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[null,"Cumulative Losses",null,null,null,null,null,"Age-to-Age Factors",null,null,null,"Notation"]
[null,"AY",1,{"$f":"C3+1","v":2},{"$f":"D3+1","v":3},null,null,"AY",1,{"$f":"I3+1","v":2},null,"AY",1,{"$f":"M3+1","v":2}]
[null,1981,5012,8269,10907,null,null,1981,{"$f":"D4/C4","v":1.6498403830806065},{"$f":"E4/D4","v":1.3190228564518081},null,1981,"F(1981,1)","F(1981,2)"]
[null,{"$f":"B4+1","v":1982},106,4285,null,null,null,{"$f":"H4+1","v":1982},{"$f":"D5/C5","v":40.424528301886795},null,null,1982,"F(1982,1)"]
[null,{"$f":"B5+1","v":1983},3410]
[null,null,null,null,null,null,null,"Mean",{"$f":"AVERAGE(I4:I5)","v":21.037184342483702},{"$f":"AVERAGE(J4:J5)","v":1.3190228564518081},null,"Mean","F(1)","F(2)"]
[null,"Notation"]
[null,"AY",1,{"$f":"C9+1","v":2},{"$f":"D9+1","v":3}]
[null,1981,"c(1981,1)","c(1981,2)","c(1981,3)"]
[null,1982,"c(1982,1)","c(1982,2)"]
[null,1983,"c(1983,1)"]
[]
[]
[null,"Incremental Losses"]
[null,"AY",1,2,3]
[null,{"$f":"B4","v":1981},5012,{"$f":"D4-C4","v":3257},{"$f":"E4-D4","v":2638}]
[null,1982,106,{"$f":"D5-C5","v":4179}]
[null,1983,3410]
[]
[null,"Notation"]
[null,"AY",1,{"$f":"C22+1","v":2},{"$f":"D22+1","v":3}]
[null,1981,"q(1981,1)","q(1981,2)","q(1981,3)"]
[null,1982,"q(1982,1)","q(1982,2)"]
[null,1983,"q(1983,1)"]

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["Slide Set II"]
["Chain-Ladder Model"]
[]
[]
[null,null,"Cumulative Losses"]
[null,null,"AY",1,{"$f":"D6+1","v":2},{"$f":"E6+1","v":3},{"$f":"F6+1","v":4},{"$f":"G6+1","v":5},null,null,null,null,null,null,null,null,"Incurred Losses","LDF","Ultimate","Reserve"]
[null,null,1981,5012,8269,10907,11805,13539,null,null,null,null,null,null,null,null,{"$f":"H7","v":13539},1,{"$f":"R7*Q7","v":13539},{"$f":"S7-Q7","v":0}]
[null,null,{"$f":"C7+1","v":1982},106,4285,5396,10666,null,null,null,null,null,null,null,null,null,{"$f":"G8","v":10666},{"$f":"HLOOKUP(1986-C8,$D$22:$L$30,9)","v":1.1468869123252858},{"$f":"R8*Q8","v":12232.695806861499},{"$f":"S8-Q8","v":1566.6958068614986}]
[null,null,{"$f":"C8+1","v":1983},3410,8992,13873,null,null,null,null,null,null,null,null,null,null,{"$f":"F9","v":13873},{"$f":"HLOOKUP(1986-C9,$D$22:$L$30,9)","v":1.580794688515089},{"$f":"R9*Q9","v":21930.364713769828},{"$f":"S9-Q9","v":8057.3647137698281}]
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[null,"Sum for Wt->","SUM",{"$f":"SUM(D7:D10)","v":14183},{"$f":"SUM(E7:E9)","v":21546},{"$f":"SUM(F7:F8)","v":16303},{"$f":"SUM(G7)","v":11805}]
[null,null,"Incremental Losses"]
[null,null,"AY",1,2,3,4,5]
[null,null,{"$f":"C7","v":1981},{"$f":"D7","v":5012},{"$f":"E7-D7","v":3257},{"$f":"F7-E7","v":2638},898,1734]
[null,null,1982,106,4179,1111,5270]
[null,null,1983,3410,5582,4881]
[null,null,{"$f":"C10","v":1984},{"$f":"D10","v":5655},5900]
[null,null,{"$f":"C11","v":1985},{"$f":"D11","v":1092}]
[]
[null,null,"Age-toAge factors",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Factor Squared Deviations"]
[null,null,"AY",1,{"$f":"D22+1","v":2},{"$f":"E22+1","v":3},{"$f":"F22+1","v":4},{"$f":"G22+1","v":5},null,null,null,null,null,null,null,null,null,"AY",1,{"$f":"S22+1","v":2},{"$f":"T22+1","v":3},{"$f":"U22+1","v":4}]
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["Answers to:"]
["Slide II.6",null,"WAD",{"$f":"SUM(E7:E11)/SUMIF(E7:E11,\">0\",D7:D11)","v":2.33385038426285},{"$f":"SUM(F7:F11)/SUMIF(F7:F11,\">0\",E7:E11)","v":1.4005383829945233},{"$f":"SUM(G7:G11)/SUMIF(G7:G11,\">0\",F7:F11)","v":1.3783352757161258},{"$f":"SUM(H7:H11)/SUMIF(H7:H11,\">0\",G7:G11)","v":1.1468869123252858},null,null,null,null,null,null,null,null,null,"(a)","Weighted Deviations",{"$f":"SUMPRODUCT(D7:D10,S23:S26)","v":156930.92255071099},{"$f":"SUMPRODUCT(E7:E9,T23:T25)","v":322.47638975933967},{"$f":"SUMPRODUCT(F7:F8,U23:U24)","v":2887.3047362280895},{"$f":"SUMPRODUCT(G7,V23)","v":0}]
[null,null,"SAD",{"$f":"AVERAGE(D23:D26)","v":11.688660830798829},{"$f":"AVERAGE(E23:E26)","v":1.3737050796139185},{"$f":"AVERAGE(F23:F26)","v":1.529490908477992},{"$f":"AVERAGE(G23:G26)","v":1.1468869123252858},null,null,null,null,null,null,null,null,null,"(b)","N-K-1",{"$f":"COUNT(S23:S26)-1","v":3},{"$f":"COUNT(T23:T26)-1","v":2},{"$f":"COUNT(U23:U26)-1","v":1},{"$f":"COUNT(V23:V26)-1","v":0}]
[null,null,"ATU",{"$f":"E30*D28","v":5.1670598847213007},{"$f":"F30*E28","v":2.2139636368992539},{"$f":"G30*F28","v":1.580794688515089},{"$f":"G29","v":1.1468869123252858},null,null,null,null,null,null,null,null,null,"©=(a)/(b)","alpha^2",{"$f":"S28/S29","v":52310.307516903667},{"$f":"T28/T29","v":161.23819487966983},{"$f":"U28/U29","v":2887.3047362280895},{"$f":"MIN(T30:U30)","v":161.23819487966983}]
[]
[null,null,"Unweighted Squared deviation of Age-toAge factors"]
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[null,null,"N-d-1",{"$f":"COUNT(D34:D37)-1","v":3},{"$f":"COUNT(E34:E37)-1","v":2},{"$f":"COUNT(F34:F37)-1","v":1}]
