{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Hellwig","No of combinations  for Hellwig","Graph"],"not_rendered":{"images":1},"read":"whole","date_system":"1900"}

{"sheet":"Hellwig","index":0,"n_rows":84,"n_cols":15,"rows_kept":84}
["Rok","Y","X1","X2","X3","X4"]
[1971,1.5,7,0.6,0.13,0.15,null,"Y - production (kPLN)"]
[1972,1.5,7,1,0.13,0.15,null,"X₁ – employment;"]
[1973,1.6,8,1,0.13,0.16,null,"X₂ – value of machinery and equipment (kPLN);"]
[1974,1.6,8,1.4,0.14,0.16,null,"X₃ – investment expenditures (k PLN);"]
[1975,2,8,1,0.13,0.17,null,"X₄ – labor productivity (kPLN per employee)."]
[1976,1.6,10,1,0.13,0.16]
[1977,2,10,1,0.13,0.15,null,"Step 1. For all pairs of variables, correlation coefficients were determined, which formed the respective matrices:"]
[1978,2,12,1.4,0.13,0.17,null,null,"R0"]
[1979,2,12,1.4,0.13,0.17,null,"Y-X1"]
[1980,2.2,12,1.6,0.12,0.17,null,"Y-X2"]
[1981,2.25,14,1.6,0.15,0.17,null,"Y-X3"]
[1982,2.35,14,1.6,0.21,0.17,null,"Y-X4",{"$nulls":4},"R"]
[1983,2.35,14,2,0.21,0.17,{"$nulls":5},"X1","X2","X3","X4"]
[1984,2.45,16,2,0.22,0.16,null,"X1-X2",null,null,"X1"]
[1985,2.5,16,2,0.22,0.16,null,"X1-X3",null,null,"X2"]
[1986,2.6,16,2,0.22,0.16,null,"X1-X4",null,null,"X3"]
[1987,2.5,16,2.1,0.22,0.18,null,"X2-X3",null,null,"X4"]
[1988,2.55,15,2.1,0.21,0.19,null,"X2-X4"]
[1989,2.6,14,2.03,0.21,0.19,null,"X3-X4"]
[1990,2.65,12,1.98,0.21,0.2]
[1991,2.7,12,2,0.21,0.24,null,"Step 2. Calculate total number of these combinations (l)",{"$nulls":5},"For four explanatory variables, one can form 15 combinations of variables, "]
[1992,2.85,12,2,0.2,0.24,{"$nulls":7},"for which integral capacities are determined (see below)."]
[1993,2.8,12,1.96,0.2,0.24,null,"l=2^k-1",{"$nulls":5},"{X1}, {X2}, {X3}, {X4}, {X1, X2}, {X1, X3}, {X1, X4}, {X2, X3}, {X2, X4}, {X3, X4},"]
[1994,2.95,12,1.95,0.2,0.25,{"$nulls":7},"{X1, X2, X3}, {X1, X2, X4}, {X1, X3, X4}, {X2, X3, X4}, {X1, X2, X3, X4}."]
[1995,3,11,1.95,0.23,0.26,null,"Step 3. Calculate the individual capacities of information "]
[1996,3.2,12,1.95,0.24,0.25,{"$nulls":7},"The individual and integral capacity of the first (single-element) combination {X1} is: "]
[1997,2.97,12,1.93,0.24,0.24]
[1998,2.85,12,1.93,0.24,0.22,{"$nulls":7},"H1=h11"]
[{"$nulls":13},"H2=h22"]
[{"$nulls":13},"H3=h33"]
[{"$nulls":13},"H4=h44"]
[]
[{"$nulls":13},"The individual and integral capacity of the fifth (first two-element) combination {X1, X2} is"]
[null,"Var combinarion","Integral capacity","Value"]
[1,"{X1}",{"$f":"\"H\"&A36","v":"H1"},{"$nulls":4},"Step 4.  Select the highest value among individual capacities",{"$nulls":5},"X1-X2","h51"]
[2,"{X2}",{"$f":"\"H\"&A37","v":"H2"},{"$nulls":11},"h52"]
[3," {X3}","H3",{"$nulls":4},"Step 5. determine the final version of the model",{"$nulls":6},"H5=h51+h52"]
[4," {X4}","H4",{"$nulls":4},"in the context of the selection of explanatory variables"]
[5,"{X1, X2}","H5",{"$nulls":10},"X1-X3","h61"]
[6," {X1, X3}","H6",{"$nulls":11},"h62"]
[7," {X1, X4}","H7",{"$nulls":11},"H6"]
[8," {X2, X3}","H8"]
[9," {X2, X4}","H9",{"$nulls":10},"X1-X4","h71"]
[10,"{X3, X4}","H10",{"$nulls":11},"h72"]
[11,"{X1, X2, X3}","H11",{"$nulls":11},"H7"]
[12," {X1, X2, X4}","H12"]
[13," {X1, X3, X4}","H13",{"$nulls":10},"X2-X3","h81"]
[14," {X2, X3, X4}","H14",{"$nulls":11},"h82"]
[15," {X1, X2, X3, X4}.","H15",{"$nulls":11},"H8"]
[]
[{"$nulls":13},"X2-X4","h91"]
[{"$nulls":14},"h92"]
[{"$nulls":14},"H9"]
[]
[{"$nulls":13},"X3-X4","h10,1"]
[{"$nulls":14},"h10,2"]
[{"$nulls":14},"H10"]
[]
[{"$nulls":13},"X1,X2,X3","h11,1"]
[{"$nulls":14},"h11,2"]
[{"$nulls":14},"h11,3"]
[{"$nulls":14},"H11"]
[]
[{"$nulls":13},"X1,X2,X4","h12,1"]
[{"$nulls":14},"h12,2"]
[{"$nulls":14},"h12,3"]
[{"$nulls":14},"H12"]
[]
[{"$nulls":13},"X1,X3,X4","h13,1"]
[{"$nulls":14},"h13,2"]
[{"$nulls":14},"h13,3"]
[{"$nulls":14},"H13"]
[]
[{"$nulls":13},"X2,X3,X4","h14,1"]
[{"$nulls":14},"h14,2"]
[{"$nulls":14},"h14,3"]
[{"$nulls":14},"H14"]
[]
[{"$nulls":13},"X1,X2,X3,X4","h15,1"]
[{"$nulls":14},"h15,2"]
[{"$nulls":14},"h15,3"]
[{"$nulls":14},"h15,4"]
[{"$nulls":14},"H15"]

