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{"sheet":"MetaData","index":0,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":false,"merged":[[2,9,2,10],[16,7,20,7],[21,7,25,7],[8,2,15,2],[1,1,1,7],[21,2,25,2],[16,2,20,2]]}
[]
[null,"Indirect RR Adjustment (IRRAD)",null,null,null,null,null,null,null,"Legend:","User info","Results"]
[null,"Procedure","Select Analysis","Input information",null,null,null,"Sheet",null,"Definitions:"]
[null,"For X and C binary:",null,null,null,null,null,null,null,"X","Exposure"]
[null,"• Find adjusted RR_X",null,"Provide RR_Obs, RR_C, P(C=1|X=0) and P(C=1|X=1) or OR_X,C",null,null,null,"Axelson_Gail",null,"C","Confounder"]
[null,null,null,null,null,null,null,null,null,"P(C|X)","Conditional probability of C given X"]
[null,"• Solve for P(C=1|X=1) & OR_X,C",null,"Provide RR_Obs, RR_X, RR_C & P(C=1|X=0)",null,null,null,null,null,"P(X)","Probability of X, used to compute P(X,C)"]
[null,null,null,null,null,null,null,null,null,"P(X,C)","Joint probability of X and C"]
[null,"For X and C categorical: ",null,"Model for RR(X,C)",null,null,null,null,null,"OR_X,C","Odds ratio of X and C"]
[null,"• Find adjusted RR_X or ERR_X",null,"Multiplicative: Provide RR_Obs, RR_C and P(C|X)",null,null,null,"IndrctAdj",null,"RR_Obs","Observed relative risk of X"]
[null,null,null,null,null,null,null,null,null,"RR_X","Adjusted (\"true\") relative risk of X at the referent category of C"]
[null,null,null,"Additive: Provide ERR_Obs, ERR_C and P(C|X)",null,null,null,null,null,"RR_C","Relative risk of C at the referent category of X"]
[null,null,null,null,null,null,null,null,null,"ERR_Obs","Observed excess relative risk of X (= RR_Obs - 1)"]
[null,null,null,"(Optional)",null,null,null,null,null,"ERR_X","Adjusted (\"true\") excess relative risk of X (= RR_X - 1)"]
[null,null,null,"Smooth & LS regression: Include C & X scores and weights",null,null,null,null,null,"ERR_C","Excess relative risk of C (= RR_C - 1)"]
[null,null,null,"Pearson correlation: C & X scores and marginal P(X)",null,null,null,null,null,"Wgt","Weights for LS regression (default = 1.0; non-positive weights set to zero)"]
[null,"For X categorical and C binary:",null,"Model for RR(X,C)",null,null,null,"Solve_P(C|X)_BinC",null,"Prior weights","Weights for smooth (default is equal weights; non-positive weights set to zero)"]
[null,"• Solve for P(C=1|X) & OR_X,C",null,"Multiplicative: Provide RR_Obs, RR_X, RR_C and P(C=1|X=0)",null,null,null,null,null,"Note: referent category for RR and ERR must be level 0"]
[]
[null,null,null,"Additive: Provide ERR_Obs, ERR_X, ERR_C and P(C=1|X=0)",null,null,null,null,null,"Joint association of X and C:"]
[null,null,null,null,null,null,null,null,null,"Multiplicative:","RR_X,C(i,j) = RR_X(i)*RR_C(j)"]
[null,"For X and C categorical:",null,"Model for RR(X,C)",null,null,null,"Solve_RRC",null,"Additive:","RR_X,C(I,j) = 1+ERR_X(i)+ERR_C(j) = RR_X(i)+RR_C(j)-1"]
[null,"• Solve for RR_C or ERR_C",null,"Multiplicative: Provide RR_Obs, RR_X and P(C|X)"]
[null,null,null,null,null,null,null,null,null,"References:","Lubin, Hauptmann and Blair Ann Epidemiol 2018:28(11);801-807"]
[null,null,null,"Additive: Provide ERR_Obs, ERR_X and P(C|X)",null,null,null,null,null,null,"Axelson Scand J Work Environ Health 1978;4:98-102"]
[null,null,null,null,null,null,null,null,null,null,"Schlesselman Am J Epidemiol 1978"]
[null,null,null,null,null,null,null,"ExampleData",null,null,"Gail et al Am J Ind Med 1988;13:119-130"]
[]
[null,null,null,null,null,null,null,null,null,"Version"]
[null,null,null,null,null,null,null,null,null,1.1000000000000001,"25 Oct 2018:","Initial coding "]
[null,null,null,null,null,null,null,null,null,1.2,"13 Nov 2018:","Enhance error trapping"]
[null,null,null,null,null,null,null,null,null,1.3,"20 Dec 2018:","Reformat & error trapping"]

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[]
[null,"Find adjusted RR_X (mult model) or ERR_X (add model)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"display=",{"$f":"COUNTBLANK(R5:R9)+SUM(R10:R14)","v":0}]
[null,null,null,null,null,null,"Mult: RR_X,C = RR_X * RR_C",null,null,null,"Joint distn P(X,C) & corr"]
[null,"RR_Obs = ",5,{"$f":"IF(C5=\"\",\"\",IF(C5>0,\"\",\"**Invalid entry**\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C5>0,C5,\"\")","v":5}]
[null,"RR_C = ",1.5,{"$f":"IF(C6=\"\",\"\",IF(C6>0,\"\",\"**Invalid entry**\"))","v":""},null,null,"RR_X = ",{"$f":"IF(S3>0,\"\",IF(R5=\"\",\"\",$R$5 / H7))","v":5.454545454545455},{"$f":"IF(H6=\"\",\"\",IF(H6>=0,\"\",\"** Invalid value **\"))","v":""},null,"Corr(X,C)=",{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>0)*(C13<1),(K8-M8*K10)/SQRT(M8*M9*K10*L10),\"NA\")))","v":-0.21821789023599245},{"$f":"IF(L6=\"\",\"\",IF(L6>=-1,IF(L6<=1,\"\",\"** Invalid value **\"),\"** Invalid value **\"))","v":""},null,null,null,null,{"$f":"IF(C6>0,C6,\"\")","v":1.5}]
[null,"P(C=1 | X=0) = ",0.4,{"$f":"IF(C7=\"\",\"\",IF(C7>0,IF(C7<1,\"\",\"**Invalid entry**\"),\"**Invalid entry**\"))","v":""},null,null,"BIAS_RR = ",{"$f":"IF(S3>0,\"\",IF(R8=\"\",\"\",($R$8 * $R$6 + (1-$R$8) ) / ($R$7 * $R$6 + (1 - $R$7))))","v":0.91666666666666663},null,null,"X=1","X=0",null,null,null,null,null,{"$f":"IF(C7>0,C7,\"\")","v":0.4}]
[null,null,null,null,null,null,null,null,null,"C=1",{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),R8*K10,\"\")))","v":0.12},{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),R7*L10,\"\")))","v":0.16000000000000003},{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),K8+L8,\"\")))","v":0.28000000000000003},null,null,null,null,{"$f":"IF(C10=\"\",D11,C10)","v":0.2}]
[null,"Enter one:",{"$f":"IF(COUNTBLANK(C10:C11)=0,\"Error: enter only one: P(C=1 | X=1) or OR_X,C\",\"\")","v":""},null,null,null,"Add: RR_X,C = RR_X + RR_C - 1",null,null,"C=0",{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),K10-K8,\"\")))","v":0.48},{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),L10-L8,\"\")))","v":0.24},{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),K9+L9,\"\")))","v":0.72},null,null,null,null,{"$f":"IF(C11=\"\",D10,C11)","v":0.37499999999999989}]
[null,"P(C=1 | X=1) = ",0.2,{"$f":"IF(COUNTBLANK(C5:C7)+COUNTBLANK(C10)=0,IF(SUM(R10:R12)>0,\"**Invalid**\",C10*(1-C7)/(C7*(1-C10))),\"\")","v":0.37499999999999989},{"$f":"IF(C10=\"\",\"\",IF(D10=\"\",\"\",IF(D10=\"**Invalid**\",\"\",\"= OR_X,C\")))","v":"= OR_X,C"},null,null,null,null,null,{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),C13,\"\")))","v":0.6},{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",IF((C13>=0)*(C13<=1),1-K10,\"\")))","v":0.4},{"$f":"IF(S3>0,\"\",IF(C13=\"\",\"\",SUM(K8:L9)))","v":1},null,null,null,"Invalid prob",{"$f":"IF(C7>0,IF(C7<1,0,1),1)","v":0},"P(C=1 | X=0)"]
[null,"OR_X,C = ",null,{"$f":"IF(COUNTBLANK(C5:C7)+COUNTBLANK(C11)=0,IF(((C11<=0)+(R12>0))>0,\"**Invalid**\",C11*C7/(C11*C7+1-C7)),\"\")","v":""},{"$f":"IF(C11=\"\",\"\",IF(D11=\"\",\"\",IF(D11=\"**Invalid**\",\"\",\"= P(C=1 | X=1)\")))","v":""},null,"ERR_X = ",{"$f":"IF(S3>0,\"\",IF(R5=\"\",\"\",(R5-1) * ((R6-1)*R7 + 1) - (R8-R7)*(R6-1)))","v":4.8999999999999995},{"$f":"IF(H11=\"\",\"\",IF(H11>=-1,\"\",\"** Invalid value **\"))","v":""},null,null,null,null,null,null,null,null,{"$f":"IF(C10=\"\",0,IF(C10>0,IF(C10<1,0,1),1))","v":0},"P(C=1 | X=1)"]
[null,null,null,null,null,null,"BIAS_ERR = ",{"$f":"IF(S3>0,\"\",IF(R5=\"\",\"\",(R5-1)/H11))","v":0.81632653061224503},null,null,null,null,null,null,null,null,null,{"$f":"IF(T12=\"\",0,IF(T12>0,IF(T12<1,0,1),1))","v":0},"P(C=1 | X=1)",{"$f":"IF(COUNTBLANK(C5:C7)+COUNTBLANK(C11)=0,IF(C11<=0,-999,C11*C7/(C11*C7+1-C7)),\"\")","v":""}]
[null,"P(X=1) = ",0.6,"(optional)",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C9=\"\",0,1)","v":0},"P(C=1 | X=1) & OR_X,C"]
[null,null,{"$f":"IF(C13=\"\",\"\",IF(R14=0,\"\",\"**Invalid entry**\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF((C13>=0)*(C13<=1)=1,0,1)","v":0},"P(X=1)"]
[null,"Solve for P(C=1|X=1) & OR_X,C"]
[]
[null,null,null,null,"Multiplicative: RR_X,C = RR_X * RR_C"]
[null,"RR_Obs = ",2,null,null,null,null,null,"Joint distn P(X,C) & correlation",null,null,null,null,null,null,null,null,"Display=",{"$f":"( (COUNTBLANK(C18:C20)+COUNTBLANK(C22))>0) + ((COUNTBLANK(C21)+COUNTBLANK(C23))<>2)","v":0}]
[null,"RR_X (fix) = ",1.5,null,null,"P(C=1 | X=1) = ",{"$f":" IF(S18>0,\"\",IF(C18=\"\",\"\",((C18/C19)*((1-$C$22)+$C$22*$C$20) -1)/($C$20-1) ))","v":0.35},null,null,"X=1","X=0",null,null,null,null,null,null,null,{"$f":"(C18>0)+(C19>0)+(C20>0)","v":3}]
[null,"RR_C = ",5,null,null,"OR_X,C = ",{"$f":"IF(S18>0,\"\",IF(G19=\"\",\"\",(G19/(1-G19))/($C$22/(1-$C$22))))","v":2.1538461538461537},null,"C=1",{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),G19*J22,\"\"))","v":0.13999999999999999},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),C22*K22,\"\"))","v":0.12},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),J20+K20,\"\"))","v":0.26},null,null,null,null,null,null,{"$f":"COUNTBLANK(C18:C20)","v":0}]
[null,null,{"$f":"IF(S20>0,\"\",IF(S19=3,\"\",\"**Invalid entry**\"))","v":""},null,null,null,{"$f":"IF(G19=\"\",\"\",IF( (G19>=tol_Pr)*(G19<=(1-tol_Pr)),\"\",\"** Invalid value **\"))","v":""},null,"C=0",{"$f":"IF(S25+S25>0,\"\",IF((C26>=0)*(C26<=1),J22-J20,\"\"))","v":0.26},{"$f":"IF(S25+S25>0,\"\",IF((C26>=0)*(C26<=1),K22-K20,\"\"))","v":0.48},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),J21+K21,\"\"))","v":0.74}]
[null,"P(C=1 | X=0) = ",0.2,null,null,null,null,null,null,{"$f":"IF(C26=\"\",\"\",IF((C26>=0)*(C26<=1),C26,\"\"))","v":0.4},{"$f":"IF(C26=\"\",\"\",IF((C26>=0)*(C26<=1),1-J22,\"\"))","v":0.6},{"$f":"IF(S25>0,\"\",IF(C26=\"\",\"\",SUM(L20:L21)))","v":1}]
[null,null,{"$f":"IF(C22=\"\",\"\",IF(R26=0,\"\",\"**Invalid entry**\"))","v":""}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(S18>0,\"\",IF(C26=\"\",\"\",IF(R27>0,\"\",\"Corr(X,C)=\")))","v":"Corr(X,C)="},{"$f":"IF(S18>0,\"\",IF(C26=\"\",\"\",IF(R27>0,\"\",IF((J20*J21*K20*K21>0),(J20-L20*J22)/SQRT(L20*L21*J22*K22),\"NA\"))))","v":0.16753067798623636}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(L24=\"\",\"\",IF( (L24>=-1)*(L24<=1),\"\",\"** Invalid value **\"))","v":""},null,null,null,null,null,"Display=",{"$f":"IF(C26=\"\",1,S18)","v":0}]
[null,"P(X=1) = ",0.4,"(optional)","Additive: RR_X,C = RR_X + RR_C - 1",null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF((C22>0)*(C22<1)=1,0,1)","v":0},"P(C=1 | X=0)"]
[null,null,{"$f":"IF(C26=\"\",\"\",IF(R27=0,\"\",\"**Invalid entry**\"))","v":""},null,null,null,null,null,"Joint distn P(X,C) & correlation",null,null,null,null,null,null,null,null,{"$f":"IF((C26>=0)*(C26<=1)=1,0,1)","v":0},"P(X=1)"]
[null,null,null,null,null,"P(C=1 | X=1) = ",{"$f":"IF(S18>0,\"\",IF(C18=\"\",\"\",(C22*C18*(C20-1) + C18-C19)/(C20-1)))","v":0.52500000000000002},null,null,"X=1","X=0"]
[null," ",null,null,null,"OR_X,C = ",{"$f":"IF(S18>0,\"\",IF(C22=\"\",\"\",(G28/(1-G28))/($C$22/(1-$C$22))))","v":4.4210526315789478},null,"C=1",{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),G28*C26,\"\"))","v":0.21000000000000002},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),C22*K31,\"\"))","v":0.12},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),J29+K29,\"\"))","v":0.33}]
[null,null,null,null,null,null,{"$f":"IF(G28=\"\",\"\",IF( (G28>=tol_Pr)*(G28<=(1-tol_Pr)),\"\",\"** Invalid value **\"))","v":""},null,"C=0",{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),J31-J29,\"\"))","v":0.19},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),K31-K29,\"\"))","v":0.48},{"$f":"IF(S25>0,\"\",IF((C26>=0)*(C26<=1),J30+K30,\"\"))","v":0.66999999999999993}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(C26=\"\",\"\",IF((C26>=0)*(C26<=1),C26,\"\"))","v":0.4},{"$f":"IF(C26=\"\",\"\",IF((C26>=0)*(C26<=1),1-J31,\"\"))","v":0.6},{"$f":"IF(S25>0,\"\",IF(C26=\"\",\"\",SUM(J29:K30)))","v":1}]
[]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(S18>0,\"\",IF(C26=\"\",\"\",IF(R27>0,\"\",\"Corr(X,C)=\")))","v":"Corr(X,C)="},{"$f":"IF(S18>0,\"\",IF(C26=\"\",\"\",IF(R27>0,\"\",IF((J29*J30*K29*K30>0),(J29-L29*J31)/SQRT(L29*L30*J31*K31),\"NA\"))))","v":0.33860596969590517}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(L33=\"\",\"\",IF( (L33>=-1)*(L33<=1)=1,\"\",\"** Invalid value **\"))","v":""}]

{"sheet":"IndrctAdj","index":2,"n_rows":102,"n_cols":56,"rows_kept":102,"cut":false,"hidden":false,"merged":[[5,20,5,22],[1,1,1,14],[99,9,99,10],[52,11,52,12],[29,1,29,5],[51,11,51,12],[98,11,98,12],[76,1,76,5],[75,9,75,13],[52,9,52,10],[6,7,6,10],[28,9,28,13],[50,9,50,12],[97,9,97,12]]}
[]
[null,"Find adjusted RR_X (mult model) or ERR_X (add model)"]
[null,null,null,null,{"$f":"IF(AD6>=AD7,\"\",\"**Warning: Too few RR_C values**\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"10-COUNTIF(E5:N5,\"\")","v":4}]
[null,null,null,"Level (C)",0,1,2,3,4,5,6,7,8,9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNTIF(E6:N6,\"<0\")","v":0}]
[null,null,null,"Confounder score (C)",0.86,1.1499999999999999,1.44,1.95,null,null,null,null,null,null,null,null,null,null,{"$f":"IF( (Corr!B26*Corr!B27<>0)*(ABS(AA24-1)<tol_Pr)=1,IF((Corr!D31=1)*(AD7=AD3)*(E3=\"\"),\"\",\"**Error: Correlation requires all X & C scores**\"),\"\")","v":""}]
[null,null,"(optional)","RR_C",1,0.84,0.66,0.5,null,null,null,null,null,null,null,null,"Correlation",{"$f":"IF((Corr!B26*Corr!B27<>0)*(ABS(AA24-1)<tol_Pr)*(Corr!D31=1)*(AD7=AD3)*(E3=\"\")=1,Corr!B29,\"NA\")","v":-9.3785636690396745E-2},{"$f":"IF(Corr!B26*Corr!B27<>0,IF(ABS(AA24-1)<tol_Pr,\"\",\"**Error: P(X,C)≠1**\"),\"\")","v":""},null,"Joint probability P(X,C)",null,null,null,null,null,null,null,null,{"$f":"10-COUNTBLANK(E6:N6)","v":4},null,{"$f":"IF(E6=\"\",0,E6)","v":1},0.84,0.66,0.5,0,0,0,0,0,0,null,null,null,{"$f":"IF(E6=\"\",0,E6-1)","v":0},-0.16000000000000003,-0.33999999999999997,-0.5,0,0,0,0,0,0]
[null,"Level (X)","P(X)","Exp Score (X)",null,null,null,"Conditional probabilites P(C|X=i)",null,null,null,null,null,null,"Sum",{"$f":"IF(COUNTBLANK(P8:P23)=16,\"\",\"Warning:\")","v":""},0,1,2,3,4,5,6,7,8,9,"P(X) =",null,null,{"$f":"MAX(AD8:AD23)","v":4},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(C=j | E=i)"]
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[]
[]
[]
[]
[null,null,{"$f":"IF(COUNTIF(C33:C47,\">0\")=COUNTIF(O9:O23,\">0\"),\"\",\"**Warning: mismatch in levels of RR_Obs & P(C|X)**\")","v":""},null,null,null,null,null,null,"Smooth with prior weights",null,null,null,null,"Total"]
[null,"Multiplicative model: RR_X,C = RR_X * RR_C",null,null,null,null,null,null,null,0.1,0.2,0.4,0.2,0.1,{"$f":"SUMIF(J30:N30,\">0\")","v":1.0000000000000002}]
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[null,8,null,null,"","",null,null,null,8,{"$f":"IF(RegSm!$D$2<2,\"\",IF(C40=\"\",\"\",IF(D16=\"\",\"\",D16)))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E40=\"\",\"\",RegSm!D156))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E40=\"\",\"\",RegSm!E156))","v":""}]
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[null,10,null,null,"","",null,null,null,10,{"$f":"IF(RegSm!$D$2<2,\"\",IF(C42=\"\",\"\",IF(D18=\"\",\"\",D18)))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E42=\"\",\"\",RegSm!D158))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E42=\"\",\"\",RegSm!E158))","v":""}]