[null,null,"Avg Var",{"$f":"SUM(D34:D37)/D39","v":367.16465823455331},{"$f":"SUM(E34:E37)/E39","v":2.2341241420365518E-2},{"$f":"SUM(F34:F37)/F39","v":0.39990137924909169}]
[null,null,"Avg SD",{"$f":"SQRT(D40)","v":19.161541123681918},{"$f":"SQRT(E40)","v":0.14946986793452893},{"$f":"SQRT(F40)","v":0.63237756067802697}]
[]
[null,null,"Weights"]
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[null,null,1981,{"$f":"D7","v":5012},{"$f":"E7","v":8269},{"$f":"F7","v":10907},{"$f":"G7","v":11805}]
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[null,null,{"$f":"C46+1","v":1983},{"$f":"D9","v":3410},{"$f":"E9","v":8992}]
[null,null,{"$f":"C47+1","v":1984},{"$f":"D10","v":5655}]
[]
[]
[null,null,"Sum Weights",{"$f":"SUM(D45:D48)","v":14183},{"$f":"SUM(E45:E48)","v":21546},{"$f":"SUM(F45:F48)","v":16303},{"$f":"SUM(G45:G48)","v":11805}]
[null,null,"Weighted LDF",{"$f":"D28","v":2.33385038426285},{"$f":"E28","v":1.4005383829945233},{"$f":"F28","v":1.3783352757161258},{"$f":"G28","v":1.1468869123252858}]
[]
[]
[null,null,"Weighted Squared deviation of Age-toAge factors"]
[null,null,"AY",1,{"$f":"D56+1","v":2},{"$f":"E56+1","v":3},{"$f":"F56+1","v":4},{"$f":"G56+1","v":5}]
[null,null,1981,{"$f":"D45*(D23-D$28)^2","v":2344.9628447672712},{"$f":"E45*(E23-E$28)^2","v":54.945694647456079},{"$f":"F45*(F23-F$28)^2","v":955.64597661085509},{"$f":"G45*(G23-G$28)^2","v":0}]
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[null,null,{"$f":"C58+1","v":1983},{"$f":"D47*(D25-D$28)^2","v":313.2748788743159},{"$f":"E47*(E25-E$28)^2","v":182.02392047934453}]
[null,null,{"$f":"C59+1","v":1984},{"$f":"D48*(D26-D$28)^2","v":477.31193930801015}]
[]
[]
[null,null,"Sum Weights",{"$f":"D12","v":14183},{"$f":"E12","v":21546},{"$f":"F12","v":16303}]
[null,null,"SumSquared",{"$f":"SUM(D57:D60)","v":156930.92255071099},{"$f":"SUM(E57:E60)","v":322.47638975933967},{"$f":"SUM(F57:F60)","v":2887.3047362280895}]
[null,null,"Weighted Var",{"$f":"SUM(D57:D60)/D63","v":11.064719914736727},{"$f":"SUM(E57:E60)/E63","v":1.4966879688078515E-2},{"$f":"SUM(F57:F60)/F63","v":0.1771026643089057}]
[null,null,"Weighted SD",{"$f":"SQRT(D65)","v":3.3263673751912504},{"$f":"SQRT(E65)","v":0.12233919931108964},{"$f":"SQRT(F65)","v":0.42083567375984859}]
[null,null,"N-d-1",{"$f":"D39","v":3},{"$f":"E39","v":2},{"$f":"F39","v":1}]
["Slide II.6",null,"σ2",{"$f":"D64/D67","v":52310.307516903667},{"$f":"E64/E67","v":161.23819487966983},{"$f":"F64/F67","v":2887.3047362280895}]
[]
[null,null,"Estimated Cumulative Losses"]
[null,null,"AY",1,{"$f":"D71+1","v":2},{"$f":"E71+1","v":3},{"$f":"F71+1","v":4},{"$f":"G71+1","v":5},"Ultimate"]
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[null,null,{"$f":"C73+1","v":1983},null,null,{"$f":"F9","v":13873},{"$f":"F74*F$52","v":19121.645280009812},{"$f":"G74*G$52","v":21930.364713769828},{"$f":"H74","v":21930.364713769828}]
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[null,null,null,null,null,"(3) / (2)^2",null,null,"1/(5) + 1/(6)","(4) x (7)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(3) / (2)^2",null,null,"1/(5) + 1/(6)","(4) x (7)"]
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[null,null,{"$f":"C106+1","v":2},{"$f":"E28","v":1.4005383829945233},{"$f":"T30","v":161.23819487966983},{"$f":"E105/D105^2","v":82.201150555460529},{"$f":"D106*G106","v":2548.5646196150324},{"$f":"E12","v":21546},{"$f":"1/G105+1/H105","v":4.3879005703448379E-4},{"$f":"I105*F105","v":3.6069047540530717E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AD106+1","v":2},{"$f":"R28","v":"Weighted Deviations"},{"$f":"AD30","v":0},{"$f":"AF105/AE105^2","v":{"$error":"#VALUE!"}},{"$f":"AE106*AH106","v":{"$error":"#VALUE!"}},{"$f":"R12","v":0},{"$f":"1/AH105+1/AI105","v":{"$error":"#VALUE!"}},{"$f":"AJ105*AG105","v":{"$error":"#VALUE!"}}]
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[null,null,null,null,null,null,null,null,"Var[R(w,d)2] = U(w)2 x Sum =",{"$f":"J107*(G107^2)","v":320349084.05715376},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Var[R(w,d)] = U(w)2 Sd  =",{"$f":"AK107*(AH107^2)","v":{"$error":"#VALUE!"}}]
[null,null,null,null,null,null,null,null,"SE =",{"$f":"SQRT(J108)","v":17898.29835646824},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SE =","[ U(w)2 Sd  ] 1/2=",{"$f":"SQRT(AK108)","v":{"$error":"#VALUE!"}}]
[]
[null,"Components of Variance Calculation for Variance of Unpaid for 1 Year"]
[null,"Age",1,{"$f":"C112+1","v":2},{"$f":"D112+1","v":3},{"$f":"E112+1","v":4}]
[null,"Year",{"$f":"1986-C112","v":1985},{"$f":"1986-D112","v":1984},{"$f":"1986-E112","v":1983},{"$f":"1986-F112","v":1982}]
[null,"F(age)",{"$f":"D52","v":2.33385038426285},{"$f":"E52","v":1.4005383829945233},{"$f":"F52","v":1.3783352757161258},{"$f":"G52","v":1.1468869123252858}]
[null,"σ2age",{"$f":"D68","v":52310.307516903667},{"$f":"E68","v":161.23819487966983},{"$f":"F68","v":2887.3047362280895},{"$f":"MIN(D115:E115)","v":161.23819487966983}]