{"sheet":"No of combinations  for Hellwig","index":1,"n_rows":11,"n_cols":2,"rows_kept":11}
[]
["l=2^k-1"]
[]
["No of Variables","Possible number of combinations"]
[1,{"$f":"2^A5-1","v":1}]
[2,{"$f":"2^A6-1","v":3}]
[3,7]
[4,15]
[5,31]
[6,63]
[7,127]

{"sheet":"Graph","index":2,"n_rows":29,"n_cols":17,"rows_kept":29}
["Rok","Y","X1","X2","X3","X4"]
[1971,1.5,7,0.6,0.13,0.15]
[1972,1.5,7,1,0.13,0.15]
[1973,1.6,8,1,0.13,0.16]
[1974,1.6,8,1.4,0.14,0.16]
[1975,2,8,1,0.13,0.17]
[1976,1.6,10,1,0.13,0.16]
[1977,2,10,1,0.13,0.15]
[1978,2,12,1.4,0.13,0.17,{"$nulls":4},"R0"]
[1979,2,12,1.4,0.13,0.17,{"$nulls":3},"Y-X1"]
[1980,2.2,12,1.6,0.12,0.17,{"$nulls":3},"Y-X2"]
[1981,2.25,14,1.6,0.15,0.17,{"$nulls":3},"Y-X3"]
[1982,2.35,14,1.6,0.21,0.17,{"$nulls":3},"Y-X4",{"$nulls":4},"R"]
[1983,2.35,14,2,0.21,0.17,{"$nulls":7},"X1","X2","X3","X4"]
[1984,2.45,16,2,0.22,0.16,{"$nulls":3},"X1-X2",null,null,"X1"]
[1985,2.5,16,2,0.22,0.16,{"$nulls":3},"X1-X3",null,null,"X2"]
[1986,2.6,16,2,0.22,0.16,{"$nulls":3},"X1-X4",null,null,"X3"]
[1987,2.5,16,2.1,0.22,0.18,{"$nulls":3},"X2-X3",null,null,"X4"]
[1988,2.55,15,2.1,0.21,0.19,{"$nulls":3},"X2-X4"]
[1989,2.6,14,2.03,0.21,0.19,{"$nulls":3},"X3-X4"]
[1990,2.65,12,1.98,0.21,0.2]
[1991,2.7,12,2,0.21,0.24,{"$nulls":8},"R'"]
[1992,2.85,12,2,0.2,0.24,{"$nulls":3},"r*=",{"$nulls":3},"X1","X2","X3","X4"]
[1993,2.8,12,1.96,0.2,0.24,{"$nulls":6},"X1"]
[1994,2.95,12,1.95,0.2,0.25,{"$nulls":6},"X2"]
[1995,3,11,1.95,0.23,0.26,{"$nulls":6},"X3"]
[1996,3.2,12,1.95,0.24,0.25,{"$nulls":6},"X4"]
[1997,2.97,12,1.93,0.24,0.24]
[1998,2.85,12,1.93,0.24,0.22]