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[null,14,null,null,"","",null,null,null,14,{"$f":"IF(RegSm!$D$2<2,\"\",IF(C46=\"\",\"\",IF(D22=\"\",\"\",D22)))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E46=\"\",\"\",RegSm!D162))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E46=\"\",\"\",RegSm!E162))","v":""}]
[null,15,null,null,"","",null,null,null,15,{"$f":"IF(RegSm!$D$2<2,\"\",IF(C47=\"\",\"\",IF(D23=\"\",\"\",D23)))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E47=\"\",\"\",RegSm!D163))","v":""},{"$f":"IF(RegSm!$D$2<2,\"\",IF(E47=\"\",\"\",RegSm!E163))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(RegSm!$D$2>1,\"Note: plots use the Excel 'smooth line' style\",\"\")","v":"Note: plots use the Excel 'smooth line' style"}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(RegSm!$D$2<2,\"\",IF(RegSm!B2<=1,\"\",IF( ((RegSm!D2 = RegSm!B2)*(RegSm!B3 = RegSm!B2))=1,\"\",\"** Error: Mismatch in RR_Obs, RR_X & X scores **\")))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,"Weighted LS Regression (fitted RRs)"]
[null,null,null,null,null,null,null,null,null,"With intrcpt",0,"1=intrcpt; 0=no intrcpt",null,{"$f":"IF(K52 <>1,IF(K52<>0,\"**Error: Value must = 1 or 0**\",\"\"),\"\")","v":""}]
[null,null,null,null,null,null,null,null,"Estimates","RR = exp(α + β*x)",null,"RR  =  1 + α + β*x",null,{"$f":"IF(RegSm!$D$2<2,\"\",IF(RegSm!A73=16,\" Use default weights (=1.0)\",IF(COUNTIF(C32:C47,\">0\")<=COUNTIF(D32:D47,\">=0\"),\"\",\"Neg/blank wgts set to zero\")))","v":""}]
[null,null,null,null,null,null,null,null,"α ",{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!C91,\"\"))","v":0},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!E91,\"\"))","v":0},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!G91,\"\"))","v":0},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!I91,\"\"))","v":0}]
[null,null,null,null,null,null,null,null,"β ",{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!D91,\"\"))","v":1.1515370786162769E-2},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!F91,\"\"))","v":1.2885535230905751E-2},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!H91,\"\"))","v":1.6024993876378398E-2},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",RegSm!J91,\"\"))","v":1.8673666993787773E-2}]
[null,null,null,null,null,null,null,null,"exp(β) ",{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",EXP(J55),\"\"))","v":1.0115819278996003},{"$f":"IF(RegSm!$D$2<2,\"\",IF(J49=\"\",EXP(K55),\"\"))","v":1.0129689114709526}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[null,null,{"$f":"IF(COUNTIF(C80:C94,\">=-1\")=COUNTIF(O9:O23,\">0\"),\"\",\"**Warning: mismatch in levels of ERR_Obs & P(C|X)**\")","v":""},null,null,null,null,null,null,"Smooth with prior weights",null,null,null,null,"Total"]
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[null,1,0.26,678.59253852182269,0.1806779432,null,null,null,null,1,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C80=\"\",\"\",IF(D9=\"\",\"\",D9)))","v":6.6524299999999998},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E80=\"\",\"\",RegSm!D178))","v":0.19053133747999995},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E80=\"\",\"\",RegSm!E178))","v":0.28899999999999998}]
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[null,3,0.66999999999999993,204.84423461094022,0.43807752439999997,null,null,null,null,3,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C82=\"\",\"\",IF(D11=\"\",\"\",D11)))","v":33.539400000000001},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E82=\"\",\"\",RegSm!D180))","v":0.47639463831999984},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E82=\"\",\"\",RegSm!E180))","v":0.72599999999999987}]
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[null,5,1.1800000000000002,80.342980609274747,0.79446647760000011,null,null,null,null,5,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C84=\"\",\"\",IF(D13=\"\",\"\",D13)))","v":53.618000000000002},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E84=\"\",\"\",RegSm!D182))","v":0.74492480715999998},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E84=\"\",\"\",RegSm!E182))","v":1.1129999999999998}]
[null,6,1.2599999999999998,192.45506233444695,0.84711228319999987,null,null,null,null,6,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C85=\"\",\"\",IF(D14=\"\",\"\",D14)))","v":80.8767},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E85=\"\",\"\",RegSm!D183))","v":0.81647028311999981},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E85=\"\",\"\",RegSm!E183))","v":1.2159999999999995}]
[null,7,null,null,"",null,null,null,null,7,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C86=\"\",\"\",IF(D15=\"\",\"\",D15)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E86=\"\",\"\",RegSm!D184))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E86=\"\",\"\",RegSm!E184))","v":""}]
[null,8,null,null,"",null,null,null,null,8,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C87=\"\",\"\",IF(D16=\"\",\"\",D16)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E87=\"\",\"\",RegSm!D185))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E87=\"\",\"\",RegSm!E185))","v":""}]
[null,9,null,null,"",null,null,null,null,9,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C88=\"\",\"\",IF(D17=\"\",\"\",D17)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E88=\"\",\"\",RegSm!D186))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E88=\"\",\"\",RegSm!E186))","v":""}]
[null,10,null,null,"",null,null,null,null,10,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C89=\"\",\"\",IF(D18=\"\",\"\",D18)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E89=\"\",\"\",RegSm!D187))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E89=\"\",\"\",RegSm!E187))","v":""}]
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[null,12,null,null,"",null,null,null,null,12,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C91=\"\",\"\",IF(D20=\"\",\"\",D20)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E91=\"\",\"\",RegSm!D189))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E91=\"\",\"\",RegSm!E189))","v":""}]
[null,13,null,null,"",null,null,null,null,13,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C92=\"\",\"\",IF(D21=\"\",\"\",D21)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E92=\"\",\"\",RegSm!D190))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E92=\"\",\"\",RegSm!E190))","v":""}]
[null,14,null,null,"",null,null,null,null,14,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C93=\"\",\"\",IF(D22=\"\",\"\",D22)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E93=\"\",\"\",RegSm!D191))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E93=\"\",\"\",RegSm!E191))","v":""}]
[null,15,null,null,"",null,null,null,null,15,{"$f":"IF(RegSm!$D$24<2,\"\",IF(C94=\"\",\"\",IF(D23=\"\",\"\",D23)))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E94=\"\",\"\",RegSm!D192))","v":""},{"$f":"IF(RegSm!$D$24<2,\"\",IF(E94=\"\",\"\",RegSm!E192))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(RegSm!$D$24>1,\"Note: plots use the Excel 'smooth line' style\",\"\")","v":"Note: plots use the Excel 'smooth line' style"}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(RegSm!$D$24<2,\"\",IF(RegSm!B24<=1,\"\",IF( ((RegSm!D24 = RegSm!B24)*(RegSm!B25 = RegSm!B24) )=1,\"\",\"** Error: Mismatch in ERR_Obs, ERR_X & X scores **\")))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,"Weighted LS Regression (fitted RRs)"]
[null,null,null,null,null,null,null,null,"Estimates","With intrcpt",0,"1=intrcpt; 0=no intrcpt",null,{"$f":"IF(K99 <>1,IF(K99<>0,\" **Error: Value must = 1 or 0**\",\"\"),\"\")","v":""}]
[null,null,null,null,null,null,null,null,"α ","ERR = α + β*x",null,null,null,{"$f":"IF(RegSm!$D$24<2,\"\",IF(RegSm!A119=16,\" Use default weights (=1.0)\",IF(COUNTIF(C79:C94,\">-1\")<=COUNTIF(D79:D94,\">-1\"),\"\",\"Neg/blank wgts set to zero\")))","v":""}]
[null,null,null,null,null,null,null,null,"β ",{"$f":"IF(RegSm!$D$24<2,\"\",IF(J96=\"\",RegSm!C137,\"\"))","v":0},{"$f":"IF(RegSm!$D$24<2,\"\",IF(J96=\"\",RegSm!E137,\"\"))","v":0}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(RegSm!$D$24<2,\"\",IF(J96=\"\",RegSm!D137,\"\"))","v":1.2417098255952984E-2},{"$f":"IF(RegSm!$D$24<2,\"\",IF(J96=\"\",RegSm!F137,\"\"))","v":1.8673666993787776E-2}]

{"sheet":"Solve_P(C|X)_BinC","index":3,"n_rows":45,"n_cols":18,"rows_kept":45,"cut":false,"hidden":false,"merged":[[1,10,1,17],[1,1,1,8]]}
[]
[null,"Solve for P(C=1|X=i) given RR_Obs, RR_X & RR_C (mult)",null,null,null,null,null,null,null,null,"Solve for P(C=1|X=i) given ERR_Obs, ERR_X & ERR_C (add)"]
[]
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[null,"(optional)",{"$f":"IF(C7=1,IF(D7=1,\" \",\"** Lowest category RR must be 1.0 **\"),\"** Lowest category RR must be 1.0 **\")","v":" "},null,null,null,null,null,null,null,"(optional)",{"$f":"IF(L7=0,IF(M7=0,\" \",\"** Lowest category ERR must be 0.0 **\"),\"** Lowest category ERR must be 0.0 **\")","v":" "}]
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[null,6.1199999999999997E-2,1.0330315953522968,1,"P(C | X=3)",0.45045260697155465,0.54954739302844535,1.2199893718522721,"",null,6.1199999999999997E-2,3.3031595352296828E-2,0,"P(C | X=3)",0.46696840464770317,0.53303159535229683,1.1414725065916054,""]
[null,4.1700000000000001E-2,1.0627103346329041,1,"P(C | X=4)",0.40593449805064385,0.59406550194935615,1.4634516277925247,"",null,4.1700000000000001E-2,6.2710334632904097E-2,0,"P(C | X=4)",0.4372896653670959,0.5627103346329041,1.2868137054199991,""]
[null,1.26E-2,1.1372769650163048,1,"P(C | X=5)",0.29408455247554288,0.70591544752445712,2.4003826164353312,"",null,1.26E-2,0.13727696501630482,0,"P(C | X=5)",0.36272303498369518,0.63727696501630482,1.756924439731133,""]
[null,6.4000000000000003E-3,1.16019842257464,1,"P(C | X=6)",0.25970236613803999,0.74029763386196001,2.8505617598742572,"",null,6.4000000000000003E-3,0.16019842257464001,0,"P(C | X=6)",0.33980157742535999,0.66019842257464001,1.9428939311491502,""]
[null,2.5999999999999999E-3,1.2274345405351776,1,"P(C | X=7)",0.15884818919723354,0.84115181080276646,5.2953188516260141,"",null,2.5999999999999999E-3,0.22743454053517764,0,"P(C | X=7)",0.27256545946482236,0.72743454053517764,2.6688434476014788,""]
[null,2.0999999999999999E-3,1.3238177636803241,1,"P(C | X=8)",1.4273354479513944E-2,0.98572664552048606,69.060615494084843,"",null,2.0999999999999999E-3,0.32381776368032411,0,"P(C | X=8)",0.17618223631967589,0.82381776368032411,4.675941121473441,""]
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[null,null,null,null,"P(C | X=12)","","","","",null,null,null,null,"P(C | X=12)","","","",""]
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[]
[]
[null,null,"P(C|X)*P(X)","P(C)",null,null,null,null,null,null,null,"P(C|X)P(X)","P(C)"]
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[]
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{"sheet":"Corr","index":4,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":true,"merged":[]}
["IndrctAdJ"]
["Correlation - Mult Find RR_X Jnt"]
[null,"C-score"]
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[null,{"$f":"SUM(B5:B20)","v":0.16273496500000001},{"$f":"SUM(C5:C20)","v":0.32474004499999998},0.23712867900000004,0.275396311,0,0,0,0,0,0,1]
[]
["E(X)=",{"$f":"MMULT(TRANSPOSE(A5:A20),L5:L20)","v":8.2470004400000008}]
["E(C)=",{"$f":"MMULT((B4:K4),TRANSPOSE(B21:K21))","v":1.39189122586}]
[]
["Var(X)",{"$f":"SUM((A5:A20)^2 * (L5:L20))- B23^2","v":295.353610310438}]
["Var(C)",{"$f":"SUM((B4:K4)^2 * (B21:K21))-B24^2","v":0.15137080635234623}]
["Cov(X,C)",{"$f":"SUM(MMULT(A5:A20,B4:K4)*(B5:K20)) - B23*B24","v":-0.62708806510345205}]
["corr=",{"$f":"B28/SQRT(B27*B26)","v":-9.3785636690396745E-2}]
[null,"Scores","Cats"]
["X",{"$f":"16-COUNTBLANK(IndrctAdj!D8:'IndrctAdj'!D23)","v":7},{"$f":"COUNTIF(L5:L20,\">0\")","v":7},{"$f":"(B31=C31)*(B32=C32)","v":1}]
["C",{"$f":"10-COUNTBLANK(IndrctAdj!E5:'IndrctAdj'!N5)","v":4},{"$f":"COUNTIF(B21:K21,\">0\")","v":4}]

{"sheet":"Solve_RRC","index":5,"n_rows":59,"n_cols":14,"rows_kept":59,"cut":false,"hidden":false,"merged":[[3,2,3,11],[1,1,1,12],[32,2,32,7],[18,6,18,7],[33,6,33,7],[17,2,17,7]]}
[]
[null,"Solve for RR_C (ERR_C), given P(C=j|X=i), RR_Obs & RR_X or ERR_Obs & ERR_X"]
[]
[null,null,"Conditional probabilites P(C|X)"]
[null,null,0,1,2,3,4,5,6,7,8,9,"Sum",{"$f":"IF(COUNTBLANK(N6:N15)=10,\"\",\"Warning:\")","v":""}]
[null,"P(C=j | X=0)",0.156,0.33300000000000002,0.25900000000000001,0.115,9.8000000000000004E-2,3.9E-2,null,null,null,null,{"$f":"IF(MultMdl!R6=0,\"\",SUM(C6:L6))","v":1},{"$f":"IF(M6=\"\",\"\",IF(ABS(M6-1)<tol_Pr,\"\",\"**P(C|X) ≠ 1**\"))","v":""}]
[null,"P(C=j | X=1)",0.20300000000000001,0.34,0.23499999999999999,0.10299999999999999,8.3000000000000004E-2,3.5999999999999997E-2,null,null,null,null,{"$f":"IF(MultMdl!R7=0,\"\",SUM(C7:L7))","v":1},{"$f":"IF(M7=\"\",\"\",IF(ABS(M7-1)<tol_Pr,\"\",\"**P(C|X) ≠ 1**\"))","v":""}]
[null,"P(C=j | X=2)",0.25600000000000001,0.36699999999999999,0.20200000000000001,7.9000000000000001E-2,6.7000000000000004E-2,2.9000000000000001E-2,null,null,null,null,{"$f":"IF(MultMdl!R8=0,\"\",SUM(C8:L8))","v":0.99999999999999989},""]
[null,"P(C=j | X=3)",0.24,0.35399999999999998,0.20100000000000001,8.7999999999999995E-2,8.5999999999999993E-2,3.1E-2,null,null,null,null,{"$f":"IF(MultMdl!R9=0,\"\",SUM(C9:L9))","v":0.99999999999999989},""]
[null,"P(C=j | X=4)",0.254,0.35,0.21,8.6999999999999994E-2,6.3E-2,3.5999999999999997E-2,null,null,null,null,{"$f":"IF(MultMdl!R10=0,\"\",SUM(C10:L10))","v":1},""]
[null,"P(C=j | X=5)",0.23799999999999999,0.35699999999999998,0.191,7.6999999999999999E-2,8.7999999999999995E-2,4.9000000000000002E-2,null,null,null,null,{"$f":"IF(MultMdl!R11=0,\"\",SUM(C11:L11))","v":1},""]
[null,"P(C=j | X=6)",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(MultMdl!R12=0,\"\",SUM(C12:L12))","v":""},""]
[null,"P(C=j | X=7)",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(MultMdl!R13=0,\"\",SUM(C13:L13))","v":""},""]
[null,"P(C=j | X=8)",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(MultMdl!R14=0,\"\",SUM(C14:L14))","v":""},""]
[null,"P(C=j | X=9)",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(MultMdl!R15=0,\"\",SUM(C15:L15))","v":""},""]
[]
[]
[null,null,"Multiplicative model: RR_X,C = RR_X * RR_C"]
[null,"Level (X)","RR_Obs","RR_X",null,null,{"$f":"IF(($C$57*$D$57)<>1,\"\",MultMdl!G19)","v":"Result: Exact Solution"}]
[null,0,1,1,"A×RR_C","b","RR_C","Category (C)",{"$f":"IF(COUNTBLANK(I21:I29)=9,\"\",\"Warning:\")","v":""}]
[null,1,1.26,1.2188522727272726,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E21=\"\",\"\",MultMdl!E21))","v":-4.1733532850394231E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F21=\"\",\"\",MultMdl!F21))","v":-4.1733532850390193E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G21=\"\",\"\",MultMdl!G21))","v":0.8400000000011687},1,{"$f":"IF(G21>=0,\"\",\"** Invalid value **\")","v":""}]