[null,"σ2age / F(d)2",{"$f":"C115/C114^2","v":9603.7589383746836},{"$f":"D115/D114^2","v":82.201150555460529},{"$f":"E115/E114^2","v":1519.7875444178317},{"$f":"F115/F114^2","v":122.58200872741106}]
[null,"Diagonal loss",{"$f":"VLOOKUP(C$113,$C$7:$Q$11,12)","v":1092},{"$f":"VLOOKUP(D$113,$C$7:$Q$11,12)","v":11555},{"$f":"VLOOKUP(E$113,$C$7:$Q$11,12)","v":13873},{"$f":"VLOOKUP(F$113,$C$7:$Q$11,12)","v":10666}]
[null,"SUM",{"$f":"D12","v":14183},{"$f":"E12","v":21546},{"$f":"F12","v":16303},{"$f":"G12","v":11805}]
[]
[]
[]
[]
[null,null,"Computation of Standard Error of Ultimate for AY 1983"]
[null,null,null,null,null,"Sigma2",null,null,"         1               1","     Sigma2"]
[null,null,null,null,null,"————",null,null,"————  +  ——","x   ————"]
[null,null,"d","f(d)","Sigma2","f(d)2","E[c(1,d)]","SUM[c(j,d)]","E[c(1,d)]     SUM","     f(d)2"]
[null,null,-1,{"$f":"C127-1","v":-2},{"$f":"D127-1","v":-3},-4,-5,-6,-7,-8]
[null,null,null,null,null,"(3) / (2)^2",null,null,"1/(5) + 1/(6)","(4) x (7)"]
[null,null,{"$f":"C103","v":4},1.1468869123252858,161.23819487966983,{"$f":"E129/D129^2","v":122.58200872741106},{"$f":"G130*D130","v":19121.645280009812},{"$f":"H103","v":11805},{"$f":"1/G129+1/H129","v":1.3700662378308653E-4},{"$f":"I129*F129","v":1.6794547152291436E-2}]
[null,null,3,1.3783352757161258,2887.3047362280895,{"$f":"E130/D130^2","v":1519.7875444178317},{"$f":"F9","v":13873},{"$f":"H104","v":16303},{"$f":"1/G130+1/H130","v":1.33420866311642E-4},{"$f":"I130*F130","v":0.20277137078587021}]
[null,null,null,null,null,"U(w) =",{"$f":"G129*D129","v":21930.364713769828},null,"Sum =",{"$f":"SUM(J129:J130)","v":0.21956591793816166}]
[null,null,null,null,null,null,null,null,"SE2 = R(w,d)2 x Sum =",{"$f":"J131*(G131^2)","v":105598229.40940541}]
[null,null,null,null,null,null,null,null,"SE =",{"$f":"SQRT(J132)","v":10276.099912389203}]
[]
[]
["Slide II.12"]
[null,null,"Computation of Standard Error of Ultimate for AY 1984",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Computation of Standard Error of Ultimate for AY 1984"]
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[null,null,null,null,null,"————",null,null,"————  +  ——","x   ————",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"————",null,null,"————  +  ——","x   ————"]
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[null,null,null,null,null,"(3) / (2)^2",null,null,"1/(5) + 1/(6)","(4) x (7)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(3) / (2)^2",null,null,"1/(5) + 1/(6)","(4) x (7)"]
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[null,null,{"$f":"C105","v":2},1.4005383829945233,161.23819487966983,{"$f":"E145/D145^2","v":82.201150555460529},{"$f":"E10","v":11555},{"$f":"H105","v":21546},{"$f":"1/G145+1/H145","v":1.3295494935553542E-4},{"$f":"I145*F145","v":1.0929049809067996E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,1.4005383829945233,161.23819487966983,82.201150555460529,11555,21546,1.3295494935553542E-4,1.0929049809067996E-2]
[null,null,null,null,null,"U(w) =",{"$f":"G143*D143","v":25582.349824370878},null,"Sum =",{"$f":"SUM(J142:J145)","v":0.21394110767826827},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"U(w) =",25582.349824370878,null,"Sd =",0.21394110767826827]
[null,null,null,null,null,null,null,null,"Var[R(w,d)2] = U(w)2 x Sum =",{"$f":"J146*(G146^2)","v":140015174.75283468},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Var[R(w,d)] = U(w)2 Sd  =",140015174.75283468]
[null,null,null,null,null,null,null,null,"SE =",{"$f":"SQRT(J147)","v":11832.800799169852},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SE =","[ U(w)2 Sd  ] 1/2=",11832.800799169852]

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["Step 1:","Data",null,"c(w,d)",null,null,null,null,null,"N = n =",{"$f":"K4","v":10}]
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[null,"d = Development Year"]
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[7,557,4020,10946,12314,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,557,4.2178765371744955]
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[10,2063]
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[null,{"$f":"B14","v":2063},{"$f":"C13","v":5395},{"$f":"D12","v":13112},{"$f":"E11","v":12314},{"$f":"F10","v":15852},{"$f":"G9","v":26180},{"$f":"H8","v":27067},{"$f":"I7","v":23466},{"$f":"J6","v":16704},{"$f":"K5","v":18834},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4285,-0.3642462076624387]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8992,-8.0706917454521479E-2]
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["Step 2:","Development Factors",null,"F(d)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9565,3.2096692143043774E-2]
