Proyecciones de los IPC, IPM, MDO y TV para la actualización de los costos unitarios en los contratos de obras civiles (página 6)
Enviado por IVÁN JOSÉ TURMERO ASTROS
NRO. DE REFERENCIA (x) | IPC (y) | x*y | x⼯b>
| y⼯b>
| |
1 | 11.937,90 | 11.937,90 | 1 | 142.513.456,41 | |
2 | 12.203,10 | 24.406,20 | 4 | 148.915.649,61 | |
3 | 12.533,90 | 37.601,70 | 9 | 157.098.649,21 | |
4 | 12.955,20 | 51.820,80 | 16 | 167.837.207,04 | |
5 | 13.374,00 | 66.870,00 | 25 | 178.863.876,00 | |
6 | 13.548,60 | 81.291,60 | 36 | 183.564.561,96 | |
7 | 13.828,50 | 96.799,50 | 49 | 191.227.412,25 | |
8 | 14.115,20 | 112.921,60 | 64 | 199.238.871,04 | |
9 | 14.366,40 | 129.297,60 | 81 | 206.393.448,96 | |
10 | 14.719,30 | 147.193,00 | 100 | 216.657.792,49 | |
11 | 14.947,60 | 164.423,60 | 121 | 223.430.745,76 | |
12 | 15.202,50 | 182.430,00 | 144 | 231.116.006,25 | |
13 | 15.540,50 | 202.026,50 | 169 | 241.507.140,25 | |
14 | 15.797,60 | 221.166,40 | 196 | 249.564.165,76 | |
15 | 15.994,50 | 239.917,50 | 225 | 255.824.030,25 | |
16 | 16.178,30 | 258.852,80 | 256 | 261.737.390,89 | |
17 | 16.500,10 | 280.501,70 | 289 | 272.253.300,01 | |
18 | 16.745,00 | 301.410,00 | 324 | 280.395.025,00 | |
19 | 17.014,60 | 323.277,40 | 361 | 289.496.613,16 | |
20 | 17.262,00 | 345.240,00 | 400 | 297.976.644,00 | |
21 | 17.409,90 | 365.607,90 | 441 | 303.104.618,01 | |
22 | 17.686,50 | 389.103,00 | 484 | 312.812.282,25 | |
23 | 17.947,40 | 412.790,20 | 529 | 322.109.166,76 | |
24 | 18.247,30 | 437.935,20 | 576 | 332.963.957,29 | |
25 | 18.470,43 | 461.760,65 | 625 | 341.156.637,49 | |
26 | 18.550,47 | 482.312,25 | 676 | 344.119.981,99 | |
27 | 18.720,57 | 505.455,31 | 729 | 350.459.637,07 | |
28 | 19.010,73 | 532.300,47 | 784 | 361.407.893,53 | |
29 | 19.200,84 | 556.824,31 | 841 | 368.672.192,19 | |
30 | 19.410,96 | 582.328,71 | 900 | 376.785.248,78 | |
31 | 19.611,07 | 607.943,17 | 961 | 384.594.062,00 | |
32 | 19.761,15 | 632.356,95 | 1024 | 390.503.231,22 | |
33 | 20.101,35 | 663.344,44 | 1089 | 404.064.136,38 | |
34 | 20.271,44 | 689.229,05 | 1156 | 410.931.386,93 | |
35 | 20.401,52 | 714.053,06 | 1225 | 416.221.857,88 | |
36 | 20.611,63 | 742.018,85 | 1296 | 424.839.483,93 | |
37 | 20.801,74 | 769.664,45 | 1369 | 432.712.469,57 | |
38 | 20.901,80 | 794.268,34 | 1444 | 436.885.178,99 | |
39 | 21.061,89 | 821.413,66 | 1521 | 443.603.161,07 | |
40 | 21.332,09 | 853.283,55 | 1600 | 455.058.013,83 | |
41 | 21.667,89 | 888.383,44 | 1681 | 469.497.406,33 | |