[null,2,1.59,1.4715834843385969,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E22=\"\",\"\",MultMdl!E22))","v":-8.7446871591189315E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F22=\"\",\"\",MultMdl!F22))","v":-8.744687159119513E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G22=\"\",\"\",MultMdl!G22))","v":0.65999999999981895},2,{"$f":"IF(G22>=0,\"\",\"** Invalid value **\")","v":""}]
[null,3,1.67,1.5759781977511484,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E23=\"\",\"\",MultMdl!E23))","v":-7.4693144631219524E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F23=\"\",\"\",MultMdl!F23))","v":-7.4693144631219788E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G23=\"\",\"\",MultMdl!G23))","v":0.50000000000048317},3,""]
[null,4,1.98,1.8480861506330766,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E24=\"\",\"\",MultMdl!E24))","v":-8.6864934411104891E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F24=\"\",\"\",MultMdl!F24))","v":-8.6864934411098355E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G24=\"\",\"\",MultMdl!G24))","v":0.39999999999982094},4,""]
[null,5,2.1800000000000002,2.0719764999867087,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E25=\"\",\"\",MultMdl!E25))","v":-7.3866864319073064E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F25=\"\",\"\",MultMdl!F25))","v":-7.3866864319078129E-2},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G25=\"\",\"\",MultMdl!G25))","v":0.30000000000012861},5,""]
[null,6,null,null,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E26=\"\",\"\",MultMdl!E26))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F26=\"\",\"\",MultMdl!F26))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G26=\"\",\"\",MultMdl!G26))","v":""},6,""]
[null,7,null,"",{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E27=\"\",\"\",MultMdl!E27))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F27=\"\",\"\",MultMdl!F27))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G27=\"\",\"\",MultMdl!G27))","v":""},7,""]
[null,8,null,null,{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!E28=\"\",\"\",MultMdl!E28))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F28=\"\",\"\",MultMdl!F28))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G28=\"\",\"\",MultMdl!G28))","v":""},8,""]
[null,9,null,null,{"$f":"IF(($C$57*$D$57)<>1,\"\", IF(MultMdl!E29=\"\",\"\",MultMdl!E29))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!F29=\"\",\"\",MultMdl!F29))","v":""},{"$f":"IF(($C$57*$D$57)<>1,\"\",IF(MultMdl!G29=\"\",\"\",MultMdl!G29))","v":""},9,""]
[null,null,{"$f":"IF(D57=0,\"**Error: Mismatch in P(C|X) and number RR_Obs or RR_X**\",\"\")","v":""}]
[]
[]
[null,null,"Additive model: RR_X,C = 1 + ERR_X + ERR_C"]
[null,"Level (X)","ERR_Obs","ERR_X",null,null,{"$f":"IF(($C$58*$D$58)<>1,\"\",AddMdl!B16)","v":"Result: Exact Solution"}]
[null,0,0,0,"A×ERR_C","-b","ERR_C","Category (C)",{"$f":"IF(COUNTBLANK(I36:I44)=9,\"\",\"Warning:\")","v":""}]
[null,1,0.26,0.16177559999999999,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C36=\"\",\"\",AddMdl!B18))","v":-9.8224400000000073E-2},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C36=\"\",\"\",AddMdl!C18))","v":-9.8224400000000017E-2},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!B31=1,AddMdl!D18,\"\"))","v":-0.15999999999999925},1,{"$f":"IF(G36>=-1,\"\",\"** Invalid value **\")","v":""}]
[null,2,0.59000000000000008,0.36434540000000004,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C37=\"\",\"\",AddMdl!B19))","v":-0.22565460000000021},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C37=\"\",\"\",AddMdl!C19))","v":-0.22565460000000004},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!C31=1,AddMdl!D19,\"\"))","v":-0.33999999999999808},2,""]
[null,3,0.66999999999999993,0.43643019999999999,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C38=\"\",\"\",AddMdl!B20))","v":-0.23356980000000008},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C38=\"\",\"\",AddMdl!C20))","v":-0.23356979999999994},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!D31=1,AddMdl!D20,\"\"))","v":-0.50000000000000622},3,""]
[null,4,0.98,0.64971879999999993,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C39=\"\",\"\",AddMdl!B21))","v":-0.33028120000000022},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C39=\"\",\"\",AddMdl!C21))","v":-0.33028120000000005},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!E31=1,AddMdl!D21,\"\"))","v":-0.60000000000000075},4,""]
[null,5,1.1800000000000002,0.80649080000000017,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C40=\"\",\"\",AddMdl!B22))","v":-0.37350920000000021},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C40=\"\",\"\",AddMdl!C22))","v":-0.37350919999999999},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!F31=1,AddMdl!D22,\"\"))","v":-0.69999999999999929},5,""]
[null,6,null,null,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C41=\"\",\"\",AddMdl!B23))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C41=\"\",\"\",AddMdl!C23))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!G31=1,AddMdl!D23,\"\"))","v":""},6,""]
[null,7,null,"",{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C42=\"\",\"\",AddMdl!B24))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C42=\"\",\"\",AddMdl!C24))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!H31=1,AddMdl!D24,\"\"))","v":""},7,""]
[null,8,null,"",{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C43=\"\",\"\",AddMdl!B25))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C43=\"\",\"\",AddMdl!C25))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!I31=1,AddMdl!D25,\"\"))","v":""},8,""]
[null,9,null,null,{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C44=\"\",\"\",AddMdl!B26))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(C44=\"\",\"\",AddMdl!C26))","v":""},{"$f":"IF(($C$58*$D$58)<>1,\"\",IF(AddMdl!J31=1,AddMdl!D26,\"\"))","v":""},9,""]
[null,null,{"$f":"IF(D58=0,\"**Error: Mismatch in P(C|X) and number ERR_Obs or ERR_X**\",\"\")","v":""}]
[null,null,{"$f":"IF(C59=0,\"\",\"**Error: One or more invalid values for P(C|X)**\")","v":""}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Display(mult)=",{"$f":"IF((SUM(M6:M15)>0)*(COUNTBLANK(C21:C29)=COUNTBLANK(D21:D29))*(COUNTBLANK(C21:C29)<9)=1,1,0)","v":1},{"$f":"IF((SUM(M6:M15)=(10-COUNTBLANK(C21:C29)))*(SUM(M6:M15)=(10-COUNTBLANK(D21:D29)))=1,1,0)","v":1}]
[null,"Display(add)=",{"$f":"IF((SUM(M6:M15)>0)*(COUNTBLANK(C36:C44)=COUNTBLANK(D36:D44))*(COUNTBLANK(C36:C44)<9)=1,1,0)","v":1},{"$f":"IF((SUM(M6:M15)=(10-COUNTBLANK(C36:C44)))*(SUM(M6:M15)=(10-COUNTBLANK(D36:D44))),1,0)","v":1}]
[null,"P(C|X) valid",{"$f":"IF((COUNTIF(C6:L15,\"<0\") + COUNTIF(C6:L15,\">1\"))>0,1,0)","v":0}]

{"sheet":"MultMdl","index":6,"n_rows":138,"n_cols":29,"rows_kept":138,"cut":false,"hidden":true,"merged":[[47,17,47,18],[1,1,1,12],[3,2,3,11],[17,2,17,7],[18,6,18,7]]}
[]
[null,"Solve for RR_C (ERR_C): Given P(C=j|X=i), RR_Obs (ERR_Obs) and RR_X (ERR_X)"]
[]
[null,null,"Conditional probabilites P(C|X)"]
[null,null,0,1,2,3,4,5,6,7,8,9,"Sum",{"$f":"IF(COUNTBLANK(N6:N15)=10,\"\",\"Warning:\")","v":""}]
[null,"P(C=j | X=0)",{"$f":"IF(Solve_RRC!C6=\"\",0,Solve_RRC!C6)","v":0.156},{"$f":"IF(Solve_RRC!D6=\"\",0,Solve_RRC!D6)","v":0.33300000000000002},{"$f":"IF(Solve_RRC!E6=\"\",0,Solve_RRC!E6)","v":0.25900000000000001},{"$f":"IF(Solve_RRC!F6=\"\",0,Solve_RRC!F6)","v":0.115},{"$f":"IF(Solve_RRC!G6=\"\",0,Solve_RRC!G6)","v":9.8000000000000004E-2},{"$f":"IF(Solve_RRC!H6=\"\",0,Solve_RRC!H6)","v":3.9E-2},{"$f":"IF(Solve_RRC!I6=\"\",0,Solve_RRC!I6)","v":0},{"$f":"IF(Solve_RRC!J6=\"\",0,Solve_RRC!J6)","v":0},{"$f":"IF(Solve_RRC!K6=\"\",0,Solve_RRC!K6)","v":0},{"$f":"IF(Solve_RRC!L6=\"\",0,Solve_RRC!L6)","v":0},{"$f":"SUM(C6:L6)","v":1},{"$f":"IF(M6=0,\"\",IF(ABS(M6-1)<tol_Pr,\"\",\"**P(C|X) ≠ 1**\"))","v":""},null,null,null,{"$f":"COUNTIF(C6:L6,\">0\")","v":6}]
[null,"P(C=j | X=1)",{"$f":"IF(Solve_RRC!C7=\"\",0,Solve_RRC!C7)","v":0.20300000000000001},{"$f":"IF(Solve_RRC!D7=\"\",0,Solve_RRC!D7)","v":0.34},{"$f":"IF(Solve_RRC!E7=\"\",0,Solve_RRC!E7)","v":0.23499999999999999},{"$f":"IF(Solve_RRC!F7=\"\",0,Solve_RRC!F7)","v":0.10299999999999999},{"$f":"IF(Solve_RRC!G7=\"\",0,Solve_RRC!G7)","v":8.3000000000000004E-2},{"$f":"IF(Solve_RRC!H7=\"\",0,Solve_RRC!H7)","v":3.5999999999999997E-2},{"$f":"IF(Solve_RRC!I7=\"\",0,Solve_RRC!I7)","v":0},{"$f":"IF(Solve_RRC!J7=\"\",0,Solve_RRC!J7)","v":0},{"$f":"IF(Solve_RRC!K7=\"\",0,Solve_RRC!K7)","v":0},{"$f":"IF(Solve_RRC!L7=\"\",0,Solve_RRC!L7)","v":0},{"$f":"SUM(C7:L7)","v":1},"",null,null,null,{"$f":"COUNTIF(C7:L7,\">0\")","v":6}]
[null,"P(C=j | X=2)",{"$f":"IF(Solve_RRC!C8=\"\",0,Solve_RRC!C8)","v":0.25600000000000001},{"$f":"IF(Solve_RRC!D8=\"\",0,Solve_RRC!D8)","v":0.36699999999999999},{"$f":"IF(Solve_RRC!E8=\"\",0,Solve_RRC!E8)","v":0.20200000000000001},{"$f":"IF(Solve_RRC!F8=\"\",0,Solve_RRC!F8)","v":7.9000000000000001E-2},{"$f":"IF(Solve_RRC!G8=\"\",0,Solve_RRC!G8)","v":6.7000000000000004E-2},{"$f":"IF(Solve_RRC!H8=\"\",0,Solve_RRC!H8)","v":2.9000000000000001E-2},{"$f":"IF(Solve_RRC!I8=\"\",0,Solve_RRC!I8)","v":0},{"$f":"IF(Solve_RRC!J8=\"\",0,Solve_RRC!J8)","v":0},{"$f":"IF(Solve_RRC!K8=\"\",0,Solve_RRC!K8)","v":0},{"$f":"IF(Solve_RRC!L8=\"\",0,Solve_RRC!L8)","v":0},0.99999999999999989,"",null,null,null,6]
[null,"P(C=j | X=3)",{"$f":"IF(Solve_RRC!C9=\"\",0,Solve_RRC!C9)","v":0.24},{"$f":"IF(Solve_RRC!D9=\"\",0,Solve_RRC!D9)","v":0.35399999999999998},{"$f":"IF(Solve_RRC!E9=\"\",0,Solve_RRC!E9)","v":0.20100000000000001},{"$f":"IF(Solve_RRC!F9=\"\",0,Solve_RRC!F9)","v":8.7999999999999995E-2},{"$f":"IF(Solve_RRC!G9=\"\",0,Solve_RRC!G9)","v":8.5999999999999993E-2},{"$f":"IF(Solve_RRC!H9=\"\",0,Solve_RRC!H9)","v":3.1E-2},{"$f":"IF(Solve_RRC!I9=\"\",0,Solve_RRC!I9)","v":0},{"$f":"IF(Solve_RRC!J9=\"\",0,Solve_RRC!J9)","v":0},{"$f":"IF(Solve_RRC!K9=\"\",0,Solve_RRC!K9)","v":0},{"$f":"IF(Solve_RRC!L9=\"\",0,Solve_RRC!L9)","v":0},0.99999999999999989,"",null,null,null,6]
[null,"P(C=j | X=4)",{"$f":"IF(Solve_RRC!C10=\"\",0,Solve_RRC!C10)","v":0.254},{"$f":"IF(Solve_RRC!D10=\"\",0,Solve_RRC!D10)","v":0.35},{"$f":"IF(Solve_RRC!E10=\"\",0,Solve_RRC!E10)","v":0.21},{"$f":"IF(Solve_RRC!F10=\"\",0,Solve_RRC!F10)","v":8.6999999999999994E-2},{"$f":"IF(Solve_RRC!G10=\"\",0,Solve_RRC!G10)","v":6.3E-2},{"$f":"IF(Solve_RRC!H10=\"\",0,Solve_RRC!H10)","v":3.5999999999999997E-2},{"$f":"IF(Solve_RRC!I10=\"\",0,Solve_RRC!I10)","v":0},{"$f":"IF(Solve_RRC!J10=\"\",0,Solve_RRC!J10)","v":0},{"$f":"IF(Solve_RRC!K10=\"\",0,Solve_RRC!K10)","v":0},{"$f":"IF(Solve_RRC!L10=\"\",0,Solve_RRC!L10)","v":0},1,"",null,null,null,6]
[null,"P(C=j | X=5)",{"$f":"IF(Solve_RRC!C11=\"\",0,Solve_RRC!C11)","v":0.23799999999999999},{"$f":"IF(Solve_RRC!D11=\"\",0,Solve_RRC!D11)","v":0.35699999999999998},{"$f":"IF(Solve_RRC!E11=\"\",0,Solve_RRC!E11)","v":0.191},{"$f":"IF(Solve_RRC!F11=\"\",0,Solve_RRC!F11)","v":7.6999999999999999E-2},{"$f":"IF(Solve_RRC!G11=\"\",0,Solve_RRC!G11)","v":8.7999999999999995E-2},{"$f":"IF(Solve_RRC!H11=\"\",0,Solve_RRC!H11)","v":4.9000000000000002E-2},{"$f":"IF(Solve_RRC!I11=\"\",0,Solve_RRC!I11)","v":0},{"$f":"IF(Solve_RRC!J11=\"\",0,Solve_RRC!J11)","v":0},{"$f":"IF(Solve_RRC!K11=\"\",0,Solve_RRC!K11)","v":0},{"$f":"IF(Solve_RRC!L11=\"\",0,Solve_RRC!L11)","v":0},1,"",null,null,null,6]
[null,"P(C=j | X=6)",{"$f":"IF(Solve_RRC!C12=\"\",0,Solve_RRC!C12)","v":0},{"$f":"IF(Solve_RRC!D12=\"\",0,Solve_RRC!D12)","v":0},{"$f":"IF(Solve_RRC!E12=\"\",0,Solve_RRC!E12)","v":0},{"$f":"IF(Solve_RRC!F12=\"\",0,Solve_RRC!F12)","v":0},{"$f":"IF(Solve_RRC!G12=\"\",0,Solve_RRC!G12)","v":0},{"$f":"IF(Solve_RRC!H12=\"\",0,Solve_RRC!H12)","v":0},{"$f":"IF(Solve_RRC!I12=\"\",0,Solve_RRC!I12)","v":0},{"$f":"IF(Solve_RRC!J12=\"\",0,Solve_RRC!J12)","v":0},{"$f":"IF(Solve_RRC!K12=\"\",0,Solve_RRC!K12)","v":0},{"$f":"IF(Solve_RRC!L12=\"\",0,Solve_RRC!L12)","v":0},0,"",null,null,null,0]
[null,"P(C=j | X=7)",{"$f":"IF(Solve_RRC!C13=\"\",0,Solve_RRC!C13)","v":0},{"$f":"IF(Solve_RRC!D13=\"\",0,Solve_RRC!D13)","v":0},{"$f":"IF(Solve_RRC!E13=\"\",0,Solve_RRC!E13)","v":0},{"$f":"IF(Solve_RRC!F13=\"\",0,Solve_RRC!F13)","v":0},{"$f":"IF(Solve_RRC!G13=\"\",0,Solve_RRC!G13)","v":0},{"$f":"IF(Solve_RRC!H13=\"\",0,Solve_RRC!H13)","v":0},{"$f":"IF(Solve_RRC!I13=\"\",0,Solve_RRC!I13)","v":0},{"$f":"IF(Solve_RRC!J13=\"\",0,Solve_RRC!J13)","v":0},{"$f":"IF(Solve_RRC!K13=\"\",0,Solve_RRC!K13)","v":0},{"$f":"IF(Solve_RRC!L13=\"\",0,Solve_RRC!L13)","v":0},0,"",null,null,null,0]
[null,"P(C=j | X=8)",{"$f":"IF(Solve_RRC!C14=\"\",0,Solve_RRC!C14)","v":0},{"$f":"IF(Solve_RRC!D14=\"\",0,Solve_RRC!D14)","v":0},{"$f":"IF(Solve_RRC!E14=\"\",0,Solve_RRC!E14)","v":0},{"$f":"IF(Solve_RRC!F14=\"\",0,Solve_RRC!F14)","v":0},{"$f":"IF(Solve_RRC!G14=\"\",0,Solve_RRC!G14)","v":0},{"$f":"IF(Solve_RRC!H14=\"\",0,Solve_RRC!H14)","v":0},{"$f":"IF(Solve_RRC!I14=\"\",0,Solve_RRC!I14)","v":0},{"$f":"IF(Solve_RRC!J14=\"\",0,Solve_RRC!J14)","v":0},{"$f":"IF(Solve_RRC!K14=\"\",0,Solve_RRC!K14)","v":0},{"$f":"IF(Solve_RRC!L14=\"\",0,Solve_RRC!L14)","v":0},0,"",null,null,null,0]
[null,"P(C=j | X=9)",{"$f":"IF(Solve_RRC!C15=\"\",0,Solve_RRC!C15)","v":0},{"$f":"IF(Solve_RRC!D15=\"\",0,Solve_RRC!D15)","v":0},{"$f":"IF(Solve_RRC!E15=\"\",0,Solve_RRC!E15)","v":0},{"$f":"IF(Solve_RRC!F15=\"\",0,Solve_RRC!F15)","v":0},{"$f":"IF(Solve_RRC!G15=\"\",0,Solve_RRC!G15)","v":0},{"$f":"IF(Solve_RRC!H15=\"\",0,Solve_RRC!H15)","v":0},{"$f":"IF(Solve_RRC!I15=\"\",0,Solve_RRC!I15)","v":0},{"$f":"IF(Solve_RRC!J15=\"\",0,Solve_RRC!J15)","v":0},{"$f":"IF(Solve_RRC!K15=\"\",0,Solve_RRC!K15)","v":0},{"$f":"IF(Solve_RRC!L15=\"\",0,Solve_RRC!L15)","v":0},0,"",null,null,null,0]
[]
[]
[null,null,"Multiplicative model: RR_X,C = RR_X * RR_C"]
[null,"Level (X)","RR_Obs","RR_X",null,null,{"$f":"IF(SUM(R6:R15)=0,\"\",IF(S60=10,IF(L48=T64,\"Result: Exact Solution\",\"Result: No unique soln\"),\"Result: No unique soln\"))","v":"Result: Exact Solution"}]
[null,0,{"$f":"IF(Solve_RRC!C20=\"\",\"\",Solve_RRC!C20)","v":1},{"$f":"IF(Solve_RRC!D20=\"\",\"\",Solve_RRC!D20)","v":1},"A×RR_C","b","RR_C","Category (C)",{"$f":"IF(COUNTBLANK(I21:I29)=9,\"\",\"Warning:\")","v":""}]
[null,1,{"$f":"IF(Solve_RRC!C21=\"\",\"\",Solve_RRC!C21)","v":1.26},{"$f":"IF(Solve_RRC!D21=\"\",\"\",Solve_RRC!D21)","v":1.2188522727272726},{"$f":"IF(C21=\"\",\"\",D36)","v":-4.1733532850394231E-2},{"$f":"IF(C21=\"\",\"\",E36)","v":-4.1733532850390193E-2},{"$f":"IF(C48=1,F36,\"\")","v":0.8400000000011687},1,{"$f":"IF(G21>=0,\"\",\"** Invalid value **\")","v":""}]
[null,2,{"$f":"IF(Solve_RRC!C22=\"\",\"\",Solve_RRC!C22)","v":1.59},{"$f":"IF(Solve_RRC!D22=\"\",\"\",Solve_RRC!D22)","v":1.4715834843385969},-8.7446871591189315E-2,-8.744687159119513E-2,{"$f":"IF(D48=1,F37,\"\")","v":0.65999999999981895},2,{"$f":"IF(G22>=0,\"\",\"** Invalid value **\")","v":""}]
[null,3,{"$f":"IF(Solve_RRC!C23=\"\",\"\",Solve_RRC!C23)","v":1.67},{"$f":"IF(Solve_RRC!D23=\"\",\"\",Solve_RRC!D23)","v":1.5759781977511484},-7.4693144631219524E-2,-7.4693144631219788E-2,{"$f":"IF(E48=1,F38,\"\")","v":0.50000000000048317},3,""]
[null,4,{"$f":"IF(Solve_RRC!C24=\"\",\"\",Solve_RRC!C24)","v":1.98},{"$f":"IF(Solve_RRC!D24=\"\",\"\",Solve_RRC!D24)","v":1.8480861506330766},-8.6864934411104891E-2,-8.6864934411098355E-2,{"$f":"IF(F48=1,F39,\"\")","v":0.39999999999982094},4,""]