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[null,{"$f":"SUM(C5:C13)/SUM(B5:B13)","v":2.9993586513353794},{"$f":"SUM(D5:D12)/SUM(C5:C12)","v":1.6235227537534538},{"$f":"SUM(E5:E11)/SUM(D5:D11)","v":1.2708881150356526},{"$f":"SUM(F5:F10)/SUM(E5:E10)","v":1.1716746330883747},{"$f":"SUM(G5:G9)/SUM(F5:F9)","v":1.113384886206463},{"$f":"SUM(H5:H8)/SUM(G5:G8)","v":1.0419346379110106},{"$f":"SUM(I5:I7)/SUM(H5:H7)","v":1.0332635537893839},{"$f":"SUM(J5:J6)/SUM(I5:I6)","v":1.0169364810075625},{"$f":"SUM(K5)/SUM(J5)","v":1.0092165898617511},1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4020,1.0993628183858497]
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[null,null,null,null,null,null,null,null,null,null,"U(w)"]
["Step 3:","Ultimate Amounts",null,null,null,null,null,null,null,null,"c(w,n)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,{"$f":"D5","v":10907},{"$f":"(E5-D$21*D5)/(D5)^$AB$2","v":-0.1885556679833009}]
[null,"d",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5396,0.70576125486797969]
["w",1,2,3,4,5,6,7,8,9,10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,13873,-0.10740509045553298]
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[2,null,null,null,null,null,null,null,null,null,{"$f":"J16*J21*K21","v":16857.953917050691},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,15836,0.12902347880117487]
[3,null,null,null,null,null,null,null,null,null,{"$f":"I16*I21*J21*K21","v":24083.37092381492},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,11702,-0.16552151103633625]
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[5,null,null,null,null,null,null,null,null,null,{"$f":"G16*G21*H21*I21*J21*K21","v":28926.736343422217}]
[6,null,null,null,null,null,null,null,null,null,{"$f":"F16*F21*G21*H21*I21*J21*K21","v":19501.10318399638},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"E5","v":11805},{"$f":"(F5-E$21*E5)/(E5)^$AB$2","v":-2.4787720763088807E-2}]
[7,null,null,null,null,null,null,null,null,null,{"$f":"E16*E21*F21*G21*H21*I21*J21*K21","v":17749.302590295185},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10666,0.12046862586530989]
[8,null,null,null,null,null,null,null,null,null,{"$f":"D16*D21*E21*F21*G21*H21*I21*J21*K21","v":24019.192509507353},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,16141,-1.0965878983920204E-2]
[9,null,null,null,null,null,null,null,null,null,{"$f":"C16*C21*D21*E21*F21*G21*H21*I21*J21*K21","v":16044.984100702153},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21266,-7.0151074356126039E-2]
[10,null,null,null,null,null,null,null,null,null,{"$f":"B16*B21*C21*D21*E21*F21*G21*H21*I21*J21*K21","v":18402.44252900036},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,22169,-8.9561734567099804E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12935,5.3837543177570439E-2]
[]
["Step 4:","Reserves",null,null,null,null,null,null,null,null,"Rw",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"F5","v":13539},{"$f":"(G5-F$21*F5)/(F5)^$AB$2","v":8.1755079817615553E-2}]
[null,"d",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"F6","v":13782},{"$f":"(G6-F$21*F6)/(F6)^$AB$2","v":1.8453743890765213E-2}]
["w",1,2,3,4,5,6,7,8,9,10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"F7","v":18735},{"$f":"(G7-F$21*F7)/(F7)^$AB$2","v":7.2310336638479494E-2}]
[1,null,null,null,null,null,null,null,null,null,{"$f":"K27-K16","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"F8","v":23425},{"$f":"(G8-F$21*F8)/(F8)^$AB$2","v":8.3630335692844572E-5}]
[2,null,null,null,null,null,null,null,null,null,{"$f":"K28-J16","v":153.95391705069051},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"F9","v":25955},{"$f":"(G9-F$21*F9)/(F9)^$AB$2","v":-0.10471603627388738}]
[3,null,null,null,null,null,null,null,null,null,{"$f":"K29-I16","v":617.37092381492039}]
[4,null,null,null,null,null,null,null,null,null,{"$f":"K30-H16","v":1636.1421634209037},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7,{"$f":"G5","v":16181},{"$f":"(H5-G$21*G5)/(G5)^$AB$2","v":7.1037366291449092E-2}]
[5,null,null,null,null,null,null,null,null,null,{"$f":"K31-G16","v":2746.736343422217},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"G6","v":15599},{"$f":"(H6-G$21*G6)/(G6)^$AB$2","v":-4.8537625281995914E-2}]
[6,null,null,null,null,null,null,null,null,null,{"$f":"K32-F16","v":3649.1031839963798},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"G7","v":22214},{"$f":"(H7-G$21*G7)/(G7)^$AB$2","v":-1.2718828061366228E-2}]
[7,null,null,null,null,null,null,null,null,null,{"$f":"K33-E16","v":5435.3025902951849},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"G8","v":26083},{"$f":"(H8-G$21*G8)/(G8)^$AB$2","v":-4.2089161765475804E-3}]
[8,null,null,null,null,null,null,null,null,null,{"$f":"K34-D16","v":10907.192509507353}]
[9,null,null,null,null,null,null,null,null,null,{"$f":"K35-C16","v":10649.984100702153},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,{"$f":"H5","v":18009},{"$f":"(I5-H$21*H5)/(H5)^$AB$2","v":-2.406585208327765E-6}]