42 | 22.094,19 | 927.955,93 | 1764 | 488.153.180,03 | |
43 | 22.517,99 | 968.273,52 | 1849 | 507.059.820,93 | |
44 | 22.697,59 | 998.693,91 | 1936 | 515.180.538,67 | |
45 | 22.982,49 | 1.034.212,00 | 2025 | 528.194.792,80 | |
46 | 23.274,19 | 1.070.612,69 | 2116 | 541.687.865,67 | |
47 | 23.530,39 | 1.105.928,27 | 2209 | 553.679.198,47 | |
48 | 23.888,29 | 1.146.637,86 | 2304 | 570.650.343,20 | |
49 | 24.123,59 | 1.182.055,85 | 2401 | 581.947.538,01 | |
50 | 24.385,49 | 1.219.274,44 | 2500 | 594.652.065,45 | |
51 | 24.730,49 | 1.261.254,93 | 2601 | 611.597.077,75 | |
52 | 24.994,59 | 1.299.718,62 | 2704 | 624.729.470,76 | |
53 | 25.198,49 | 1.335.519,91 | 2809 | 634.963.839,29 | |
54 | 25.389,29 | 1.371.021,60 | 2916 | 644.615.987,27 | |
55 | 25.718,09 | 1.414.494,89 | 3025 | 661.420.093,04 | |
56 | 25.969,99 | 1.454.319,37 | 3136 | 674.440.319,80 | |
57 | 26.246,59 | 1.496.055,56 | 3249 | 688.883.425,18 | |
58 | 26.500,99 | 1.537.057,35 | 3364 | 702.302.408,94 | |
59 | 26.655,89 | 1.572.697,44 | 3481 | 710.536.409,29 | |
60 | 26.939,49 | 1.616.369,33 | 3600 | 725.736.058,39 | |
61 | 27.207,39 | 1.659.650,72 | 3721 | 740.242.006,92 | |
62 | 27.514,29 | 1.705.885,91 | 3844 | 757.036.089,79 | |
63 | 27.744,41 | 1.747.898,14 | 3969 | 769.752.555,53 | |
64 | 27.831,46 | 1.781.213,44 | 4096 | 774.590.167,74 | |
65 | 28.008,56 | 1.820.556,14 | 4225 | 784.479.212,03 | |
66 | 28.305,72 | 1.868.177,51 | 4356 | 801.213.775,63 | |
67 | 28.505,83 | 1.909.890,42 | 4489 | 812.582.181,48 | |
68 | 28.725,95 | 1.953.364,31 | 4624 | 825.179.959,55 | |
69 | 28.936,06 | 1.996.588,05 | 4761 | 837.295.493,87 | |
70 | 29.096,14 | 2.036.730,04 | 4900 | 846.585.562,62 | |
71 | 29.446,34 | 2.090.689,82 | 5041 | 867.086.672,06 | |
72 | 29.626,43 | 2.133.103,07 | 5184 | 877.725.441,94 | |
x | y | x*y | x⼯b>
| y⼯b>
| |
2.628,00 | 1.502.792,22 | 62.897.663,81 | 127.020,00 | 33.732.313.541,91 | |
Valores totales | |||||
Se sustituyen los valores en la ecuación de r, y se obtiene:
El coeficiente de correlación da un valor bastante cercano a 1 (0.94) lo que indica que el grado de influencia de la variable independiente (Mes) con respecto a la variable dependiente (IPC) es fuerte, esto quiere decir que el 94% de las variaciones de y (IPC) están controladas por la variación de x (Mes).
Luego de esto se procede a realizar los pronósticos para los meses que corresponden a los años 2005 y 2007, por cuanto este método se utiliza en pronósticos a mediano plazo (de 1 hasta 2 años).