[null,5,{"$f":"IF(Solve_RRC!C25=\"\",\"\",Solve_RRC!C25)","v":2.1800000000000002},{"$f":"IF(Solve_RRC!D25=\"\",\"\",Solve_RRC!D25)","v":2.0719764999867087},-7.3866864319073064E-2,-7.3866864319078129E-2,{"$f":"IF(G48=1,F40,\"\")","v":0.30000000000012861},5,""]
[null,6,{"$f":"IF(Solve_RRC!C26=\"\",\"\",Solve_RRC!C26)","v":""},{"$f":"IF(Solve_RRC!D26=\"\",\"\",Solve_RRC!D26)","v":""},"","",{"$f":"IF(H48=1,F41,\"\")","v":""},6,""]
[null,7,{"$f":"IF(Solve_RRC!C27=\"\",\"\",Solve_RRC!C27)","v":""},{"$f":"IF(Solve_RRC!D27=\"\",\"\",Solve_RRC!D27)","v":""},{"$f":"IF(C27=\"\",\"\",D42)","v":""},{"$f":"IF(C27=\"\",\"\",E42)","v":""},{"$f":"IF(I48=1,F42,\"\")","v":""},7,""]
[null,8,{"$f":"IF(Solve_RRC!C28=\"\",\"\",Solve_RRC!C28)","v":""},{"$f":"IF(Solve_RRC!D28=\"\",\"\",Solve_RRC!D28)","v":""},"","",{"$f":"IF(J48=1,F43,\"\")","v":""},8,""]
[null,9,{"$f":"IF(Solve_RRC!C29=\"\",\"\",Solve_RRC!C29)","v":""},{"$f":"IF(Solve_RRC!D29=\"\",\"\",Solve_RRC!D29)","v":""},"","",{"$f":"IF(K48=1,F44,\"\")","v":""},9,""]
[null,null,{"$f":"IF(C34<C33,\"Error: # RRs < # P(C|X=i)\",IF(C34>C33,\"Note: # RR_Obs > # P(C | X=i)\",\"\"))","v":""},null,null,null,{"$f":"IF(C34<C33,\"\",IF(G19=\"Result: No Unique soln\",CONCATENATE(G36,G39,G37),IF(G19=\"Result: Inf # of Solns\",G38,\"\")))","v":""}]
[]
[]
[null,"#P(C|X)",{"$f":"COUNTIF(M6:M15,\"=1\")","v":6}]
[null,"#RR_Obs",{"$f":"MIN(10-COUNTBLANK(C20:C29),10-COUNTBLANK(D20:D29))","v":6}]
[null,null,"Diff","A×RR_C","b","RR_C"]
[null,null,{"$f":"ROUND(D36-E36,Rnd_solve)","v":0},{"$f":"MMULT(C51:K59,F36:F44)","v":-4.1733532850394231E-2},{"$f":"B51","v":-4.1733532850390193E-2},{"$f":"MMULT(C63:K71,B51:B59)","v":0.8400000000011687},"** Check: # rows/cols: RR_C solves first "]
[null,null,0,-8.7446871591189315E-2,{"$f":"B52","v":-8.744687159119513E-2},0.65999999999981895," eqns **",null,"`"]
[null,null,0,-7.4693144631219524E-2,{"$f":"B53","v":-7.4693144631219788E-2},0.50000000000048317,{"$f":"IF(G40<L48,\"** Check: I < J **\",\"\")","v":""}]
[null,null,0,-8.6864934411104891E-2,-8.6864934411098355E-2,0.39999999999982094,{"$f":"COUNTIF(C36:C44,\"=0\")","v":9}]
[null,null,0,-7.3866864319073064E-2,-7.3866864319078129E-2,0.30000000000012861,{"$f":"COUNTIF(R6:R15,\">0\") - 1","v":5}]
[null,null,0,0,0,0]
[null,null,0,0,0,0]
[null,null,0,0,0,0]
[null,null,0,0,0,0]
[]
[null,"RR_C"]
[null,1,{"$f":"IF(F36=0,0,F36)","v":0.8400000000011687},{"$f":"IF(F37=0,0,F37)","v":0.65999999999981895},{"$f":"IF(F38=0,0,F38)","v":0.50000000000048317},{"$f":"IF(F39=0,0,F39)","v":0.39999999999982094},{"$f":"IF(F40=0,0,F40)","v":0.30000000000012861},{"$f":"IF(F41=0,0,F41)","v":0},{"$f":"IF(F42=0,0,F42)","v":0},{"$f":"IF(F43=0,0,F43)","v":0},{"$f":"IF(F44=0,0,F44)","v":0}]
[null,{"$f":"ROUND(SUM(C6:C15)>0,1)","v":1},1,1,1,1,1,0,0,0,0,{"$f":"SUM(C48:K48)","v":5},null,null,null,null,null,"Check results",null,"Conditional distributions"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"RR_Obs","RR_X",null,"∑_j π_j RR_C(j)","RR_X",0,1,2,3,4,5,6,7,8,9]
[null,"b","A",null,null,null,null,null,null,null,null,"Det",null,null,{"$f":"IF(C20=\"\",0,C20)","v":1},{"$f":"IF(D20=\"\",0,D20)","v":1},0,{"$f":"MMULT($B$47:$K$47,TRANSPOSE(T50:AC50))","v":0.7150600000003855},{"$f":"IF(R50=0,1,ROUND((O50/P50)/(R50/$R$50),Rnd_solve))","v":1},{"$f":"IF(C6=\"\",0,C6)","v":0.156},{"$f":"IF(D6=\"\",0,D6)","v":0.33300000000000002},{"$f":"IF(E6=\"\",0,E6)","v":0.25900000000000001},{"$f":"IF(F6=\"\",0,F6)","v":0.115},{"$f":"IF(G6=\"\",0,G6)","v":9.8000000000000004E-2},{"$f":"IF(H6=\"\",0,H6)","v":3.9E-2},{"$f":"IF(I6=\"\",0,I6)","v":0},{"$f":"IF(J6=\"\",0,J6)","v":0},{"$f":"IF(K6=\"\",0,K6)","v":0},{"$f":"IF(L6=\"\",0,L6)","v":0}]
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[null,{"$f":"IF($P52=0,0,$O52/$P52*C$6-C8)","v":-8.744687159119513E-2},{"$f":"IF($P52=0,0,D8-$O52/$P52*D$6)","v":7.2038989735126457E-3},-7.7841411909490121E-2,-4.5253908762901029E-2,-3.8885939641428696E-2,-1.3138282102201217E-2,0,0,0,0,{"$f":"MDETERM(C51:D52)","v":5.6607627331972188E-4},null,null,1.59,1.4715834843385969,2,{"$f":"MMULT($B$47:$K$47,TRANSPOSE(T52:AC52 ))","v":0.77260000000042228},{"$f":"IF(R52=0,1,ROUND((O52/P52)/(R52/$R$50),Rnd_solve))","v":1},0.25600000000000001,0.36699999999999999,0.20200000000000001,7.9000000000000001E-2,6.7000000000000004E-2,2.9000000000000001E-2,0,0,0,0]
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[null,0,0,0,0,0,0,0,0,0,0,{"$f":"MDETERM(C51:H56)","v":0},null,null,0,0,6,{"$f":"MMULT($B$47:$K$47,TRANSPOSE(T56:AC56))","v":0},1,0,0,0,0,0,0,0,0,0,0]
[null,0,0,0,0,0,0,0,0,0,0,{"$f":"MDETERM(C51:I57)","v":0},null,null,0,0,7,{"$f":"MMULT($B$47:$K$47,TRANSPOSE(T57:AC57))","v":0},1,0,0,0,0,0,0,0,0,0,0]
[null,0,0,0,0,0,0,0,0,0,0,{"$f":"MDETERM(C51:J58)","v":0},null,null,0,0,8,{"$f":"MMULT($B$47:$K$47,TRANSPOSE(T58:AC58))","v":0},1,0,0,0,0,0,0,0,0,0,0]
[null,{"$f":"IF($P59=0,0,$O59/$P59*C$6-C15)","v":0},0,0,0,0,0,0,0,0,0,{"$f":"MDETERM(C51:K59)","v":0},null,null,0,0,9,{"$f":"MMULT($B$47:$K$47,TRANSPOSE(T59:AC59))","v":0},1,0,0,0,0,0,0,0,0,0,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNTIF(S50:S59,\"=1\")","v":10},{"$f":"IF(SUM(T50:T59)>0,1,0)","v":1},{"$f":"IF(SUM(U50:U59)>0,1,0)","v":1},1,1,1,1,0,0,0,0]
[null,"A^-1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"."]
[null,null,1,2,3,4,5,6,7,8,9]
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{"sheet":"AddMdl","index":7,"n_rows":120,"n_cols":28,"rows_kept":120,"cut":false,"hidden":true,"merged":[[31,16,31,17],[15,1,15,3],[0,0,0,4],[1,3,1,12]]}
["For ERR_Obs and ERR_X fixed, solve for ERR_C"]
[null,null,null,"Conditional probabilites P(C|X)"]
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[{"$f":"IF(Solve_RRC!C44=\"\",0,Solve_RRC!C44)","v":0},{"$f":"IF(Solve_RRC!D44=\"\",0,Solve_RRC!D44)","v":0},"P(C=j | E=9)",{"$f":"IF(Solve_RRC!C15=\"\",0,Solve_RRC!C15)","v":0},{"$f":"IF(Solve_RRC!D15=\"\",0,Solve_RRC!D15)","v":0},{"$f":"IF(Solve_RRC!E15=\"\",0,Solve_RRC!E15)","v":0},{"$f":"IF(Solve_RRC!F15=\"\",0,Solve_RRC!F15)","v":0},{"$f":"IF(Solve_RRC!G15=\"\",0,Solve_RRC!G15)","v":0},{"$f":"IF(Solve_RRC!H15=\"\",0,Solve_RRC!H15)","v":0},{"$f":"IF(Solve_RRC!I15=\"\",0,Solve_RRC!I15)","v":0},{"$f":"IF(Solve_RRC!J15=\"\",0,Solve_RRC!J15)","v":0},{"$f":"IF(Solve_RRC!K15=\"\",0,Solve_RRC!K15)","v":0},{"$f":"IF(Solve_RRC!L15=\"\",0,Solve_RRC!L15)","v":0},0,"",0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"((N4 =1)+(N4 =0))*((N5 =1)+(N5 =0))*((N6=1)+(N6=0))*((N7=1)+(N7=0))*((N8=1)+(N8=0))*((N9=1)+(N9=0))*((N10=1)+(N10=0))*((N11=1)+(N11=0))*((N12=1)+(N12=0))*((N13=1)+(N13=0))","v":1}]
[]
[null,{"$f":"IF(SUM(P4:P13)=0,\"\",IF(R44=10,IF(S48=K31,\"Result: Exact Solution\",\"Result: No unique soln\"),\"Result: No unique soln\"))","v":"Result: Exact Solution"}]
[null,"A×ERR_C","-b","ERR_C","Level"]
[{"$f":"COUNTIF(F18:F26,\"=0\")","v":9},{"$f":"MMULT(B34:J42,D18:D26)","v":-9.8224400000000073E-2},{"$f":"A34","v":-9.8224400000000017E-2},{"$f":"MMULT(B46:J54,A34:A42)","v":-0.15999999999999925},1,{"$f":"ROUND(B18-C18,Rnd_solve)","v":0}]
[{"$f":"COUNTIF(Solve_RRC!R6:R15,\">0\") - 1","v":-1},-0.22565460000000021,{"$f":"A35","v":-0.22565460000000004},-0.33999999999999808,2,{"$f":"ROUND(B19-C19,Rnd_solve)","v":0}]
[null,-0.23356980000000008,-0.23356979999999994,-0.50000000000000622,3,0]
[null,-0.33028120000000022,-0.33028120000000005,-0.60000000000000075,4,0]
[null,-0.37350920000000021,-0.37350919999999999,-0.69999999999999929,5,0]
[null,0,0,0,6,0]
[null,0,0,0,7,0]
[null,0,0,0,8,0]
[null,0,0,0,9,0]
[]
[]
["ERR_c"]
[0,{"$f":"IF(D18=0,0,D18)","v":-0.15999999999999925},{"$f":"IF(D19=0,0,D19)","v":-0.33999999999999808},{"$f":"IF(D20=0,0,D20)","v":-0.50000000000000622},{"$f":"IF(D21=0,0,D21)","v":-0.60000000000000075},{"$f":"IF(D22=0,0,D22)","v":-0.69999999999999929},{"$f":"IF(D23=0,0,D23)","v":0},{"$f":"IF(D24=0,0,D24)","v":0},{"$f":"IF(D25=0,0,D25)","v":0},{"$f":"IF(D26=0,0,D26)","v":0}]
[{"$f":"ROUND(SUM(D4:D13)>0,1)","v":1},{"$f":"ROUND(SUM(E4:E13)>0,1)","v":1},1,1,1,1,0,0,0,0,{"$f":"SUM(B31:J31)","v":5}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Check results"]
["-b","A",null,null,null,null,null,null,null,null,"Det",null,null,null,null,null,"∑_j π_j ERR_C(j)","ERR_X","Conditional probabilites P(C|X=i)"]
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{"sheet":"RegSm","index":8,"n_rows":194,"n_cols":35,"rows_kept":194,"cut":false,"hidden":true,"merged":[[141,0,141,4],[170,0,170,4],[119,2,119,5],[2,14,2,17],[2,7,2,10],[24,5,24,6],[24,7,24,8],[73,2,73,5],[73,6,73,9],[139,0,139,4],[168,0,168,4],[73,11,73,12],[73,13,73,14],[119,13,119,14]]}
[" Find RR_X: Fitted Mult RR model with Excel (not used)",null,null,null,null,null,null,"Intercept=",{"$f":"IF(IndrctAdj!K52=1,1,IF(IndrctAdj!K52=\"Y\",1,0))","v":0},null,null,null,null,null,"Return"]
["No RR_X=",{"$f":"16-COUNTBLANK(A5:A20)","v":7},"no. scrs =",{"$f":"16-COUNTBLANK(D5:D20)","v":7},null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(P5:P20)","v":1.6197531328253537E-2},null,{"$f":"SUM(R5:R20)","v":1.8860517797473424E-2}]
["No RR_Obs=",{"$f":"16-COUNTBLANK(B5:B20)","v":7},null,null,null,null,null,"Fitted - log-linear (OLS)",null,null,null,null,"RR_X-1","RR_obs-1","Fitted - linear (OLS)"]
["RR_X","RR_obs","Const","x",null,"ln(RR_X)","ln(RR_obs)","alpha","Beta","alpha","Beta",null,"ERR_X","ERR_obs","alpha","Beta","alpha","Beta"]
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[{"$f":"IF(IndrctAdj!E46=\"\",\"\",IndrctAdj!E46)","v":""},{"$f":"IF(IndrctAdj!C46=\"\",\"\",IndrctAdj!C46)","v":""},1,{"$f":"IF(IndrctAdj!D22=\"\",\"\",IndrctAdj!D22)","v":""},15,"","",{"$f":"IF($B$2=E19,INTERCEPT($F$5:F19,$D$5:D19)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E19,LINEST($F$5:F19,$D$5:D19,$I$1),\"\")","v":""},{"$f":"IF($B$2=E19,INTERCEPT($G$5:G19,$D$5:D19)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E19,LINEST($G$5:G19,$D$5:D19,$I$1),\"\")","v":""},null,"","",{"$f":"IF($B$2=E19,INTERCEPT($M$5:M19,$D$5:D19)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E19,LINEST($M$5:M19,$D$5:D19,$I$1),\"\")","v":""},{"$f":"IF($B$2=E19,INTERCEPT($N$5:N19,$D$5:D19)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E19,LINEST($N$5:N19,$D$5:D19,$I$1),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E47=\"\",\"\",IndrctAdj!E47)","v":""},{"$f":"IF(IndrctAdj!C47=\"\",\"\",IndrctAdj!C47)","v":""},1,{"$f":"IF(IndrctAdj!D23=\"\",\"\",IndrctAdj!D23)","v":""},16,{"$f":"IF(A20=\"\",\"\",LN(A20))","v":""},{"$f":"IF(B20=\"\",\"\",LN(B20))","v":""},{"$f":"IF($B$2=E20,INTERCEPT($F$5:F20,$D$5:D20)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E20,LINEST($F$5:F20,$D$5:D20,$I$1),\"\")","v":""},{"$f":"IF($B$2=E20,INTERCEPT($G$5:G20,$D$5:D20)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E20,LINEST($G$5:G20,$D$5:D20,$I$1),\"\")","v":""},null,{"$f":"IF(A20=\"\",\"\",A20-1)","v":""},{"$f":"IF(B20=\"\",\"\",B20-1)","v":""},{"$f":"IF($B$2=E20,INTERCEPT($M$5:M20,$D$5:D20)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E20,LINEST($M$5:M20,$D$5:D20,$I$1),\"\")","v":""},{"$f":"IF($B$2=E20,INTERCEPT($N$5:N20,$D$5:D20)*$I$1,\"\")","v":""},{"$f":"IF($B$2=E20,LINEST($N$5:N20,$D$5:D20,$I$1),\"\")","v":""}]
[null,null,null,null,null,null,"Return",{"$f":"SUM(H5:H20)","v":0},{"$f":"SUM(I5:I20)","v":1.1470477280392896E-2},0,1.28169445056812E-2,null,null,"Return",{"$f":"SUM(O5:O20)","v":0},{"$f":"SUM(P5:P20)","v":1.6197531328253537E-2},0,1.8860517797473424E-2]
[]
[" Find ERR_X: Fitted ERR Add model with Excel (not used)"]
["No ERR_X=",{"$f":"16-COUNTBLANK(A27:A42)","v":7},"no. scrs =",{"$f":"16-COUNTBLANK(D27:D42)","v":7},null,null,null,"Intercept=",{"$f":"IF(IndrctAdj!K99=1,1,IF(IndrctAdj!K99=\"Y\",1,0))","v":0}]
["No ERR_Obs=",{"$f":"16-COUNTBLANK(B27:B42)","v":7},null,null,null,"X",null,"Obs"]
["ERR_X","ERR_obs",null,"x",null,"alpha","Beta","alpha","Beta"]
[{"$f":"IF(IndrctAdj!E79=\"\",\"\",IndrctAdj!E79)","v":0},{"$f":"IF(IndrctAdj!C79=\"\",\"\",IndrctAdj!C79)","v":0},1,{"$f":"IF(IndrctAdj!D8=\"\",\"\",IndrctAdj!D8)","v":0},1]
[{"$f":"IF(IndrctAdj!E80=\"\",\"\",IndrctAdj!E80)","v":0.1806779432},{"$f":"IF(IndrctAdj!C80=\"\",\"\",IndrctAdj!C80)","v":0.26},1,{"$f":"IF(IndrctAdj!D9=\"\",\"\",IndrctAdj!D9)","v":6.6524299999999998},2,{"$f":"IF($B$24=E28,INTERCEPT($A$27:A28,$D$27:D28)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E28,LINEST($A$27:A28,$D$27:D28,$I$24),\"\")","v":""},{"$f":"IF($B$24=E28,INTERCEPT($B$27:B28,$D$27:D28)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E28,LINEST($B$27:B28,$D$27:D28,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E81=\"\",\"\",IndrctAdj!E81)","v":0.37226203880000008},{"$f":"IF(IndrctAdj!C81=\"\",\"\",IndrctAdj!C81)","v":0.59000000000000008},1,{"$f":"IF(IndrctAdj!D10=\"\",\"\",IndrctAdj!D10)","v":23.531600000000001},3,{"$f":"IF($B$24=E29,INTERCEPT($A$27:A29,$D$27:D29)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E29,LINEST($A$27:A29,$D$27:D29,$I$24),\"\")","v":""},{"$f":"IF($B$24=E29,INTERCEPT($B$27:B29,$D$27:D29)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E29,LINEST($B$27:B29,$D$27:D29,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E82=\"\",\"\",IndrctAdj!E82)","v":0.43807752439999997},{"$f":"IF(IndrctAdj!C82=\"\",\"\",IndrctAdj!C82)","v":0.66999999999999993},1,{"$f":"IF(IndrctAdj!D11=\"\",\"\",IndrctAdj!D11)","v":33.539400000000001},4,{"$f":"IF($B$24=E30,INTERCEPT($A$27:A30,$D$27:D30)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E30,LINEST($A$27:A30,$D$27:D30,$I$24),\"\")","v":""},{"$f":"IF($B$24=E30,INTERCEPT($B$27:B30,$D$27:D30)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E30,LINEST($B$27:B30,$D$27:D30,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E83=\"\",\"\",IndrctAdj!E83)","v":0.64598389359999997},{"$f":"IF(IndrctAdj!C83=\"\",\"\",IndrctAdj!C83)","v":0.98},1,{"$f":"IF(IndrctAdj!D12=\"\",\"\",IndrctAdj!D12)","v":43.674599999999998},5,{"$f":"IF($B$24=E31,INTERCEPT($A$27:A31,$D$27:D31)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E31,LINEST($A$27:A31,$D$27:D31,$I$24),\"\")","v":""},{"$f":"IF($B$24=E31,INTERCEPT($B$27:B31,$D$27:D31)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E31,LINEST($B$27:B31,$D$27:D31,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E84=\"\",\"\",IndrctAdj!E84)","v":0.79446647760000011},{"$f":"IF(IndrctAdj!C84=\"\",\"\",IndrctAdj!C84)","v":1.1800000000000002},1,{"$f":"IF(IndrctAdj!D13=\"\",\"\",IndrctAdj!D13)","v":53.618000000000002},6,{"$f":"IF($B$24=E32,INTERCEPT($A$27:A32,$D$27:D32)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E32,LINEST($A$27:A32,$D$27:D32,$I$24),\"\")","v":""},{"$f":"IF($B$24=E32,INTERCEPT($B$27:B32,$D$27:D32)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E32,LINEST($B$27:B32,$D$27:D32,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E85=\"\",\"\",IndrctAdj!E85)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C85=\"\",\"\",IndrctAdj!C85)","v":1.2599999999999998},1,{"$f":"IF(IndrctAdj!D14=\"\",\"\",IndrctAdj!D14)","v":80.8767},7,{"$f":"IF($B$24=E33,INTERCEPT($A$27:A33,$D$27:D33)*$I$24,\"\")","v":0},{"$f":"IF($B$24=E33,LINEST($A$27:A33,$D$27:D33,$I$24),\"\")","v":1.2568879307991523E-2},{"$f":"IF($B$24=E33,INTERCEPT($B$27:B33,$D$27:D33)*$I$24,\"\")","v":0},{"$f":"IF($B$24=E33,LINEST($B$27:B33,$D$27:D33,$I$24),\"\")","v":1.8860517797473424E-2}]