[10,null,null,null,null,null,null,null,null,null,{"$f":"K36-B16","v":16339.44252900036},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"H6","v":15496},{"$f":"(I6-H$21*H6)/(H6)^$AB$2","v":1.0167008936480842E-2}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(K42:K51)","v":52135.228261210155},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"H7","v":22863},{"$f":"(I7-H$21*H7)/(H7)^$AB$2","v":-6.8890622528402544E-3}]
[]
["Step 5:","Factor Variances"]
[null,"d"]
["w",1,2,3,4,5,6,7,8,9,10]
[1,{"$f":"B5*((C5/B5)-B$21)^2","v":9127.8521764430443},766.70323007955812,387.77918790155445,7.2533591429237827,90.493228355756941,81.654300195150569,1.0430186743138156E-7,3.6651672329751204,0]
[2,{"$f":"B6*((C6/B6)-B$21)^2","v":148468.19227749083},568.51365962786701,2687.7419281177658,154.79234959746537,4.6933314255416487,36.749700759972967,1.6017916237915588,4.2180364816128897]
[3,{"$f":"B7*((C7/B7)-B$21)^2","v":447.86914181032694},58.570349872898305,160.03689499177494,1.9409633510062136,97.961282942670636,3.5935273972735735,1.0850592031555373]
[4,{"$f":"B8*((C8/B8)-B$21)^2","v":5168.6774339513531},775.67034968005419,95.831441231475182,104.65366997975588,1.6383522415154973E-4,0.46205970286792503]
[5,{"$f":"B9*((C9/B9)-B$21)^2","v":36227.408907765472},{"$f":"C9*((D9/C9)-C$21)^2","v":9.8538404890148339},{"$f":"D9*((E9/D9)-D$21)^2","v":263.62281178587432},{"$f":"E9*((F9/E9)-E$21)^2","v":1.7782429499712239E-2},{"$f":"F9*((G9/F9)-F$21)^2","v":284.60820940438595}]
[6,{"$f":"B10*((C10/B10)-B$21)^2","v":2403.5267388884881},{"$f":"C10*((D10/C10)-C$21)^2","v":237.95566895219744},{"$f":"D10*((E10/D10)-D$21)^2","v":320.60403094552936},{"$f":"E10*((F10/E10)-E$21)^2","v":37.491852451557044}]
[7,{"$f":"B11*((C11/B11)-B$21)^2","v":9909.298742945839},{"$f":"C11*((D11/C11)-C$21)^2","v":4858.566397926098},{"$f":"D11*((E11/D11)-D$21)^2","v":233.04041248871235}]
[8,{"$f":"B12*((C12/B12)-B$21)^2","v":6202.9991362532628},{"$f":"C12*((D12/C12)-C$21)^2","v":483.85050630335559}]
[9,{"$f":"B13*((C13/B13)-B$21)^2","v":5112.0105968004518}]
[]
["sd2",{"$f":"SUM(B57:B65)/($K$1-B56-1)","v":27883.479394043632},{"$f":"SUM(C57:C65)/($K$1-C56-1)","v":1108.5262861330064},691.44278457711437,61.229995390441616,119.43905399089483,40.819862685088346,1.3434254656244817,7.8832037145880101,{"$f":"MIN(I67^2/H67,MIN(H67,I67))","v":1.3434254656244817}]
[]
[]
["Step 6:","Cumulative Sum (but for the diagonal)"]
[null,"d"]
["w",1,2,3,4,5,6,7,8,9,10]
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
["Swc(w,d)",{"$f":"SUM(B5:B13)","v":21829},{"$f":"SUM(C5:C12)","v":60078},{"$f":"SUM(D5:D11)","v":84426},{"$f":"SUM(E5:E10)","v":94982},{"$f":"SUM(F5:F9)","v":95436},{"$f":"SUM(G5:G8)","v":80077},{"$f":"SUM(H5:H7)","v":56368},{"$f":"SUM(I5:I6)","v":34777},{"$f":"SUM(J5:J5)","v":18662}]
[]
["Step 7:","Future Projections",null,"E[c(w,d)]",null,null,null,null,null,null,null,"E[c(w,n)]"]
[null,"d"]
["w",1,2,3,4,5,6,7,8,9,10]
[1,null,null,null,null,null,null,null,null,null,null,{"$f":"K5*K$21","v":18834}]
[2,null,null,null,null,null,null,null,null,{"$f":"J6","v":16704},{"$f":"J89*J$21","v":16857.953917050691},16857.953917050691]
[3,null,null,null,null,null,null,null,{"$f":"I7","v":23466},{"$f":"I90*I$21","v":23863.431463323461},24083.37092381492,24083.37092381492]
[4,null,null,null,null,null,null,{"$f":"H8","v":27067},{"$f":"H91*H$21","v":27967.344610417254},28441.013011243544,28703.142163420904,28703.142163420904]
[5,null,null,null,null,null,{"$f":"G9","v":26180},{"$f":"G92*G$21","v":27277.848820510259},28185.207012009985,28662.565235263111,28926.736343422217,28926.736343422217]
[6,null,null,null,null,{"$f":"F10","v":15852},{"$f":"F93*F$21","v":17649.377216144851},18389.497459058726,19001.197496947865,19323.010917475865,19501.10318399638,19501.10318399638]
[7,null,null,null,{"$f":"E11","v":12314},{"$f":"E94*E$21","v":14428.001431850247},{"$f":"F94*F$21","v":16063.918732387274},16737.553347861834,17294.303853951122,17587.20850271258,17749.302590295185,17749.302590295185]
[8,null,null,{"$f":"D12","v":13112},{"$f":"D95*D$21","v":16663.884964347475},{"$f":"E95*E$21","v":19524.651301428712},{"$f":"F95*F$21","v":21738.451667462075},22650.0457668831,23403.466782581825,23799.839153256144,24019.192509507353,24019.192509507353]
[9,null,{"$f":"C13","v":5395},{"$f":"C96*C$21","v":8758.9052564998838},{"$f":"D96*D$21","v":11131.588591209007},{"$f":"E96*E$21","v":13042.599978295551},{"$f":"F96*F$21","v":14521.433692671009},15130.384756521918,15633.675123724561,15898.454565535923,16044.984100702153,16044.984100702153]
[10,{"$f":"B14","v":2063},{"$f":"B97*B$21","v":6187.6768977048878},{"$f":"C97*C$21","v":10045.834236298468},{"$f":"D97*D$21","v":12767.131336529985},{"$f":"E97*E$21","v":14958.923924319861},{"$f":"F97*F$21","v":16655.039811250004},17353.46287512824,17930.700720907145,18234.383693119078,18402.44252900036,18402.44252900036]
[]
[]
["Step 8:","Mean Square Error of an AY w (row)",null,null,null,"MSE(Rw)",null,null,null,null,null,"SE(Rw)"]
[null,"d"]
["w",1,2,3,4,5,6,7,8,9,10]
[1]