MES (x) | NRO. DE REFERENCIA (x) | IPC (y) |
Ene-98 | 01 | 11.937,90 |
Feb-98 | 02 | 12.203,10 |
Mar-98 | 03 | 12.533,90 |
Abr-98 | 04 | 12.955,20 |
May-98 | 05 | 13.374,00 |
Jun-98 | 06 | 13.548,60 |
Jul-98 | 07 | 13.828,50 |
Ago-98 | 08 | 14.115,20 |
Sep-98 | 09 | 14.366,40 |
Oct-98 | 10 | 14.719,30 |
Nov-98 | 11 | 14.947,60 |
Dic-98 | 12 | 15.202,50 |
Ene-99 | 13 | 15.540,50 |
Feb-99 | 14 | 15.797,60 |
Mar-99 | 15 | 15.994,50 |
Abr-99 | 16 | 16.178,30 |
May-99 | 17 | 16.500,10 |
Jun-99 | 18 | 16.745,00 |
Jul-99 | 19 | 17.014,60 |
Ago-99 | 20 | 17.262,00 |
Sep-99 | 21 | 17.409,90 |
Oct-99 | 22 | 17.686,50 |
Nov-99 | 23 | 17.947,40 |
Dic-99 | 24 | 18.247,30 |
Ene-00 | 25 | 18.470,43 |
Feb-00 | 26 | 18.550,47 |
Mar-00 | 27 | 18.720,57 |
Abr-00 | 28 | 19.010,73 |
May-00 | 29 | 19.200,84 |
Jun-00 | 30 | 19.410,96 |
Jul-00 | 31 | 19.611,07 |
Ago-00 | 32 | 19.761,15 |
Sep-00 | 33 | 20.101,35 |
Oct-00 | 34 | 20.271,44 |
Nov-00 | 35 | 20.401,52 |
Dic-00 | 36 | 20.611,63 |
Ene-01 | 37 | 20.801,74 |
Feb-01 | 38 | 20.901,80 |
Mar-01 | 39 | 21.061,89 |
Abr-01 | 40 | 21.332,09 |
May-01 | 41 | 21.667,89 |
Jun-01 | 42 | 22.094,19 |
Jul-01 | 43 | 22.517,99 |
Ago-01 | 44 | 22.697,59 |
Sep-01 | 45 | 22.982,49 |
Oct-01 | 46 | 23.274,19 |
Nov-01 | 47 | 23.530,39 |
Dic-01 | 48 | 23.888,29 |
Ene-02 | 49 | 24.123,59 |
Feb-02 | 50 | 24.385,49 |
Mar-02 | 51 | 24.730,49 |
Abr-02 | 52 | 24.994,59 |
May-02 | 53 | 25.198,49 |
Jun-02 | 54 | 25.389,29 |
Jul-02 | 55 | 25.718,09 |
Ago-02 | 56 | 25.969,99 |
Sep-02 | 57 | 26.246,59 |
Oct-02 | 58 | 26.500,99 |
Nov-02 | 59 | 26.655,89 |
Dic-02 | 60 | 26.939,49 |
Ene-03 | 61 | 27.207,39 |
Feb-03 | 62 | 27.514,29 |
Mar-03 | 63 | 27.744,41 |
Abr-03 | 64 | 27.831,46 |
May-03 | 65 | 28.008,56 |
Jun-03 | 66 | 28.305,72 |
Jul-03 | 67 | 28.505,83 |
Ago-03 | 68 | 28.725,95 |
Sep-03 | 69 | 28.936,06 |
Oct-03 | 70 | 29.096,14 |
Nov-03 | 71 | 29.446,34 |
Dic-03 | 72 | 29.626,43 |
Ene-05 | 85 | 33.419,95 |
Feb-05 | 86 | 33.678,67 |
Mar-05 | 87 | 33.937,39 |
Abr-05 | 88 | 34.196,11 |
May-05 | 89 | 34.454,83 |
Jun-05 | 90 | 34.713,55 |
Jul-05 | 91 | 34.972,27 |
Ago-05 | 92 | 35.230,99 |
Sep-05 | 93 | 35.489,71 |
Oct-05 | 94 | 35.748,43 |
Nov-05 | 95 | 36.007,15 |
Dic-05 | 96 | 36.265,87 |
Ene-06 | 97 | 36.524,59 |
Feb-06 | 98 | 36.783,31 |
Mar-06 | 99 | 37.042,03 |
Abr-06 | 100 | 37.300,75 |
May-06 | 101 | 37.559,47 |
Jun-06 | 102 | 37.818,19 |
Jul-06 | 103 | 38.076,91 |
Ago-06 | 104 | 38.335,63 |
Sep-06 | 105 | 38.594,35 |
Oct-06 | 106 | 38.853,07 |
Nov-06 | 107 | 39.111,79 |
Dic-06 | 108 | 39.370,51 |
Ene-07 | 109 | 39.629,23 |
Feb-07 | 110 | 39.887,95 |
Mar-07 | 111 | 40.146,67 |
Abr-07 | 112 | 40.405,39 |
May-07 | 113 | 40.664,11 |
Jun-07 | 114 | 40.922,83 |
Jul-07 | 115 | 41.181,55 |
Ago-07 | 116 | 41.440,27 |
Sep-07 | 117 | 41.698,99 |
Oct-07 | 118 | 41.957,71 |
Nov-07 | 119 | 42.216,43 |
Dic-07 | 120 | 42.475,15 |
Ahora se procede a comparar los gráficos de Variación y % de variación del IPC histórico con el IPC pronosticado:
Gráfico # 6.10 Variación IPC histórico.