[{"$f":"IF(IndrctAdj!E86=\"\",\"\",IndrctAdj!E86)","v":""},{"$f":"IF(IndrctAdj!C86=\"\",\"\",IndrctAdj!C86)","v":""},1,{"$f":"IF(IndrctAdj!D15=\"\",\"\",IndrctAdj!D15)","v":""},8,{"$f":"IF($B$24=E34,INTERCEPT($A$27:A34,$D$27:D34)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E34,LINEST($A$27:A34,$D$27:D34,$I$24),\"\")","v":""},{"$f":"IF($B$24=E34,INTERCEPT($B$27:B34,$D$27:D34)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E34,LINEST($B$27:B34,$D$27:D34,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E87=\"\",\"\",IndrctAdj!E87)","v":""},{"$f":"IF(IndrctAdj!C87=\"\",\"\",IndrctAdj!C87)","v":""},1,{"$f":"IF(IndrctAdj!D16=\"\",\"\",IndrctAdj!D16)","v":""},9,{"$f":"IF($B$24=E35,INTERCEPT($A$27:A35,$D$27:D35)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E35,LINEST($A$27:A35,$D$27:D35,$I$24),\"\")","v":""},{"$f":"IF($B$24=E35,INTERCEPT($B$27:B35,$D$27:D35)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E35,LINEST($B$27:B35,$D$27:D35,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E88=\"\",\"\",IndrctAdj!E88)","v":""},{"$f":"IF(IndrctAdj!C88=\"\",\"\",IndrctAdj!C88)","v":""},1,{"$f":"IF(IndrctAdj!D17=\"\",\"\",IndrctAdj!D17)","v":""},10,{"$f":"IF($B$24=E36,INTERCEPT($A$27:A36,$D$27:D36)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E36,LINEST($A$27:A36,$D$27:D36,$I$24),\"\")","v":""},{"$f":"IF($B$24=E36,INTERCEPT($B$27:B36,$D$27:D36)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E36,LINEST($B$27:B36,$D$27:D36,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E89=\"\",\"\",IndrctAdj!E89)","v":""},{"$f":"IF(IndrctAdj!C89=\"\",\"\",IndrctAdj!C89)","v":""},1,{"$f":"IF(IndrctAdj!D18=\"\",\"\",IndrctAdj!D18)","v":""},11,{"$f":"IF($B$24=E37,INTERCEPT($A$27:A37,$D$27:D37)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E37,LINEST($A$27:A37,$D$27:D37,$I$24),\"\")","v":""},{"$f":"IF($B$24=E37,INTERCEPT($B$27:B37,$D$27:D37)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E37,LINEST($B$27:B37,$D$27:D37,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E90=\"\",\"\",IndrctAdj!E90)","v":""},{"$f":"IF(IndrctAdj!C90=\"\",\"\",IndrctAdj!C90)","v":""},1,{"$f":"IF(IndrctAdj!D19=\"\",\"\",IndrctAdj!D19)","v":""},12,{"$f":"IF($B$24=E38,INTERCEPT($A$27:A38,$D$27:D38)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E38,LINEST($A$27:A38,$D$27:D38,$I$24),\"\")","v":""},{"$f":"IF($B$24=E38,INTERCEPT($B$27:B38,$D$27:D38)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E38,LINEST($B$27:B38,$D$27:D38,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E91=\"\",\"\",IndrctAdj!E91)","v":""},{"$f":"IF(IndrctAdj!C91=\"\",\"\",IndrctAdj!C91)","v":""},1,{"$f":"IF(IndrctAdj!D20=\"\",\"\",IndrctAdj!D20)","v":""},13,{"$f":"IF($B$24=E39,INTERCEPT($A$27:A39,$D$27:D39)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E39,LINEST($A$27:A39,$D$27:D39,$I$24),\"\")","v":""},{"$f":"IF($B$24=E39,INTERCEPT($B$27:B39,$D$27:D39)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E39,LINEST($B$27:B39,$D$27:D39,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E92=\"\",\"\",IndrctAdj!E92)","v":""},{"$f":"IF(IndrctAdj!C92=\"\",\"\",IndrctAdj!C92)","v":""},1,{"$f":"IF(IndrctAdj!D21=\"\",\"\",IndrctAdj!D21)","v":""},14,{"$f":"IF($B$24=E40,INTERCEPT($A$27:A40,$D$27:D40)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E40,LINEST($A$27:A40,$D$27:D40,$I$24),\"\")","v":""},{"$f":"IF($B$24=E40,INTERCEPT($B$27:B40,$D$27:D40)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E40,LINEST($B$27:B40,$D$27:D40,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E93=\"\",\"\",IndrctAdj!E93)","v":""},{"$f":"IF(IndrctAdj!C93=\"\",\"\",IndrctAdj!C93)","v":""},1,{"$f":"IF(IndrctAdj!D22=\"\",\"\",IndrctAdj!D22)","v":""},15,{"$f":"IF($B$24=E41,INTERCEPT($A$27:A41,$D$27:D41)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E41,LINEST($A$27:A41,$D$27:D41,$I$24),\"\")","v":""},{"$f":"IF($B$24=E41,INTERCEPT($B$27:B41,$D$27:D41)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E41,LINEST($B$27:B41,$D$27:D41,$I$24),\"\")","v":""}]
[{"$f":"IF(IndrctAdj!E94=\"\",\"\",IndrctAdj!E94)","v":""},{"$f":"IF(IndrctAdj!C94=\"\",\"\",IndrctAdj!C94)","v":""},1,{"$f":"IF(IndrctAdj!D23=\"\",\"\",IndrctAdj!D23)","v":""},16,{"$f":"IF($B$24=E42,INTERCEPT($A$27:A42,$D$27:D42)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E42,LINEST($A$27:A42,$D$27:D42,$I$24),\"\")","v":""},{"$f":"IF($B$24=E42,INTERCEPT($B$27:B42,$D$27:D42)*$I$24,\"\")","v":""},{"$f":"IF($B$24=E42,LINEST($B$27:B42,$D$27:D42,$I$24),\"\")","v":""},null,null,null,null,null,null,null,null,null,"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D14),$C$57:L66),$C$5:$D14)),MMULT(MMULT(TRANSPOSE($C$5:$D14),$C$57:L66),$F$5:$F14))"]
[null,null,null,null,"Return",{"$f":"SUM(F27:F42)","v":0},{"$f":"SUM(G27:G42)","v":1.2568879307991523E-2},0,1.8860517797473424E-2]
[]
[]
["Find RR_X: Multiplicative model: Wgt reg: b = (X'WX)^-1 X'Wy",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Multiplicative model: Wgt reg: b = (X'WX)^-1 X'Wy"]
["W/ intercept",null,null,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,null,"No intercept",2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
["ln(RR_X)","b_0",null,{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D6 ),C57:D58),C5:D6 )),MMULT(MMULT(TRANSPOSE(C5:D6 ),C57:D58),F5:F6 ))","v":-1.1102230246251565E-16},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D7 ),C57:E59),C5:D7 )),MMULT(MMULT(TRANSPOSE(C5:D7 ),C57:E59),F5:F7 ))","v":8.3157354587797105E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D8 ),C57:F60),C5:D8 )),MMULT(MMULT(TRANSPOSE(C5:D8 ),C57:F60),F5:F8 ))","v":9.9932399879204381E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D9 ),C57:G61),C5:D9 )),MMULT(MMULT(TRANSPOSE(C5:D9 ),C57:G61),F5:F9 ))","v":0.10140027346385427},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D10),C57:H62),C5:D10)),MMULT(MMULT(TRANSPOSE(C5:D10),C57:H62),F5:F10))","v":0.10272792841256273},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D11),C57:I63),C5:D11)),MMULT(MMULT(TRANSPOSE(C5:D11),C57:I63),F5:F11))","v":0.14196693814115913},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D12),C57:J64),C5:D12)),MMULT(MMULT(TRANSPOSE(C5:D12),C57:J64),F5:F12))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D13),C57:K65),C5:D13)),MMULT(MMULT(TRANSPOSE(C5:D13),C57:K65),F5:F13))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D14),$C$57:L66),$C$5:$D14)),MMULT(MMULT(TRANSPOSE($C$5:$D14),$C$57:L66),$F5:$F14))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$15),$C$57:M67),$C$5:$D$15)),MMULT(MMULT(TRANSPOSE($C$5:$D$15),$C$57:M67),$F5:$F15))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$16),$C$57:N68),$C$5:$D$16)),MMULT(MMULT(TRANSPOSE($C$5:$D$16),$C$57:N68),$F5:$F16))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$17),$C$57:O69),$C$5:$D$17)),MMULT(MMULT(TRANSPOSE($C$5:$D$17),$C$57:O69),$F5:$F17))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$17),$C$57:O69),$C$5:$D$17)),MMULT(MMULT(TRANSPOSE($C$5:$D$17),$C$57:O69),$F5:$F17))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$19),$C$57:Q71),$C$5:$D$19)),MMULT(MMULT(TRANSPOSE($C$5:$D$19),$C$57:Q71),$F5:$F19))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$20),$C$57:R72),$C$5:$D$20)),MMULT(MMULT(TRANSPOSE($C$5:$D$20),$C$57:R72),$F5:$F20))","v":{"$error":"#VALUE!"}},null,null,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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["ln(RR_obs)","b_0",null,{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D6),C57:D58),C5:D6)),MMULT(MMULT(TRANSPOSE(C5:D6),C57:D58),G5:G6))","v":-1.1102230246251565E-16},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D7),C57:E59),C5:D7)),MMULT(MMULT(TRANSPOSE(C5:D7),C57:E59),G5:G7))","v":7.4965395975959304E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D8),C57:F60),C5:D8)),MMULT(MMULT(TRANSPOSE(C5:D8),C57:F60),G5:G8))","v":9.7528502177124055E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D9),C57:G61),C5:D9)),MMULT(MMULT(TRANSPOSE(C5:D9),C57:G61),G5:G9))","v":0.1012004249804962},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D10),C57:H62),C5:D10)),MMULT(MMULT(TRANSPOSE(C5:D10),C57:H62),G5:G10))","v":0.10488677306275906},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D11),C57:I63),C5:D11)),MMULT(MMULT(TRANSPOSE(C5:D11),C57:I63),G5:G11))","v":0.15305702034090374},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D12),C57:J64),C5:D12)),MMULT(MMULT(TRANSPOSE(C5:D12),C57:J64),G5:G12))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C5:D13),C57:K65),C5:D13)),MMULT(MMULT(TRANSPOSE(C5:D13),C57:K65),G5:G13))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D14),$C$57:L66),$C$5:$D14)),MMULT(MMULT(TRANSPOSE($C$5:$D14),$C$57:L66),$G5:$G14))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$15),$C$57:M67),$C$5:$D$15)),MMULT(MMULT(TRANSPOSE($C$5:$D$15),$C$57:M67),$G5:$G15))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$16),$C$57:N68),$C$5:$D$16)),MMULT(MMULT(TRANSPOSE($C$5:$D$16),$C$57:N68),$G5:$G16))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$17),$C$57:O69),$C$5:$D$17)),MMULT(MMULT(TRANSPOSE($C$5:$D$17),$C$57:O69),$G5:$G17))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$18),$C$57:P70),$C$5:$D$18)),MMULT(MMULT(TRANSPOSE($C$5:$D$18),$C$57:P70),$G5:$G18))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$19),$C$57:Q71),$C$5:$D$19)),MMULT(MMULT(TRANSPOSE($C$5:$D$19),$C$57:Q71),$G5:$G19))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$5:$D$20),$C$57:R72),$C$5:$D$20)),MMULT(MMULT(TRANSPOSE($C$5:$D$20),$C$57:R72),$G5:$G20))","v":{"$error":"#VALUE!"}},null,null,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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[null,{"$f":"IF( $A$73=16,1*(IndrctAdj!C43<>\"\"),IF(IndrctAdj!D43<=0,0,IndrctAdj!D43))","v":0},0,0,0,0,0,0,0,0,0,0,0,{"$f":"B68","v":0},0,0,0,0]
[null,{"$f":"IF( $A$73=16,1*(IndrctAdj!C44<>\"\"),IF(IndrctAdj!D44<=0,0,IndrctAdj!D44))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B69","v":0},0,0,0]
[null,{"$f":"IF( $A$73=16,1*(IndrctAdj!C45<>\"\"),IF(IndrctAdj!D45<=0,0,IndrctAdj!D45))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B70","v":0},0,0]
[null,{"$f":"IF( $A$73=16,1*(IndrctAdj!C46<>\"\"),IF(IndrctAdj!D46<=0,0,IndrctAdj!D46))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B71","v":0},0]
[null,{"$f":"IF( $A$73=16,1*(IndrctAdj!C47<>\"\"),IF(IndrctAdj!D47<=0,0,IndrctAdj!D47))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B72","v":0}]
[{"$f":"COUNTBLANK(IndrctAdj!D32:'IndrctAdj'!D47)","v":9}]
[null,null,"Log-linear (WLS)",null,null,null,"Linear (WLS)",null,null,null,null,"RR = exp(α + β*x)",null,"RR  =  1 + α + β*x"]
[null,null,"alpha","ln(RR_X)","alpha","ln(RR_obs)","alpha","ERR_X","alpha","ERR_obs",null,"RR_X(i)","RR_Obs","RR_X(i)","RR_Obs"]
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[null,4,{"$f":"IF($B$2=4, F48*$I$1+W48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F49*$I$1+W49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F50*$I$1+W50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F51*$I$1+W51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F52*$I$1+W52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F53*$I$1+W53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F54*$I$1+W54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=4, F55*$I$1+W55*(1-$I$1),\"\")","v":""},null,1.3112424189819145,1.3542086489917888,1.3770937459013859,1.4394212622310163]
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[null,9,{"$f":"IF($B$2=9, K48*$I$1+AB48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K49*$I$1+AB49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K50*$I$1+AB50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K51*$I$1+AB51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K52*$I$1+AB52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K53*$I$1+AB53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K54*$I$1+AB54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=9, K55*$I$1+AB55*(1-$I$1),\"\")","v":""},null,"","","",""]
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[null,11,{"$f":"IF($B$2=11,M48*$I$1+AD48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M49*$I$1+AD49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M50*$I$1+AD50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M51*$I$1+AD51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M52*$I$1+AD52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M53*$I$1+AD53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M54*$I$1+AD54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=11,M55*$I$1+AD55*(1-$I$1),\"\")","v":""},null,"","","",""]
[null,12,{"$f":"IF($B$2=12,N48*$I$1+AE48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N49*$I$1+AE49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N50*$I$1+AE50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N51*$I$1+AE51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N52*$I$1+AE52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N53*$I$1+AE53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N54*$I$1+AE54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=12,N55*$I$1+AE55*(1-$I$1),\"\")","v":""},null,"","","",""]
[null,13,{"$f":"IF($B$2=13,O48*$I$1+AF48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O49*$I$1+AF49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O50*$I$1+AF50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O51*$I$1+AF51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O52*$I$1+AF52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O53*$I$1+AF53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O54*$I$1+AF54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=13,O55*$I$1+AF55*(1-$I$1),\"\")","v":""},null,"","","",""]
[null,14,{"$f":"IF($B$2=14,P48*$I$1+AG48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P49*$I$1+AG49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P50*$I$1+AG50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P51*$I$1+AG51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P52*$I$1+AG52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P53*$I$1+AG53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P54*$I$1+AG54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=14,P55*$I$1+AG55*(1-$I$1),\"\")","v":""},null,"","","",""]
[null,15,{"$f":"IF($B$2=15,Q48*$I$1+AH48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q49*$I$1+AH49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q50*$I$1+AH50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q51*$I$1+AH51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q52*$I$1+AH52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q53*$I$1+AH53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q54*$I$1+AH54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=15,Q55*$I$1+AH55*(1-$I$1),\"\")","v":""},null,"","","",""]
[null,16,{"$f":"IF($B$2=16,R48*$I$1+AI48*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R49*$I$1+AI49*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R50*$I$1+AI50*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R51*$I$1+AI51*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R52*$I$1+AI52*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R53*$I$1+AI53*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R54*$I$1+AI54*(1-$I$1),\"\")","v":""},{"$f":"IF($B$2=16,R55*$I$1+AI55*(1-$I$1),\"\")","v":""},null,"","","",""]