[2,null,null,null,null,null,null,null,null,{"$f":"(J$67/(J$21^2))*((1/J89)+(1/J$83))","v":1.4964151299398678E-4},null,{"$f":"SQRT(K28^2*SUM(B104:J104))","v":206.220059401112}]
[3,null,null,null,null,null,null,null,{"$f":"(I$67/(I$21^2))*((1/I90)+(1/I$83))","v":5.4403601407751944E-4},1.2595124490012247E-4,null,623.37667263196499]
[4,null,null,null,null,null,null,{"$f":"(H$67/(H$21^2))*((1/H91)+(1/H$83))","v":6.8812427104998847E-5},4.9175222456789437E-4,1.1705507743484113E-4,null,747.17522508149045]
[5,null,null,null,null,null,{"$f":"(G$67/(G$21^2))*((1/G92)+(1/G$83))","v":1.9057709436459242E-3},6.8453081539663642E-5,4.8964541676043089E-4,1.1669660083534163E-4,null,1469.4571495894306]
[6,null,null,null,null,{"$f":"(F$67/(F$21^2))*((1/F93)+(1/F$83))","v":7.0877396607216059E-3},2.5999512655504493E-3,9.0749370779642213E-5,6.2036637391050305E-4,1.3893897341269321E-4,null,2001.856930931855]
[7,null,null,null,{"$f":"(E$67/(E$21^2))*((1/E94)+(1/E$83))","v":4.0916006990525857E-3},{"$f":"(F$67/(F$21^2))*((1/F94)+(1/F$83))","v":7.6876343591701663E-3},2.8102150991040206E-3,9.7502808037493364E-5,6.5996111422344822E-4,1.4567607957641994E-4,null,2209.2420936420785]
[8,null,null,{"$f":"(D$67/(D$21^2))*((1/D95)+(1/D$83))","v":3.7719880185388417E-2},{"$f":"(E$67/(E$21^2))*((1/E95)+(1/E$83))","v":3.1461202876267177E-3},{"$f":"(F$67/(F$21^2))*((1/F95)+(1/F$83))","v":5.9444189831518437E-3},2.1992159543890045E-3,7.7878204420712686E-5,5.4490398786196737E-4,1.2609893197893491E-4,null,5357.869297697076]
[9,null,{"$f":"(C$67/(C$21^2))*((1/C96)+(1/C$83))","v":8.4954142750416628E-2},{"$f":"(D$67/(D$21^2))*((1/D96)+(1/D$83))","v":5.3946234788295085E-2},{"$f":"(E$67/(E$21^2))*((1/E96)+(1/E$83))","v":4.4763363992122709E-3},{"$f":"(F$67/(F$21^2))*((1/F96)+(1/F$83))","v":8.3969850555109804E-3},3.0588433952570726E-3,1.0548846857748479E-4,7.0678025879175057E-4,1.5364242927232632E-4,null,6333.1658657363632]
[10,{"$f":"(B$67/(B$21^2))*((1/B97)+(1/B$83))","v":1.6444080821275886},{"$f":"(C$67/(C$21^2))*((1/C97)+(1/C$83))","v":7.4967802467380495E-2},{"$f":"(D$67/(D$21^2))*((1/D97)+(1/D$83))","v":4.7684994708248406E-2},{"$f":"(E$67/(E$21^2))*((1/E97)+(1/E$83))","v":3.9630478241252116E-3},{"$f":"(F$67/(F$21^2))*((1/F97)+(1/F$83))","v":7.4506169175641542E-3},2.7271401927579141E-3,9.4834535713963486E-5,6.4431729527605777E-4,{"$f":"(J$67/(J$21^2))*((1/J97)+(1/J$83))","v":1.430142596422144E-4},null,24566.287910989606]
[]
[]
["Step 9:","Overall Mean Square Error (triangular entires calculate covariance terms)",null,null,null,null,null,null,null,null,null,"SE(R)"]
[null,"d"]
["w",1,2,3,4,5,6,7,8,9,10]
[1]
[2,null,null,null,null,null,null,null,null,{"$f":"(2*J$67/(J$21^2))/J$83","v":1.4135677391005798E-4},null,{"$f":"L104^2+(K28*SUM(K29:K$36)*SUM(B119:J119))","v":465340.56916692451}]
[3,null,null,null,null,null,null,null,{"$f":"(2*I$67/(I$21^2))/I$83","v":4.3838226418086535E-4},1.4135677391005798E-4,null,{"$f":"L105^2+(K29*SUM(K30:K$36)*SUM(B120:J120))","v":2529638.7208055421}]
[4,null,null,null,null,null,null,{"$f":"(2*H$67/(H$21^2))/H$83","v":4.4646634253035386E-5},4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L106^2+(K30*SUM(K31:K$36)*SUM(B121:J121))","v":2792115.2062884094}]
[5,null,null,null,null,null,{"$f":"(2*G$67/(G$21^2))/G$83","v":9.3910205077595444E-4},4.4646634253035386E-5,4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L107^2+(K31*SUM(K32:K$36)*SUM(B122:J122))","v":6488259.6399562107}]
[6,null,null,null,null,{"$f":"(2*F$67/(F$21^2))/F$83","v":2.0191727607964719E-3},9.3910205077595444E-4,4.4646634253035386E-5,4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L108^2+(K32*SUM(K33:K$36)*SUM(B123:J123))","v":9332319.9376750775}]
[7,null,null,null,{"$f":"(2*E$67/(E$21^2))/E$83","v":9.3915842171438915E-4},{"$f":"(2*F$67/(F$21^2))/F$83","v":2.0191727607964719E-3},9.3910205077595444E-4,4.4646634253035386E-5,4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L109^2+(K33*SUM(K34:K$36)*SUM(B124:J124))","v":9573230.7322587669}]
[8,null,null,{"$f":"(2*D$67/(D$21^2))/D$83","v":1.0141341200164303E-2},{"$f":"(2*E$67/(E$21^2))/E$83","v":9.3915842171438915E-4},{"$f":"(2*F$67/(F$21^2))/F$83","v":2.0191727607964719E-3},9.3910205077595444E-4,4.4646634253035386E-5,4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L110^2+(K34*SUM(K35:K$36)*SUM(B125:J125))","v":40839052.869523734}]
[9,null,{"$f":"(2*C$67/(C$21^2))/C$83","v":1.4000507083484727E-2},{"$f":"(2*D$67/(D$21^2))/D$83","v":1.0141341200164303E-2},{"$f":"(2*E$67/(E$21^2))/E$83","v":9.3915842171438915E-4},{"$f":"(2*F$67/(F$21^2))/F$83","v":2.0191727607964719E-3},9.3910205077595444E-4,4.4646634253035386E-5,4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L111^2+(K35*SUM(K36:K$36)*SUM(B126:J126))","v":48572421.973246217}]
