,null,10,2.52,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$f":"IF(ISBLANK(B16),\"\",1)","v":""},"",""]
[14,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,11,2.8,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$f":"IF(ISBLANK(B17),\"\",1)","v":""},"",""]
[15,null,null,"","","",null,"Functional Form",null,null,null,null,null,null,null,null,null,null,12,3.08,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$f":"IF(ISBLANK(B18),\"\",1)","v":""},"",""]
[16,null,null,"","","",null," y ={","Maximum, ",null,null,"if x< MSL",null,null,null,null,null,null,13,3.36,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[17,null,null,"","","",null,null,"Maximum + Rate Constant × (- MSL + x)",null,null,"if x ≥ MSL",null,null,null,null,null,null,14,3.64,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[18,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,15,3.92,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[19,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,16,4.2,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[20,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,17,4.4800000000000004,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[21,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,18,4.76,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[22,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,19,5.04,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[23,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,20,5.32,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[24,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,21,5.6,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[25,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,22,5.88,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[26,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,23,6.16,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[27,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,24,6.44,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[28,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,25,6.72,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[29,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,26,7,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[30,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,27,7.28,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[31,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,28,7.56,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[32,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,29,7.84,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[33,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,30,8.1199999999999992,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[34,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,31,8.4,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[35,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,32,8.68,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[36,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,33,8.9600000000000009,2.2803324470446751,{"$f":"--TRIM(SUBSTITUTE(B36,CHAR(160),\"\"))","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"},"","",""]
[37,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,34,9.24,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[38,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,35,9.52,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[39,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,36,9.8000000000000007,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[40,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,37,10.08,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[41,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,38,10.36,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[42,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,39,10.64,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[43,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,40,10.92,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
[44,null,null,"","","",null,null,null,null,null,null,null,null,null,null,null,null,41,11.2,2.2803324470446751,{"$error":"#VALUE!"},{"$error":"#VALUE!"},"","",""]
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[null,"Fitting the Broken-Line (descending Quadratic) Model to Ingredient Tolerance Data"]
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[4,21,2.2690000000000001,-1.4455753751101419E-3,2.2704455753751103,9.203868120818448E-7,null,"Max or Min","Rate Constant","MSL","SSE",null,null,null,null,null,null,null,1,{"$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$8)","v":2.2798751776493504},{"$f":"--TRIM(SUBSTITUTE(B4,CHAR(160),\"\"))","v":0},2.278,1,3.9999332398245842,9.4296809654631046E-3,"inv(Q0)"]
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