[null,"RETURN",{"$f":"SUM(C76:C90)","v":0},{"$f":"SUM(D76:D90)","v":1.1515370786162769E-2},{"$f":"SUM(E76:E90)","v":0},{"$f":"SUM(F76:F90)","v":1.2885535230905751E-2},0,1.6024993876378398E-2,0,1.8673666993787773E-2,null,"Fitted_exp(X)","Fitted_exp(Obs)","Fitted_lin(X)","Fitted_lin(Obs)"]
[]
[]
[]
[]
["Find ERR_X: Additive model: Wgt reg: b = (X'WX)^-1 X'Wy",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x"]
[null,null,null,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,null,null,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
["ERR_X","b_0",null,{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D28),C103:D104),C27:D28)),MMULT(MMULT(TRANSPOSE(C27:D28),C103:D104),A27:A28))","v":-5.5511151231257827E-17},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D29),C103:E105),C27:D29)),MMULT(MMULT(TRANSPOSE(C27:D29),C103:E105),A27:A29))","v":5.654547895925971E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D30),C103:F106),C27:D30)),MMULT(MMULT(TRANSPOSE(C27:D30),C103:F106),A27:A30))","v":7.0769983489977206E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D31),C103:G107),C27:D31)),MMULT(MMULT(TRANSPOSE(C27:D31),C103:G107),A27:A31))","v":6.4813157729501913E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D32),C103:H108),C27:D32)),MMULT(MMULT(TRANSPOSE(C27:D32),C103:H108),A27:A32))","v":6.1707986462923192E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D33),C103:I109),C27:D33)),MMULT(MMULT(TRANSPOSE(C27:D33),C103:I109),A27:A33))","v":9.7199074151022913E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D34),C103:J110),C27:D34)),MMULT(MMULT(TRANSPOSE(C27:D34),C103:J110),A27:A34))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D35),C103:K111),C27:D35)),MMULT(MMULT(TRANSPOSE(C27:D35),C103:K111),A27:A35))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$36),$C$103:$L$112),$C$27:$D$36)),MMULT(MMULT(TRANSPOSE($C$27:$D$36),$C$103:$L$112),$A$27:$A$36))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$37),$C$103:$M$113),$C$27:$D$37)),MMULT(MMULT(TRANSPOSE($C$27:$D$37),$C$103:$M$113),$A$27:$A$37))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$38),$C$103:$N$114),$C$27:$D$38)),MMULT(MMULT(TRANSPOSE($C$27:$D$38),$C$103:$N$114),$A$27:$A$38))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$39),$C$103:$O$115),$C$27:$D$39)),MMULT(MMULT(TRANSPOSE($C$27:$D$39),$C$103:$O$115),$A$27:$A$39))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$40),$C$103:$P$116),$C$27:$D$40)),MMULT(MMULT(TRANSPOSE($C$27:$D$40),$C$103:$P$116),$A$27:$A$40))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$41),$C$103:$Q$117),$C$27:$D$41)),MMULT(MMULT(TRANSPOSE($C$27:$D$41),$C$103:$Q$117),$A$27:$A$41))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$42),$C$103:$R$118),$C$27:$D$42)),MMULT(MMULT(TRANSPOSE($C$27:$D$42),$C$103:$R$118),$A$27:$A$42))","v":{"$error":"#VALUE!"}},null,null,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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["ERR_obs","b_0",null,{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D28),C103:D104),C27:D28)),MMULT(MMULT(TRANSPOSE(C27:D28),C103:D104),B27:B28))","v":-1.1102230246251565E-16},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D29),C103:E105),C27:D29)),MMULT(MMULT(TRANSPOSE(C27:D29),C103:E105),B27:B29))","v":6.9862901067196947E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D30),C103:F106),C27:D30)),MMULT(MMULT(TRANSPOSE(C27:D30),C103:F106),B27:B30))","v":9.5667311557413814E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D31),C103:G107),C27:D31)),MMULT(MMULT(TRANSPOSE(C27:D31),C103:G107),B27:B31))","v":8.960144144701998E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D32),C103:H108),C27:D32)),MMULT(MMULT(TRANSPOSE(C27:D32),C103:H108),B27:B32))","v":8.7732588410147971E-2},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D33),C103:I109),C27:D33)),MMULT(MMULT(TRANSPOSE(C27:D33),C103:I109),B27:B33))","v":0.14628530485251034},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D34),C103:J110),C27:D34)),MMULT(MMULT(TRANSPOSE(C27:D34),C103:J110),B27:B34))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE(C27:D35),C103:K111),C27:D35)),MMULT(MMULT(TRANSPOSE(C27:D35),C103:K111),B27:B35))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$36),$C$103:$L$112),$C$27:$D$36)),MMULT(MMULT(TRANSPOSE($C$27:$D$36),$C$103:$L$112),$B$27:$B$36))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$37),$C$103:$M$113),$C$27:$D$37)),MMULT(MMULT(TRANSPOSE($C$27:$D$37),$C$103:$M$113),$B$27:$B$37))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$38),$C$103:$N$114),$C$27:$D$38)),MMULT(MMULT(TRANSPOSE($C$27:$D$38),$C$103:$N$114),$B$27:$B$38))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$39),$C$103:$O$115),$C$27:$D$39)),MMULT(MMULT(TRANSPOSE($C$27:$D$39),$C$103:$O$115),$B$27:$B$39))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$40),$C$103:$P$116),$C$27:$D$40)),MMULT(MMULT(TRANSPOSE($C$27:$D$40),$C$103:$P$116),$B$27:$B$40))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$41),$C$103:$Q$117),$C$27:$D$41)),MMULT(MMULT(TRANSPOSE($C$27:$D$41),$C$103:$Q$117),$B$27:$B$41))","v":{"$error":"#VALUE!"}},{"$f":"MMULT(MINVERSE(MMULT(MMULT(TRANSPOSE($C$27:$D$42),$C$103:$R$118),$C$27:$D$42)),MMULT(MMULT(TRANSPOSE($C$27:$D$42),$C$103:$R$118),$B$27:$B$42))","v":{"$error":"#VALUE!"}},null,null,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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["wgt","wgt"]
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[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C85<>\"\"),IF(IndrctAdj!D85<=0,0,IndrctAdj!D85))","v":192.45506233444695},0,0,0,0,0,0,{"$f":"B109","v":192.45506233444695},0,0,0,0,0,0,0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C86<>\"\"),IF(IndrctAdj!D86<=0,0,IndrctAdj!D86))","v":0},0,0,0,0,0,0,0,{"$f":"B110","v":0},0,0,0,0,0,0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C87<>\"\"),IF(IndrctAdj!D87<=0,0,IndrctAdj!D87))","v":0},0,0,0,0,0,0,0,0,{"$f":"B111","v":0},0,0,0,0,0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C88<>\"\"),IF(IndrctAdj!D88<=0,0,IndrctAdj!D88))","v":0},0,0,0,0,0,0,0,0,0,{"$f":"B112","v":0},0,0,0,0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C89<>\"\"),IF(IndrctAdj!D89<=0,0,IndrctAdj!D89))","v":0},0,0,0,0,0,0,0,0,0,0,{"$f":"B113","v":0},0,0,0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C90<>\"\"),IF(IndrctAdj!D90<=0,0,IndrctAdj!D90))","v":0},0,0,0,0,0,0,0,0,0,0,0,{"$f":"B114","v":0},0,0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C91<>\"\"),IF(IndrctAdj!D91<=0,0,IndrctAdj!D91))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B115","v":0},0,0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C92<>\"\"),IF(IndrctAdj!D92<=0,0,IndrctAdj!D92))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B116","v":0},0,0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C93<>\"\"),IF(IndrctAdj!D93<=0,0,IndrctAdj!D93))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B117","v":0},0]
[null,{"$f":"IF( $A$119=16,1*(IndrctAdj!C94<>\"\"),IF(IndrctAdj!D94<=0,0,IndrctAdj!D94))","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"B118","v":0}]
[{"$f":"COUNTBLANK(IndrctAdj!D79:'IndrctAdj'!D94)","v":9}]
[null,null,"Linear (WLS)",null,null,null,null,null,null,null,null,null,null,"ERR  =  α + β*x"]
[null,null,"alpha","ERR_X","alpha","ERR_obs",null,null,null,null,null,null,null,"RR_X(i)","RR_Obs"]
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[null,3,{"$f":"IF($B$24=3, E98*$I$24+V98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=3, E99*$I$24+V99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=3, E100*$I$24+V100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=3, E101*$I$24+V101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,8.2603876950849309E-2,0.12422526251948361]
[null,4,{"$f":"IF($B$24=4, F98*$I$24+W98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=4, F99*$I$24+W99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=4, F100*$I$24+W100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=4, F101*$I$24+W101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,0.29219418931978325,0.43942126223101646]
[null,5,{"$f":"IF($B$24=5, G98*$I$24+X98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=5, G99*$I$24+X99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=5, G100*$I$24+X100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=5, G101*$I$24+X101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,0.41646202524570952,0.62630358677144571]
[null,6,{"$f":"IF($B$24=6, H98*$I$24+Y98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=6, H99*$I$24+Y99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=6, H100*$I$24+Y100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=6, H101*$I$24+Y101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,0.54231179948944419,0.81556493648688355]
[null,7,{"$f":"IF($B$24=7, I98*$I$24+Z98*(1-$I$24),\"\")","v":0},{"$f":"IF($B$24=7, I99*$I$24+Z99*(1-$I$24),\"\")","v":1.2417098255952984E-2},{"$f":"IF($B$24=7, I100*$I$24+Z100*(1-$I$24),\"\")","v":0},{"$f":"IF($B$24=7, I101*$I$24+Z101*(1-$I$24),\"\")","v":1.8673666993787776E-2},null,null,null,null,null,null,null,0.66577997428768709,1.0012446768729131]
[null,8,{"$f":"IF($B$24=8, J98*$I$24+AA98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=8, J99*$I$24+AA99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=8, J100*$I$24+AA100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=8, J101*$I$24+AA101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,1.0042539305172327,1.5102645633564757]
[null,9,{"$f":"IF($B$24=9, K98*$I$24+AB98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=9, K99*$I$24+AB99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=9, K100*$I$24+AB100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=9, K101*$I$24+AB101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,10,{"$f":"IF($B$24=10,L98*$I$24+AC98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=10,L99*$I$24+AC99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=10,L100*$I$24+AC100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=10,L101*$I$24+AC101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,11,{"$f":"IF($B$24=11,M98*$I$24+AD98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=11,M99*$I$24+AD99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=11,M100*$I$24+AD100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=11,M101*$I$24+AD101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,12,{"$f":"IF($B$24=12,N98*$I$24+AE98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=12,N99*$I$24+AE99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=12,N100*$I$24+AE100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=12,N101*$I$24+AE101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,13,{"$f":"IF($B$24=13,O98*$I$24+AF98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=13,O99*$I$24+AF99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=13,O100*$I$24+AF100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=13,O101*$I$24+AF101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,14,{"$f":"IF($B$24=14,P98*$I$24+AG98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=14,P99*$I$24+AG99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=14,P100*$I$24+AG100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=14,P101*$I$24+AG101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,15,{"$f":"IF($B$24=15,Q98*$I$24+AH98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=15,Q99*$I$24+AH99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=15,Q100*$I$24+AH100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=15,Q101*$I$24+AH101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,16,{"$f":"IF($B$24=16,R98*$I$24+AI98*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=16,R99*$I$24+AI99*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=16,R100*$I$24+AI100*(1-$I$24),\"\")","v":""},{"$f":"IF($B$24=16,R101*$I$24+AI101*(1-$I$24),\"\")","v":""},null,null,null,null,null,null,null,"",""]
[null,"RETURN",{"$f":"SUM(C122:C136)","v":0},{"$f":"SUM(D122:D136)","v":1.2417098255952984E-2},0,1.8673666993787776E-2,null,null,null,null,null,null,null,"Fitted_lin(X)","Fitted_lin(Obs)"]
[]
[]
["Mult model: Smooth with prior weights"]
[]
["Prior weights",null,null,null,null,null,"Total"]
[{"$f":"IF(IndrctAdj!$O$30=0,0.2,MAX(IndrctAdj!J30,0))","v":0.1},{"$f":"IF(IndrctAdj!$O$30=0,0.2,MAX(IndrctAdj!K30,0))","v":0.2},{"$f":"IF(IndrctAdj!$O$30=0,0.2,MAX(IndrctAdj!L30,0))","v":0.4},{"$f":"IF(IndrctAdj!$O$30=0,0.2,MAX(IndrctAdj!M30,0))","v":0.2},{"$f":"IF(IndrctAdj!$O$30=0,0.2,MAX(IndrctAdj!N30,0))","v":0.1},null,{"$f":"SUM(A143:E143)","v":1.0000000000000002}]
[]
["RR_X(i)","RR_Obs",null,"Smooth(X)","Smooth(Obs)"]
[1,1]
[1,1]
[{"$f":"IndrctAdj!E32","v":1},{"$f":"IndrctAdj!C32","v":1},null,{"$f":"(A146*$A$143+A147*$B$143+A148*$C$143+A149*$D$143 +A150*$E$143)/$G$143","v":1.0979674601832852},{"$f":"(B146*$A$143+B147*$B$143+B148*$C$143+B149*$D$143 +B150*$E$143)/$G$143","v":1.111}]
[{"$f":"IF(IndrctAdj!E33=\"\",A148,IndrctAdj!E33)","v":1.2487883933412958},{"$f":"IF(IndrctAdj!C33=\"\",B148,IndrctAdj!C33)","v":1.26},null,{"$f":"(A147*$A$143+A148*$B$143+A149*$C$143+A150*$D$143 +A151*$E$143)/$G$143","v":1.2532796211432993},{"$f":"(B147*$A$143+B148*$B$143+B149*$C$143+B150*$D$143 +B151*$E$143)/$G$143","v":1.2889999999999999}]
[{"$f":"IF(IndrctAdj!E34=\"\",A149,IndrctAdj!E34)","v":1.4820978151502622},{"$f":"IF(IndrctAdj!C34=\"\",B149,IndrctAdj!C34)","v":1.59},null,1.4401940075305928,1.5199999999999996]
[{"$f":"IF(IndrctAdj!E35=\"\",A150,IndrctAdj!E35)","v":1.5734470077672871},{"$f":"IF(IndrctAdj!C35=\"\",B150,IndrctAdj!C35)","v":1.67},null,1.6190534912899188,1.7259999999999995]
[{"$f":"IF(IndrctAdj!E36=\"\",A151,IndrctAdj!E36)","v":1.8290780124877151},{"$f":"IF(IndrctAdj!C36=\"\",B151,IndrctAdj!C36)","v":1.98},null,1.8083163027078004,1.9469999999999996]
[{"$f":"IF(IndrctAdj!E37=\"\",A152,IndrctAdj!E37)","v":2.0256068332127941},{"$f":"IF(IndrctAdj!C37=\"\",B152,IndrctAdj!C37)","v":2.1800000000000002},null,1.9593966805644061,2.1129999999999995]
[{"$f":"IF(IndrctAdj!E38=\"\",A153,IndrctAdj!E38)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C38=\"\",B153,IndrctAdj!C38)","v":2.2599999999999998},null,2.0486810039030363,2.2159999999999997]
[{"$f":"IF(IndrctAdj!E39=\"\",A154,IndrctAdj!E39)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C39=\"\",B154,IndrctAdj!C39)","v":2.2599999999999998},null,2.0805416153363301,2.2519999999999993]
[{"$f":"IF(IndrctAdj!E40=\"\",A155,IndrctAdj!E40)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C40=\"\",B155,IndrctAdj!C40)","v":2.2599999999999998},null,{"$f":"(A154*$A$143+A155*$B$143+A156*$C$143+A157*$D$143 +A158*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B154*$A$143+B155*$B$143+B156*$C$143+B157*$D$143 +B158*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"IF(IndrctAdj!E41=\"\",A156,IndrctAdj!E41)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C41=\"\",B156,IndrctAdj!C41)","v":2.2599999999999998},null,2.0866454800167231,2.2599999999999993]