[10,{"$f":"(2*B$67/(B$21^2))/B$83","v":0.28397906189764066},{"$f":"(2*C$67/(C$21^2))/C$83","v":1.4000507083484727E-2},{"$f":"(2*D$67/(D$21^2))/D$83","v":1.0141341200164303E-2},{"$f":"(2*E$67/(E$21^2))/E$83","v":9.3915842171438915E-4},{"$f":"(2*F$67/(F$21^2))/F$83","v":2.0191727607964719E-3},9.3910205077595444E-4,4.4646634253035386E-5,4.3838226418086535E-4,1.4135677391005798E-4,null,{"$f":"L112^2","v":603502501.7256341}]
[]
[null,null,null,null,null,null,null,null,null,null,"Mack Overall Mean Square Error ==>",{"$f":"SQRT(SUM(L119:L127))","v":26909.01115564366}]
[]
[null,null,null,null,null,null,null,null,null,null,"Assuming Independence ==>",{"$f":"SQRT(SUMSQ(L104:L112))","v":26160.182284157414}]
[null,null,null,null,null,null,null,null,null,null,"Assuming 100% Correlation ==>",{"$f":"SUM(L104:L112)","v":43514.651205700975}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Question on II.25"]
[]
[null,"Year","Ultimate","IBNR","SE(Rw)","SE(R)"]
[null,1,{"$f":"L88","v":18834},{"$f":"K42","v":0}]
[null,2,{"$f":"L89","v":16857.953917050691},{"$f":"K43","v":153.95391705069051},{"$f":"L104","v":206.220059401112},{"$f":"E178^2+(K28*SUM(K$29:K29)*SUM(B119:J119))","v":99917.048172554409}]
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[]
[null,"Total",null,{"$f":"SUM(D177:D179)","v":771.32484086561089},null,{"$f":"SQRT(SUM(F177:F179))","v":698.9388558051802}]
[]
[]
[null,"Gamma beta",null,null,{"$f":"D181/SUM(F177:F179)","v":1.5789157206436209E-3}]
[null,"Gamma alpha",null,null,{"$f":"E184*D181","v":1.2178569169656523}]
[null,"1/Beta",null,null,{"$f":"1/E184","v":633.34602786294715}]
[null,"95th Percentile",null,null,{"$f":"GAMMAINV(0.95,E185,E186)","v":2156.8053979773913}]

{"sheet":"Distribution","index":3,"n_rows":291,"n_cols":12,"rows_kept":291,"cut":false,"hidden":false,"merged":[]}
["Lognormal Parameters",null,null,null,null,null,null,null,"Gamma Parameters"]
[]
[null,"X ~ lognormal"]
["Þ","ln[X] ~ Normal(m,s)"]
[]
["if  ","M = E[X] = em+0.5s2 =",null,null,{"$f":"SUM('Mack Calc & Last Ex'!K42:K52)","v":104270.45652242031},null,null,null,null,"b = M/V",null,{"$f":"(E7/E6)","v":6944.3915901419268}]
[null,"V = Var[X] = e2m+2s2 - e2m+s2 =",null,null,{"$f":"'Mack Calc & Last Ex'!L129^2","v":724094881.37455499},null,null,null,null,"a =  M/b",null,{"$f":"E6/L6","v":15.015060019144062}]
[null,"cv =",null,null,{"$f":"E7^0.5/E6","v":0.25806937125913193}]
[]
["and","s2 = ln(1+cv2)",null,null,{"$f":"LN(1+E8^2)","v":6.4475832030853525E-2}]
[null,"s =  ",null,null,{"$f":"E10^0.5","v":0.2539209168832956}]
[null,"m = lnE[X] -0.5*s2  =",null,null,{"$f":"LN(E6)-0.5*E10","v":11.522505430030616}]
[]
[]
[null,"75th Percentile",null,null,{"$f":"LOGINV(0.75,E12,E11)","v":119823.18607902953},null,null,null,null,null,null,{"$f":"GAMMAINV(0.75,L7,L6)","v":120945.31053844985}]
[]
[]
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["Slide II.18"]
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[null,null,null,null,"Mean Reserve",null,{"$f":"E6","v":104270.45652242031}]
[null,null,null,null,"Standard Error",null,{"$f":"E7^0.5","v":26909.01115564366}]
[null,null,null,null,"75th Percentile (logNormal)",null,{"$f":"E15","v":119823.18607902953}]
[null,null,null,null,"75th Percentile (Gamma)",null,{"$f":"L15","v":120945.31053844985}]
[]
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{"sheet":"Diagnostics","index":4,"n_rows":99,"n_cols":24,"rows_kept":99,"cut":false,"hidden":false,"merged":[]}
["Slide II.21",{"$f":"\"Cum. (\"&TEXT(C29,\"0\")&\") vs. Cum. (\"&TEXT(C29-1,\"0\")&\")\"","v":"Cum. (1) vs. Cum. (0)"},null,null,null,null,null,null,null,{"$f":"\"Incr. (\"&TEXT(C29,\"0\")&\") vs. Cum. (\"&TEXT(C29-1,\"0\")&\")\"","v":"Incr. (1) vs. Cum. (0)"}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,{"$f":"\"Corr. = \"&TEXT(L40,\"0.000\")","v":"Corr. = 0.695"},null,null,{"$f":"\"P-Value = \"&TEXT(L43,\"0.000\")","v":"P-Value = 0.115"},null,{"$f":"\"Int. P-Value = \"&TEXT(L56,\"0.000\")","v":"Int. P-Value = 0.626"},null,null,{"$f":"\"Corr. = \"&TEXT(L53,\"0.000\")","v":"Corr. = -0.117"},null,null,null,null,{"$f":"\"P-Value = \"&TEXT(L56,\"0.000\")","v":"P-Value = 0.626"}]
[]
[]
[]
[]
[]
[null,"Column:",1,null,"Delta:",1]
[]
[null,"Regression Calculations for X-Y Plots"]
[null,"Ratio Only Model: Y = βX + ε"]
[null,null,"X","Y","Rows","Weights","X'","Y'",null,null,"Regression without Intercept",null,null,null,"Regression with Intercept"]
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[null,{"$f":"IF(B38=\"\",\"\",IF(B38+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B38+1))","v":6},{"$f":"IF(B39=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B39-'Mack Calc & Last Ex'!$A$5,$C$29))","v":1513},{"$f":"IF(C39=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B39-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":6445},1,38.897300677553446,38.897300677553453,165.69273157093986,null,null,null,"Slope","Intercept",null,null,"Slope","Intercept"]