[{"$f":"IF(IndrctAdj!E42=\"\",A157,IndrctAdj!E42)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C42=\"\",B157,IndrctAdj!C42)","v":2.2599999999999998},null,2.0866454800167231,2.2599999999999993]
[{"$f":"IF(IndrctAdj!E43=\"\",A158,IndrctAdj!E43)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C43=\"\",B158,IndrctAdj!C43)","v":2.2599999999999998},null,2.0866454800167231,{"$f":"(B157*$A$143+B158*$B$143+B159*$C$143+B160*$D$143 +B161*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"IF(IndrctAdj!E44=\"\",A159,IndrctAdj!E44)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C44=\"\",B159,IndrctAdj!C44)","v":2.2599999999999998},null,{"$f":"(A158*$A$143+A159*$B$143+A160*$C$143+A161*$D$143 +A162*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B158*$A$143+B159*$B$143+B160*$C$143+B161*$D$143 +B162*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"IF(IndrctAdj!E45=\"\",A160,IndrctAdj!E45)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C45=\"\",B160,IndrctAdj!C45)","v":2.2599999999999998},null,{"$f":"(A159*$A$143+A160*$B$143+A161*$C$143+A162*$D$143 +A163*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B159*$A$143+B160*$B$143+B161*$C$143+B162*$D$143 +B163*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"IF(IndrctAdj!E46=\"\",A161,IndrctAdj!E46)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C46=\"\",B161,IndrctAdj!C46)","v":2.2599999999999998},null,{"$f":"(A160*$A$143+A161*$B$143+A162*$C$143+A163*$D$143 +A164*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B160*$A$143+B161*$B$143+B162*$C$143+B163*$D$143 +B164*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"IF(IndrctAdj!E47=\"\",A162,IndrctAdj!E47)","v":2.0866454800167236},{"$f":"IF(IndrctAdj!C47=\"\",B162,IndrctAdj!C47)","v":2.2599999999999998},null,{"$f":"(A161*$A$143+A162*$B$143+A163*$C$143+A164*$D$143 +A165*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B161*$A$143+B162*$B$143+B163*$C$143+B164*$D$143 +B165*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"A163","v":2.0866454800167236},{"$f":"B163","v":2.2599999999999998},null,{"$f":"(A162*$A$143+A163*$B$143+A164*$C$143+A165*$D$143 +A165*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B162*$A$143+B163*$B$143+B164*$C$143+B165*$D$143 +B165*$E$143)/$G$143","v":2.2599999999999993}]
[{"$f":"A164","v":2.0866454800167236},{"$f":"B164","v":2.2599999999999998},null,{"$f":"(A163*$A$143+A164*$B$143+A165*$C$143+A165*$D$143 +A165*$E$143)/$G$143","v":2.0866454800167231},{"$f":"(B163*$A$143+B164*$B$143+B165*$C$143+B165*$D$143 +B165*$E$143)/$G$143","v":2.2599999999999993}]
[]
[]
[]
["Additive model: Smooth with prior weights"]
[]
["Prior weights",null,null,null,null,null,"Total"]
[{"$f":"IF(IndrctAdj!$O$77=0,0.2,IndrctAdj!J77)","v":0.1},{"$f":"IF(IndrctAdj!$O$77=0,0.2,IndrctAdj!K77)","v":0.2},{"$f":"IF(IndrctAdj!$O$77=0,0.2,IndrctAdj!L77)","v":0.4},{"$f":"IF(IndrctAdj!$O$77=0,0.2,IndrctAdj!M77)","v":0.2},{"$f":"IF(IndrctAdj!$O$77=0,0.2,IndrctAdj!N77)","v":0.1},null,{"$f":"SUM(A172:E172)","v":1.0000000000000002}]
[]
["ERR_X(i)","ERR_Obs",null,"Smooth(X)","Smooth(Obs)"]
[0,0]
[0,0]
[0,0,null,{"$f":"(A175*$A$172+A176*$B$172+A177*$C$172+A178*$D$172 +A179*$E$172)/$G$172","v":7.3361792519999997E-2},{"$f":"(B175*$A$172+B176*$B$172+B177*$C$172+B178*$D$172 +B179*$E$172)/$G$172","v":0.11099999999999999}]
[{"$f":"IF(IndrctAdj!E80=\"\",A177,IndrctAdj!E80)","v":0.1806779432},{"$f":"IF(IndrctAdj!C80=\"\",B177,IndrctAdj!C80)","v":0.26},null,{"$f":"(A176*$A$172+A177*$B$172+A178*$C$172+A179*$D$172 +A180*$E$172)/$G$172","v":0.19053133747999995},0.28899999999999998]
[{"$f":"IF(IndrctAdj!E81=\"\",A178,IndrctAdj!E81)","v":0.37226203880000008},{"$f":"IF(IndrctAdj!C81=\"\",B178,IndrctAdj!C81)","v":0.59000000000000008},null,0.33725429839999999,0.51999999999999991]
[{"$f":"IF(IndrctAdj!E82=\"\",A179,IndrctAdj!E82)","v":0.43807752439999997},{"$f":"IF(IndrctAdj!C82=\"\",B179,IndrctAdj!C82)","v":0.66999999999999993},null,0.47639463831999984,0.72599999999999987]
[{"$f":"IF(IndrctAdj!E83=\"\",A180,IndrctAdj!E83)","v":0.64598389359999997},{"$f":"IF(IndrctAdj!C83=\"\",B180,IndrctAdj!C83)","v":0.98},null,0.6268397900399999,0.94699999999999973]
[{"$f":"IF(IndrctAdj!E84=\"\",A181,IndrctAdj!E84)","v":0.79446647760000011},{"$f":"IF(IndrctAdj!C84=\"\",B181,IndrctAdj!C84)","v":1.1800000000000002},null,{"$f":"(A180*$A$172+A181*$B$172+A182*$C$172+A183*$D$172 +A184*$E$172)/$G$172","v":0.74492480715999998},1.1129999999999998]
[{"$f":"IF(IndrctAdj!E85=\"\",A182,IndrctAdj!E85)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C85=\"\",B182,IndrctAdj!C85)","v":1.2599999999999998},null,{"$f":"(A181*$A$172+A182*$B$172+A183*$C$172+A184*$D$172 +A185*$E$172)/$G$172","v":0.81647028311999981},{"$f":"(B181*$A$172+B182*$B$172+B183*$C$172+B184*$D$172 +B185*$E$172)/$G$172","v":1.2159999999999995}]
[{"$f":"IF(IndrctAdj!E86=\"\",A183,IndrctAdj!E86)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C86=\"\",B183,IndrctAdj!C86)","v":1.2599999999999998},null,{"$f":"(A182*$A$172+A183*$B$172+A184*$C$172+A185*$D$172 +A186*$E$172)/$G$172","v":0.84184770263999975},1.2519999999999996]
[{"$f":"IF(IndrctAdj!E87=\"\",A184,IndrctAdj!E87)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C87=\"\",B184,IndrctAdj!C87)","v":1.2599999999999998},null,{"$f":"(A183*$A$172+A184*$B$172+A185*$C$172+A186*$D$172 +A187*$E$172)/$G$172","v":0.84711228319999976},1.2599999999999993]
[{"$f":"IF(IndrctAdj!E88=\"\",A185,IndrctAdj!E88)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C88=\"\",B185,IndrctAdj!C88)","v":1.2599999999999998},null,0.84711228319999976,1.2599999999999993]
[{"$f":"IF(IndrctAdj!E89=\"\",A186,IndrctAdj!E89)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C89=\"\",B186,IndrctAdj!C89)","v":1.2599999999999998},null,0.84711228319999976,1.2599999999999993]
[{"$f":"IF(IndrctAdj!E90=\"\",A187,IndrctAdj!E90)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C90=\"\",B187,IndrctAdj!C90)","v":1.2599999999999998},null,0.84711228319999976,1.2599999999999993]
[{"$f":"IF(IndrctAdj!E91=\"\",A188,IndrctAdj!E91)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C91=\"\",B188,IndrctAdj!C91)","v":1.2599999999999998},null,0.84711228319999976,1.2599999999999993]
[{"$f":"IF(IndrctAdj!E92=\"\",A189,IndrctAdj!E92)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C92=\"\",B189,IndrctAdj!C92)","v":1.2599999999999998},null,0.84711228319999976,1.2599999999999993]
[{"$f":"IF(IndrctAdj!E93=\"\",A190,IndrctAdj!E93)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C93=\"\",B190,IndrctAdj!C93)","v":1.2599999999999998},null,0.84711228319999976,1.2599999999999993]
[{"$f":"IF(IndrctAdj!E94=\"\",A191,IndrctAdj!E94)","v":0.84711228319999987},{"$f":"IF(IndrctAdj!C94=\"\",B191,IndrctAdj!C94)","v":1.2599999999999998},null,0.84711228319999976,{"$f":"(B190*$A$172+B191*$B$172+B192*$C$172+B193*$D$172 +B194*$E$172)/$G$172","v":1.2599999999999993}]
[{"$f":"A192","v":0.84711228319999987},{"$f":"B192","v":1.2599999999999998},null,{"$f":"(A191*$A$172+A192*$B$172+A193*$C$172+A194*$D$172 +A194*$E$172)/$G$172","v":0.84711228319999976},{"$f":"(B191*$A$172+B192*$B$172+B193*$C$172+B194*$D$172 +B194*$E$172)/$G$172","v":1.2599999999999993}]
[{"$f":"A193","v":0.84711228319999987},1.2599999999999998,null,{"$f":"(A192*$A$172+A193*$B$172+A194*$C$172+A194*$D$172 +A194*$E$172)/$G$172","v":0.84711228319999976},{"$f":"(B192*$A$172+B193*$B$172+B194*$C$172+B194*$D$172 +B194*$E$172)/$G$172","v":1.2599999999999993}]

{"sheet":"ExampleData","index":9,"n_rows":72,"n_cols":12,"rows_kept":72,"cut":false,"hidden":false,"merged":[[4,6,4,7],[4,9,4,10],[1,0,1,10],[32,6,32,11],[16,13,16,16],[17,13,17,16],[16,6,16,9],[17,6,17,9]]}
[]
["Data from examples in Lubin, Hauptmann and Blair (Ann Epidemiol 2018:28(11);801-807)"]
[]
["(a) Leukemia following pediatric CT scanning and confounding by cancer susceptibility syndromes (CSS)"]
[null,null,null,null,null,null,"Down syndrome",null,null,"All CSS"]
["Dose (Gy)","RR_Obs","Wgt","P(X)","Mean",null,"P(C=0|X=i)","P(C=1|X=i)",null,"P(C=0|X=i)","P(C=1|X=i)"]
["<5",1,7.5,0.34192667795091525,2.3199999999999998,null,0.99839999999999995,1.6000000000000001E-3,null,{"$f":"1-K7","v":0.99717999999999996},2.82E-3]
["5-9",1.44,7.2890312160627548,0.25498683020111179,7.08,null,0.99712000000000001,2.8800000000000002E-3,null,{"$f":"1-K8","v":0.99492400000000003},5.0760000000000007E-3]
["10-14",2.0299999999999998,5.7874104585270354,0.12393440260595252,12.34,null,0.99583999999999995,4.1600000000000005E-3,null,0.99266799999999999,7.3320000000000008E-3]
["15-19",1.53,5.0743446786143229,0.1422698539148847,16.54,null,0.99456,5.4400000000000004E-3,null,0.99041199999999996,9.588000000000001E-3]
["20-29",2.02,2.7995520311125381,4.0978324597047151E-2,24.69,null,0.99328000000000005,6.7200000000000003E-3,null,0.98815600000000003,1.1844E-2]
["30+",3.18,6.3234622860141254,9.5903910730088554E-2,51.13,null,0.99199999999999999,8.0000000000000002E-3,null,0.9859,1.4100000000000001E-2]
[]
[null,null,null,null,null,"RR_C =",null,20,null,null,16]
[]
["(b1) Coronary heart disease and cigarette smoking in the Agricultural Heath Study - Uses \"IndrctAdj\" "]
[null,null,null,null,null,null,"P(C|X) - NHANES ages 50-80"]
[null,null,null,null,null,null,"HDL (mmol/L)"]
["Pack-years","RR_Obs","Wgt","ERR_Obs","P(X)","Mean","<1.00","1.00-1.29","1.30-1.59","≥1.60"]
[0,1,250,0,0.621,0,0.14313599999999999,0.32052199999999997,0.24514900000000001,0.29119299999999998]
["1-19",1.26,678.59253852182269,0.26,0.218,6.6524299999999998,0.16232500000000002,0.31692500000000001,0.23321500000000001,0.28753499999999999]
["20-29",1.59,269.8590076390488,0.59000000000000008,5.2999999999999999E-2,23.531600000000001,0.22681599999999999,0.35488700000000001,0.23813500000000001,0.18016199999999999]
["30-29",1.67,204.84423461094022,0.66999999999999993,3.9E-2,33.539400000000001,0.21522200000000002,0.36678400000000005,0.19762299999999999,0.22037099999999998]
["40-49",1.98,174.89185122952264,0.98,2.5000000000000001E-2,43.674599999999998,0.255994,0.35098999999999997,0.198911,0.194105]
["50-59",2.1800000000000002,80.342980609274747,1.1800000000000002,1.4999999999999999E-2,53.618000000000002,0.26041199999999998,0.33719199999999999,0.18612100000000001,0.21627500000000002]
["≥60",2.2599999999999998,192.45506233444695,1.2599999999999998,2.9000000000000001E-2,80.8767,0.26688699999999999,0.33310400000000001,0.20542199999999999,0.19458700000000001]
[]
[null,null,null,null,null,"Confounder score = ",0.86,1.1499999999999999,1.44,1.95]
[null,null,null,null,null,"RR_C = ",1,0.84,0.66,0.5]
[]
[]
["(b2) Coronary heart disease and cigarette smoking in the Agricultural Heath Study - Uses \"Solve_RRC\" "]
[null,null,null,null,null,null,"P(C|X) - NHANES ages 50-80"]
[null,null,null,null,null,null,"HDL (mmol/L)"]
["Pack-years","Mean","RR_Obs","RR_X","ERR_Obs","ERR_X","<1.00","1.00-1.29","1.30-1.59","1.60-179","1.80-2.19","≥2.20"]
[0,0,1,1,0,0,0.156,0.33300000000000002,0.25900000000000001,0.115,9.8000000000000004E-2,3.9E-2]
["1-19",6.6524299999999998,1.26,1.2188522727272726,0.26,0.16177559999999999,0.20300000000000001,0.34,0.23499999999999999,0.10299999999999999,8.3000000000000004E-2,3.5999999999999997E-2]
["20-29",23.531600000000001,1.59,1.4715834843385969,0.59000000000000008,0.36434540000000004,0.25600000000000001,0.36699999999999999,0.20200000000000001,7.9000000000000001E-2,6.7000000000000004E-2,2.9000000000000001E-2]
["30-29",33.539400000000001,1.67,1.5759781977511484,0.66999999999999993,0.43643019999999999,0.24,0.35399999999999998,0.20100000000000001,8.7999999999999995E-2,8.5999999999999993E-2,3.1E-2]
["40-49",43.674599999999998,1.98,1.8480861506330766,0.98,0.64971879999999993,0.254,0.35,0.21,8.6999999999999994E-2,6.3E-2,3.5999999999999997E-2]
["≥50",62,2.2000000000000002,2.0719764999867087,1.2,0.80649080000000017,0.23799999999999999,0.35699999999999998,0.191,7.6999999999999999E-2,8.7999999999999995E-2,4.9000000000000002E-2]
[]
[null,null,null,null,null,"Confounder score = ",0.86,1.1499999999999999,1.44,1.69,1.96,2.4700000000000002]
[null,null,null,null,null,"RR_C = ",1,0.84,0.66,0.5,0.4,0.3]
[]
["(c) Pooled analysis of studies of nuclear industry workers and mortality from all cancers except leukemia (INWORKS) - Uses \"Solve P(C|X) (binary)\""]
[]
["Dose (mGy)","P(X)","RR_Obs","RR_X","Wgt","ERR_Obs","Mean",null,"RR_C","P(C=1|X=0)"]
["<5",0.54726185480486778,1,1,1.7134176383642634E-3,0,0.6,null,2,0.5]
["5-<20",0.21459295006294588,1.0047381919029477,1,3.5885964912280703E-3,4.7381919029476638E-3,10.75,null,2,0.7]
["20-<50",0.11151909357952161,1.014853188946508,1,3.9887429643527201E-3,1.4853188946508E-2,31.7,null,4,0.5]
["50-<100",6.1214855224506926E-2,1.0330315953522968,1,4.5408560311284048E-3,3.3031595352296828E-2,70.099999999999994,null,4,0.7]
["100-<200",4.1701636592530421E-2,1.0627103346329041,1,5.6382978723404252E-3,6.2710334632904097E-2,146.9]
["200-<300",1.2641628199748216E-2,1.1372769650163048,1,6.1794871794871795E-3,0.13727696501630482,240.6]
["300-<400",6.399496433067562E-3,1.16019842257464,1,8.7142857142857143E-3,0.16019842257464001,341.4]
["400-<500",2.570289550986152E-3,1.2274345405351776,1,9.7999999999999997E-3,0.22743454053517764,442.3]
["≥500",2.0981955518254302E-3,1.3238177636803241,1,0.01,0.32381776368032411,630.79999999999995]
[]
["(d) Body mass index and all causes mortality - Uses \"Solve P(C|X) (binary)\""]
[]
["BMI","RR_Obs","RR_X",null,"RR_C","P(C=1|X=0)"]
["18.5-24.9",1,1,"**",10,5]
["25-29.9",0.99,1.1100000000000001,null,10,0.01]
["30-34.9",1.25,1.44,null,20,0.01]
["≥35",1.62,1.92,null,5,0.05]
[null,null,null,null,10,0.05]
["<18.5",1.68,1.47,null,5,0.1]
[null,null,null,null,10,0.1,null,null,null,null,"`"]
[null,null,null,null,2,0.3]
[null,null,null,null,5,0.3]
[]
["** Note: referent category must be lowest level"]

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["IndrctAdj",null,null,"P(X|C) start/end",0.04,0.6,{"$f":"(F1-E1)/15","v":3.7333333333333329E-2},{"$f":"(F1-E1)/20","v":2.7999999999999997E-2},0.1]
[null,null,"Score C",0,1,2,0,0,0,0,0,0,0]
[null,null,"RR_C = ",1,{"$f":"EXP($I$1*E2)","v":1.1051709180756477},{"$f":"EXP($I$1*F2)","v":1.2214027581601699},1,1,1,1,1,1,1,null,null,"ERR=",0.2]
[null,null,null,"P(X|C)"]
["Level (X)","P(X)","X",0,1,2,3,4,5,6,7,8,9,"Sum",null,"Level (X)","RR_Obs","Wgt",null,"ERR_Obs","Wgt"]
[0,4.4999999999999998E-2,{"$f":"A6","v":0},0.1,0.2,0.7,null,null,null,null,null,null,null,{"$f":"SUM(D6:M6)","v":1},null,0,{"$f":"1+$Q$3*P6","v":1},0.5,null,{"$f":"$Q$3*P6","v":0},0.5]
[1,{"$f":"B6*(1+$G$1)","v":4.6679999999999992E-2},{"$f":"A7","v":1},0.10333333333333335,0.20666666666666669,0.69,null,null,null,null,null,null,null,{"$f":"SUM(D7:M7)","v":1},null,1,{"$f":"1+$Q$3*P7","v":1.2},0.5,null,{"$f":"$Q$3*P7","v":0.2},0.5]
[2,{"$f":"B7*(1+$G$1)","v":4.8422719999999989E-2},2,0.1067777777777778,0.21355555555555561,0.67966666666666664,null,null,null,null,null,null,null,1,null,2,1.4,0.5,null,0.4,0.5]
[3,5.0230501546666646E-2,3,0.11033703703703708,0.22067407407407416,0.66898888888888874,null,null,null,null,null,null,null,1,null,3,1.6,0.5,null,0.60000000000000009,0.5]
[4,5.2105773604408864E-2,4,0.114014938271605,0.22802987654321,0.65795518518518503,null,null,null,null,null,null,null,1,null,4,1.8,0.5,null,0.8,0.5]
[5,5.4051055818973459E-2,5,0.11781543621399185,0.2356308724279837,0.64655369135802443,null,null,null,null,null,null,null,1,null,5,2,0.5,null,1,0.5]
[6,5.6068961902881798E-2,6,0.12174261742112492,0.24348523484224985,0.63477214773662527,null,null,null,null,null,null,null,1,null,6,2.2000000000000002,0.5,null,1.2000000000000002,0.5]
[7,5.8162203147256043E-2,7,0.12580070466849577,0.25160140933699154,0.62259788599451271,null,null,null,null,null,null,null,1,null,7,2.4000000000000004,0.5,null,1.4000000000000001,0.5]
[8,6.0333592064753597E-2,8,0.12999406149077897,0.25998812298155793,0.6100178155276631,null,null,null,null,null,null,null,1,null,8,2.6,0.5,null,1.6,0.5]
[9,6.2586046168504397E-2,9,0.13432719687380495,0.26865439374760991,0.59701840937858508,null,null,null,null,null,null,null,1,null,9,2.8,0.5,null,1.8,0.5]
[10,6.4922591892128553E-2,10,0.1388047701029318,0.27760954020586359,0.58358568969120461,null,null,null,null,null,null,null,1,null,10,3,0.5,null,2,0.5]
[11,6.7346368656101344E-2,11,0.14343159577302952,0.28686319154605905,0.56970521268091145,null,null,null,null,null,null,null,1,null,11,3.2,0.5,null,2.2000000000000002,0.5]
[12,6.9860633085929116E-2,12,0.14821264896546385,0.2964252979309277,0.55536205310360842,null,null,null,null,null,null,null,1,null,12,3.4000000000000004,0.5,null,2.4000000000000004,0.5]
[13,7.2468763387803795E-2,13,0.15315307059764599,0.30630614119529198,0.54054078820706208,null,null,null,null,null,null,null,1,null,13,3.6,0.5,null,2.6,0.5]
[14,7.5174263887615125E-2,14,0.15825817295090086,0.31651634590180172,0.52522548114729739,null,null,null,null,null,null,null,1,null,14,3.8000000000000003,0.5,null,2.8000000000000003,0.5]
[15,{"$f":"1-SUM(B6:B20)","v":0.11658652483697718},15,0.16353344538259756,0.32706689076519513,0.50939966385220736,null,null,null,null,null,null,null,1,null,15,4,0.5,null,3,0.5]
[null,{"$f":"SUM(B6:B21)","v":1}]
[null,null,"RR_C = ",1,10]
[null,null,"X",0,1,2,3,4,5,6,7,8,9]
[null,null,0,0.1,0.2,0.7]
[null,null,1,0.10333333333333335,0.20666666666666669,0.69]
[null,null,2,0.1067777777777778,0.21355555555555561,0.67966666666666664]
[null,null,3,0.11033703703703708,0.22067407407407416,0.66898888888888874]
[null,null,4,0.114014938271605,0.22802987654321,0.65795518518518503]
[null,null,5,0.11781543621399185,0.2356308724279837,0.64655369135802443]
[null,null,6,0.12174261742112492,0.24348523484224985,0.63477214773662527]
[null,null,7,0.12580070466849577,0.25160140933699154,0.62259788599451271]
[null,null,8,0.12999406149077897,0.25998812298155793,0.6100178155276631]
[null,null,9,0.13432719687380495,0.26865439374760991,0.59701840937858508]
[null,null,10,0.1388047701029318,0.27760954020586359,0.58358568969120461]
[null,null,11,0.14343159577302952,0.28686319154605905,0.56970521268091145]
[null,null,12,0.14821264896546385,0.2964252979309277,0.55536205310360842]
[null,null,13,0.15315307059764599,0.30630614119529198,0.54054078820706208]
[null,null,14,0.15825817295090086,0.31651634590180172,0.52522548114729739]
[null,null,15,0.16353344538259756,0.32706689076519513,0.50939966385220736]
[]
[null,null,"Score C",0,1,2,3,4,5,6,7,8,9]
[null,null,"RR_C = ",1,1.028395684421425,1.0575976837366112,1.0876288938088261,1.1185128606450452,1.1502737988572274,1.1829366106478107,1.2165269053343162,1.2510710194283623,1.2865960372848406]
[null,null,null,"P(X|C)"]
[null,null,"X",0,1,2,3,4,5,6,7,8,9]
[null,null,0,0.04,4.1120000000000004E-2,4.2271360000000008E-2,4.3454958080000008E-2,4.467169690624001E-2,4.5922504419614735E-2,4.7208334543363949E-2,4.853016791057814E-2,4.9889012612074332E-2,0.59693196552812888]
[null,null,1,4.1493333333333327E-2,4.2655146666666657E-2,4.3849490773333326E-2,4.5077276514986657E-2,4.6339440257406286E-2,4.7636944584613664E-2,4.8970779032982845E-2,5.0341960845906364E-2,5.1751535749591744E-2,0.58188409224117921]
[null,null,2,4.3042417777777765E-2,4.4247605475555542E-2,4.5486538428871098E-2,4.6760161504879487E-2,4.8069446027016113E-2,4.9415390515772567E-2,5.0799021450214199E-2,5.22213940508202E-2,5.368359308424317E-2,0.56627443168484981]
[null,null,3,4.4649334708148129E-2,4.5899516079976277E-2,4.7184702530215616E-2,4.8505874201061658E-2,4.9864038678691387E-2,5.1260231761694745E-2,5.26955182510222E-2,5.4170992762050819E-2,5.5687780559388243E-2,0.55008201046775085]
[null,null,4,4.6316243203918986E-2,4.7613098013628716E-2,4.8946264758010324E-2,5.0316760171234612E-2,5.1725629456029182E-2,5.3173947080797999E-2,5.4662817599060345E-2,5.6193376491834035E-2,5.7766791033605387E-2,0.53328507219188048]
[null,null,5,4.8045382950198626E-2,4.9390653672804187E-2,5.0773591975642705E-2,5.2195252550960705E-2,5.3656719622387605E-2,5.5159107771814458E-2,5.6703562789425267E-2,5.8291262547529178E-2,5.992341789886E-2,0.51586104822037715]
[null,null,6,4.9839077247006036E-2,5.1234571409922207E-2,5.2669139409400031E-2,5.4143875312863236E-2,5.5659903821623405E-2,5.7218381128628863E-2,5.8820495800230473E-2,6.0467469682636929E-2,6.2160558833750768E-2,0.49778652735393802]
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[null,null,8,5.3629859613114304E-2,5.5131495682281505E-2,5.667517756138539E-2,5.8262082533104179E-2,5.9893420844031098E-2,6.1570436627663969E-2,6.329440885323856E-2,6.5066652301129235E-2,6.6888518565560856E-2,0.45958794741849085]
[null,null,9,5.5632041038670567E-2,5.7189738187753345E-2,5.8791050857010439E-2,6.0437200281006735E-2,6.2129441888874926E-2,6.3869066261763419E-2,6.5657400117092798E-2,6.7495807320371401E-2,6.9385689925341804E-2,0.43941256412211449]
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[null,null,11,5.9863438805423407E-2,6.1539615091975267E-2,6.3262724314550572E-2,6.5034080595357993E-2,6.6855034852028025E-2,6.8726975827884812E-2,7.0651331151065588E-2,7.2629568423295432E-2,7.4663196339147711E-2,0.39677403459927119]
[null,null,12,6.209834052082587E-2,6.3837094055408994E-2,6.5624532688960444E-2,6.7462019604251341E-2,6.9350956153170384E-2,7.1292782925459153E-2,7.3288980847372009E-2,7.5341072311098434E-2,7.7450622335809197E-2,0.37425359855764417]
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[]
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[]
["Solve_RRC"]
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[]
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[]
[]
[null,null,null,null,null,null,null,"P(C|X) - NHANES ages 50-80"]
[null,null,null,null,null,null,null,"HDL (mmol/L)"]
["Pack-years","RR_Obs","Wgt","ERR_Obs","P(X)","Mean",null,"<1.00","1.00-1.29","1.30-1.59","≥1.60"]
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["1-19",1.26,678.59253852182269,0.26,0.218,6.6524299999999998,null,0.16232500000000002,0.31692500000000001,0.23321500000000001,0.28753499999999999,null,1.26,1.2487883933412958,null,{"$f":"M116-1","v":0.26},0.24878839334129577]
["20-29",1.59,269.8590076390488,0.59000000000000008,5.2999999999999999E-2,23.531600000000001,null,0.22681599999999999,0.35488700000000001,0.23813500000000001,0.18016199999999999,null,1.59,1.4820978151502622,null,0.59000000000000008,0.48209781515026218]
["30-29",1.67,204.84423461094022,0.66999999999999993,3.9E-2,33.539400000000001,null,0.21522200000000002,0.36678400000000005,0.19762299999999999,0.22037099999999998,null,1.67,1.5734470077672871,null,0.66999999999999993,0.57344700776728708]
["40-49",1.98,174.89185122952264,0.98,2.5000000000000001E-2,43.674599999999998,null,0.255994,0.35098999999999997,0.198911,0.194105,null,1.98,1.8290780124877151,null,0.98,0.82907801248771507]
["50-59",2.1800000000000002,80.342980609274747,1.1800000000000002,1.4999999999999999E-2,53.618000000000002,null,0.26041199999999998,0.33719199999999999,0.18612100000000001,0.21627500000000002,null,2.1800000000000002,2.0256068332127941,null,1.1800000000000002,1.0256068332127941]
["≥60",2.2599999999999998,192.45506233444695,1.2599999999999998,2.9000000000000001E-2,80.8767,null,0.26688699999999999,0.33310400000000001,0.20542199999999999,0.19458700000000001,null,2.2599999999999998,2.0866454800167236,null,1.2599999999999998,1.0866454800167236]
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[]
[]
[]
[null,null,null,null,null,null,"RR_C = ",1,0.84,0.66,0.5]
[null,null,null,null,null,null,"ERR_C = ",0,-0.16000000000000003,-0.33999999999999997,-0.5]
[]
[]
["(b) Coronary heart disease and cigarette smoking in the Agricultural Heath Study  "]
[null,null,null,null,null,null,null,"P(C|X) - NHANES ages 50-80"]
[null,null,null,null,null,null,null,"HDL (mmol/L)",null,null,null,null,null,null,null,null,null,"duplicate:",1,1,0]
["Pack-years","RR_Obs","Wgt","ERR_Obs","P(X)","Mean",null,"<1.00","1.00-1.29","1.30-1.59","≥1.60",null,null,null,null,null,null,0,1,2,3,4,5,6,7,8,9]
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["1-19",1.26,678.59253852182269,0.26,0.218,6.6524299999999998,null,8.1162500000000012E-2,0.15846250000000001,0.1166075,0.14376749999999999,8.1162500000000012E-2,0.15846250000000001,0.1166075,0.14376749999999999,null,null,8.1162500000000012E-2,0.15846250000000001,{"$f":"IF(T$134=1,J137,IF(T$134=\"\",\"\",1-SUM($R137:S137)))","v":0.1166075},{"$f":"IF(U$134=1,K137,IF(U$134=\"\",\"\",1-SUM($R137:T137)))","v":0.64376749999999994},{"$f":"IF(V$134=1,L137,IF(V$134=\"\",\"\",1-SUM($R137:U137)))","v":""},{"$f":"IF(W$134=1,M137,IF(W$134=\"\",\"\",1-SUM($R137:V137)))","v":""},{"$f":"IF(X$134=1,N137,IF(X$134=\"\",\"\",1-SUM($R137:W137)))","v":""},{"$f":"IF(Y$134=1,O137,IF(Y$134=\"\",\"\",1-SUM($R137:X137)))","v":""},{"$f":"IF(Z$134=1,P137,IF(Z$134=\"\",\"\",1-SUM($R137:Y137)))","v":""},{"$f":"IF(AA$134=1,Q137,IF(AA$134=\"\",\"\",1-SUM($R137:Z137)))","v":""}]
["20-29",1.59,269.8590076390488,0.59000000000000008,5.2999999999999999E-2,23.531600000000001,null,0.11340799999999999,0.1774435,0.11906750000000001,9.0080999999999994E-2,0.11340799999999999,0.1774435,0.11906750000000001,9.0080999999999994E-2,null,null,0.11340799999999999,0.1774435,{"$f":"IF(T$134=1,J138,IF(T$134=\"\",\"\",1-SUM($R138:S138)))","v":0.11906750000000001},{"$f":"IF(U$134=1,K138,IF(U$134=\"\",\"\",1-SUM($R138:T138)))","v":0.59008100000000008},{"$f":"IF(V$134=1,L138,IF(V$134=\"\",\"\",1-SUM($R138:U138)))","v":""},{"$f":"IF(W$134=1,M138,IF(W$134=\"\",\"\",1-SUM($R138:V138)))","v":""},{"$f":"IF(X$134=1,N138,IF(X$134=\"\",\"\",1-SUM($R138:W138)))","v":""},{"$f":"IF(Y$134=1,O138,IF(Y$134=\"\",\"\",1-SUM($R138:X138)))","v":""},{"$f":"IF(Z$134=1,P138,IF(Z$134=\"\",\"\",1-SUM($R138:Y138)))","v":""},{"$f":"IF(AA$134=1,Q138,IF(AA$134=\"\",\"\",1-SUM($R138:Z138)))","v":""}]
["30-29",1.67,204.84423461094022,0.66999999999999993,3.9E-2,33.539400000000001,null,0.10761100000000001,0.18339200000000003,9.8811499999999997E-2,0.11018549999999999,0.10761100000000001,0.18339200000000003,9.8811499999999997E-2,0.11018549999999999,null,null,0.10761100000000001,0.18339200000000003,{"$f":"IF(T$134=1,J139,IF(T$134=\"\",\"\",1-SUM($R139:S139)))","v":9.8811499999999997E-2},{"$f":"IF(U$134=1,K139,IF(U$134=\"\",\"\",1-SUM($R139:T139)))","v":0.61018550000000005},{"$f":"IF(V$134=1,L139,IF(V$134=\"\",\"\",1-SUM($R139:U139)))","v":""},{"$f":"IF(W$134=1,M139,IF(W$134=\"\",\"\",1-SUM($R139:V139)))","v":""},{"$f":"IF(X$134=1,N139,IF(X$134=\"\",\"\",1-SUM($R139:W139)))","v":""},{"$f":"IF(Y$134=1,O139,IF(Y$134=\"\",\"\",1-SUM($R139:X139)))","v":""},{"$f":"IF(Z$134=1,P139,IF(Z$134=\"\",\"\",1-SUM($R139:Y139)))","v":""},{"$f":"IF(AA$134=1,Q139,IF(AA$134=\"\",\"\",1-SUM($R139:Z139)))","v":""}]
["40-49",1.98,174.89185122952264,0.98,2.5000000000000001E-2,43.674599999999998,null,0.127997,0.17549499999999998,9.9455500000000002E-2,9.70525E-2,0.127997,0.17549499999999998,9.9455500000000002E-2,9.70525E-2,null,null,0.127997,0.17549499999999998,{"$f":"IF(T$134=1,J140,IF(T$134=\"\",\"\",1-SUM($R140:S140)))","v":9.9455500000000002E-2},{"$f":"IF(U$134=1,K140,IF(U$134=\"\",\"\",1-SUM($R140:T140)))","v":0.59705249999999999},{"$f":"IF(V$134=1,L140,IF(V$134=\"\",\"\",1-SUM($R140:U140)))","v":""},{"$f":"IF(W$134=1,M140,IF(W$134=\"\",\"\",1-SUM($R140:V140)))","v":""},{"$f":"IF(X$134=1,N140,IF(X$134=\"\",\"\",1-SUM($R140:W140)))","v":""},{"$f":"IF(Y$134=1,O140,IF(Y$134=\"\",\"\",1-SUM($R140:X140)))","v":""},{"$f":"IF(Z$134=1,P140,IF(Z$134=\"\",\"\",1-SUM($R140:Y140)))","v":""},{"$f":"IF(AA$134=1,Q140,IF(AA$134=\"\",\"\",1-SUM($R140:Z140)))","v":""}]
["50-59",2.1800000000000002,80.342980609274747,1.1800000000000002,1.4999999999999999E-2,53.618000000000002,null,0.13020599999999999,0.168596,9.3060500000000004E-2,0.10813750000000001,0.13020599999999999,0.168596,9.3060500000000004E-2,0.10813750000000001,null,null,0.13020599999999999,0.168596,{"$f":"IF(T$134=1,J141,IF(T$134=\"\",\"\",1-SUM($R141:S141)))","v":9.3060500000000004E-2},{"$f":"IF(U$134=1,K141,IF(U$134=\"\",\"\",1-SUM($R141:T141)))","v":0.6081375},{"$f":"IF(V$134=1,L141,IF(V$134=\"\",\"\",1-SUM($R141:U141)))","v":""},{"$f":"IF(W$134=1,M141,IF(W$134=\"\",\"\",1-SUM($R141:V141)))","v":""},{"$f":"IF(X$134=1,N141,IF(X$134=\"\",\"\",1-SUM($R141:W141)))","v":""},{"$f":"IF(Y$134=1,O141,IF(Y$134=\"\",\"\",1-SUM($R141:X141)))","v":""},{"$f":"IF(Z$134=1,P141,IF(Z$134=\"\",\"\",1-SUM($R141:Y141)))","v":""},{"$f":"IF(AA$134=1,Q141,IF(AA$134=\"\",\"\",1-SUM($R141:Z141)))","v":""}]
["≥60",2.2599999999999998,192.45506233444695,1.2599999999999998,2.9000000000000001E-2,80.8767,null,0.13344349999999999,0.16655200000000001,0.102711,9.7293500000000005E-2,0.13344349999999999,0.16655200000000001,0.102711,9.7293500000000005E-2,null,null,{"$f":"H142","v":0.13344349999999999},0.16655200000000001,{"$f":"IF(T$134=1,J142,IF(T$134=\"\",\"\",1-SUM($R142:S142)))","v":0.102711},{"$f":"IF(U$134=1,K142,IF(U$134=\"\",\"\",1-SUM($R142:T142)))","v":0.59729350000000003},{"$f":"IF(V$134=1,L142,IF(V$134=\"\",\"\",1-SUM($R142:U142)))","v":""},{"$f":"IF(W$134=1,M142,IF(W$134=\"\",\"\",1-SUM($R142:V142)))","v":""},{"$f":"IF(X$134=1,N142,IF(X$134=\"\",\"\",1-SUM($R142:W142)))","v":""},{"$f":"IF(Y$134=1,O142,IF(Y$134=\"\",\"\",1-SUM($R142:X142)))","v":""},{"$f":"IF(Z$134=1,P142,IF(Z$134=\"\",\"\",1-SUM($R142:Y142)))","v":""},{"$f":"IF(AA$134=1,Q142,IF(AA$134=\"\",\"\",1-SUM($R142:Z142)))","v":""}]
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[]
[null,null,null,null,null,null,"RR_C = ",1,0.84,0.66,0.5]
[null,null,null,null,null,null,"ERR_C = ",0,-0.16000000000000003,-0.33999999999999997,-0.5]
[]
[]
[null,null,null,null,null,null,null,"<1.00","1.00-1.29","1.30-1.59","≥1.60"]
[null,null,null,null,null,null,null,0.14313599999999999,0.32052199999999997,0.24514900000000001,0.29119299999999998]
[null,null,null,null,null,null,null,0.16232500000000002,0.31692500000000001,0.23321500000000001,0.28753499999999999]
[null,null,null,null,null,null,null,0.22681599999999999,0.35488700000000001,0.23813500000000001,0.18016199999999999]
[null,null,null,null,null,null,null,0.21522200000000002,0.36678400000000005,0.19762299999999999,0.22037099999999998]
[null,null,null,null,null,null,null,0.255994,0.35098999999999997,0.198911,0.194105]
[null,null,null,null,null,null,null,0.26041199999999998,0.33719199999999999,0.18612100000000001,0.21627500000000002]
[null,null,null,null,null,null,null,0.26688699999999999,0.33310400000000001,0.20542199999999999,0.19458700000000001]

{"sheet":"Tolerance","index":11,"n_rows":4,"n_cols":2,"rows_kept":4,"cut":false,"hidden":false,"merged":[]}
["Set tolerance values"]
[]
["Tolerance for sum of probabilities",9.9999999999999995E-7]
["Rounding decimal digits",8]