[null,{"$f":"IF(B39=\"\",\"\",IF(B39+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B39+1))","v":7},{"$f":"IF(B40=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B40-'Mack Calc & Last Ex'!$A$5,$C$29))","v":557},{"$f":"IF(C40=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B40-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":4020},1,23.600847442411894,23.600847442411894,170.33286664002839,null,null,"Corr:",{"$f":"CORREL(RegressY1Values,RegressX1Values)","v":0.69482069992203066},null,null,"Corr:",{"$f":"CORREL(RegressY1Values,RegressX1Values)","v":0.69482069992203066}]
[null,{"$f":"IF(B40=\"\",\"\",IF(B40+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B40+1))","v":8},{"$f":"IF(B41=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B41-'Mack Calc & Last Ex'!$A$5,$C$29))","v":1351},{"$f":"IF(C41=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B41-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":6947},1,36.755951898978211,36.755951898978211,189.00340328808412,null,null,"SE",{"$f":"K35","v":1.1302032773653081},{"$f":"L35","v":{"$error":"#N/A"}},null,"SE",{"$f":"O35","v":1.1377642343239496},{"$f":"P35","v":56.033524875244431}]
[null,{"$f":"IF(B41=\"\",\"\",IF(B41+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B41+1))","v":9},{"$f":"IF(B42=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B42-'Mack Calc & Last Ex'!$A$5,$C$29))","v":3133},{"$f":"IF(C42=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B42-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":5395},1,55.97320787662612,55.973207876626113,96.385399455600989,null,null,"t-Ratio",{"$f":"(K34-1)/L41","v":1.7690257065934343},{"$f":"(L34-1)/M41","v":{"$error":"#N/A"}},null,"t-Ratio",{"$f":"(O34-1)/P41","v":-3.88366759180869},{"$f":"P34/Q41","v":6.2048148347450729}]
[null,null,null,null,null,null,null,null,null,null,"P-Value",{"$f":"TDIST(ABS(L42),L37,2)","v":0.11485656153923127},{"$f":"TDIST(ABS(M42),L37,2)","v":{"$error":"#N/A"}},null,"P-Value",{"$f":"TDIST(ABS(P42),P37,2)","v":6.0244022940754904E-3},{"$f":"TDIST(ABS(Q42),P37,2)","v":4.4317133605621602E-4}]
[]
[null,"Ratio + Intercept Model: Y = α + βX + ε"]
[null,null,"I","X","Y","Y - X","I'","X'","Y' - X'",null,"Regression with Intercept",null,null,null,"Regression with Intercept",null,null,null,null,null,"Scale Range"]
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[null,{"$f":"IF(B48=\"\",\"\",IF(B48+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B48+1))","v":3},{"$f":"IF(B49=\"\",\"\",1)","v":1},{"$f":"IF(B49=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B49-'Mack Calc & Last Ex'!$A$5,$C$29))","v":3410},{"$f":"IF(C49=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B49-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":8992},{"$f":"IF(B49=\"\",\"\",E49-D49)","v":5582},1.7124693631268541E-2,58.395205282625732,95.590039849741004,null,0.93491280297193713,53.716676759062686,null,null,1.3737962502395659E-2,1948.1504503422293]
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[null,{"$f":"IF(B53=\"\",\"\",IF(B53+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B53+1))","v":8},1,{"$f":"IF(B54=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B54-'Mack Calc & Last Ex'!$A$5,$C$29))","v":1351},{"$f":"IF(C54=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B54-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":6947},5596,2.7206478089547161E-2,36.755951898978211,152.24745138910592,null,"SE",{"$f":"K48","v":0.4213074872998292},{"$f":"L48","v":516.30820396411298},null,"SE",{"$f":"O48","v":0.34862824966432743},{"$f":"P48","v":1066.1621949398823},null,null,null,{"$f":"MAX(U51,U53)","v":-1},{"$f":"MAX(V51,V53)","v":2}]
[null,{"$f":"IF(B54=\"\",\"\",IF(B54+1>'Mack Calc & Last Ex'!$A$5+10-$C$29-1,\"\",B54+1))","v":9},1,{"$f":"IF(B55=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B55-'Mack Calc & Last Ex'!$A$5,$C$29))","v":3133},{"$f":"IF(C55=\"\",\"\",OFFSET('Mack Calc & Last Ex'!$A$5,$B55-'Mack Calc & Last Ex'!$A$5,$C$29+1))","v":5395},2262,1.7865690353216123E-2,55.973207876626113,40.41219157897487,null,"t-Ratio",{"$f":"K47/L54","v":0.50900181855109528},{"$f":"(L47-1)/M54","v":8.3829886266071885},null,"t-Ratio",{"$f":"O47/P54","v":-0.31225832436953876},{"$f":"(P47-1)/Q54","v":4.7951167917328519}]
[null,null,null,null,null,null,null,null,null,null,"P-Value",{"$f":"TDIST(ABS(L55),L50,2)","v":0.62639861673859321},{"$f":"TDIST(ABS(M55),L50,2)","v":6.7540066666371554E-5},null,"P-Value",{"$f":"TDIST(ABS(P55),P50,2)","v":0.76394038645704487},{"$f":"TDIST(ABS(Q55),P50,2)","v":1.9774084241871879E-3}]
[null,null,null,null,null,null,null,null,null,null,"C.o.V.",{"$f":"ABS(K48/K47)","v":1.9646295230271693},{"$f":"ABS(L48/L47)","v":0.11926164465702181},null,"C.o.V.",{"$f":"ABS(O48/O47)","v":3.2024766738213861},{"$f":"ABS(P48/P47)","v":0.20850470963860412}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Slide II.25"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Ratio Only Model: Y = βX + ε"]
[null,null,"X","Y","Forecast","Residuals","Standardized","Weights","Weighted"]
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