Gráfico # 6.11 Variación IPC pronosticado.
Gráfico # 6.12 % Variación IPC data histórica.
Gráfico # 6.13 % Variación IPC pronosticado.
CASO IPM:
Variable independiente: x = Meses.
Variable dependiente: y = IPM
Número de datos: 72
MES (x) | NRO. DE REFERENCIA (x) | IPM (y) |
Ene-98 | 01 | 8.482,70 |
Feb-98 | 02 | 8.584,30 |
Mar-98 | 03 | 8.761,70 |
Abr-98 | 04 | 8.963,70 |
May-98 | 05 | 9.136,90 |
Jun-98 | 06 | 9.325,00 |
Jul-98 | 07 | 9.515,00 |
Ago-98 | 08 | 9.706,30 |
Sep-98 | 09 | 9.859,50 |
Oct-98 | 10 | 10.035,40 |
Nov-98 | 11 | 10.152,90 |
Dic-98 | 12 | 10.714,60 |
Ene-99 | 13 | 10.322,60 |
Feb-99 | 14 | 10.436,50 |
Mar-99 | 15 | 10.571,70 |
Abr-99 | 16 | 10.748,80 |
May-99 | 17 | 10.938,80 |
Jun-99 | 18 | 11.106,70 |
Jul-99 | 19 | 11.118,00 |
Ago-99 | 20 | 11.241,40 |
Sep-99 | 21 | 11.362,10 |
Oct-99 | 22 | 11.598,70 |
Nov-99 | 23 | 11.730,70 |
Dic-99 | 24 | 11.893,50 |
Ene-00 | 25 | 12.072,00 |
Feb-00 | 26 | 12.246,70 |
Mar-00 | 27 | 12.345,10 |
Abr-00 | 28 | 12.538,50 |
May-00 | 29 | 12.622,80 |
Jun-00 | 30 | 12.731,20 |
Jul-00 | 31 | 12.882,30 |
Ago-00 | 32 | 13.113,80 |
Sep-00 | 33 | 13.452,00 |
Oct-00 | 34 | 13.612,20 |
Nov-00 | 35 | 13.716,10 |
Dic-00 | 36 | 13.884,50 |
Ene-01 | 37 | 13.945,30 |
Feb-01 | 38 | 14.023,10 |
Mar-01 | 39 | 14.129,70 |
Abr-01 | 40 | 14.282,70 |
May-01 | 41 | 14.463,20 |
Jun-01 | 42 | 14.894,20 |
Jul-01 | 43 | 15.007,40 |
Ago-01 | 44 | 14.941,20 |
Sep-01 | 45 | 15.184,30 |
Oct-01 | 46 | 15.162,60 |
Nov-01 | 47 | 15.269,80 |
Dic-01 | 48 | 15.304,30 |
Ene-02 | 49 | 15.569,50 |
Feb-02 | 50 | 15.900,30 |
Mar-02 | 51 | 16.321,60 |
Abr-02 | 52 | 16.740,40 |
May-02 | 53 | 16.915,00 |
Jun-02 | 54 | 17.194,90 |
Jul-02 | 55 | 17.481,60 |
Ago-02 | 56 | 17.732,80 |
Sep-02 | 57 | 18.085,70 |
Oct-02 | 58 | 18.314,00 |
Nov-02 | 59 | 18.568,90 |
Dic-02 | 60 | 18.906,90 |
Ene-03 | 61 | 19.164,00 |
Feb-03 | 62 | 19.360,90 |
Mar-03 | 63 | 19.544,70 |
Abr-03 | 64 | 19.866,50 |
May-03 | 65 | 20.111,40 |
Jun-03 | 66 | 20.381,00 |
Jul-03 | 67 | 20.628,40 |
Ago-03 | 68 | 20.776,30 |
Sep-03 | 69 | 21.052,90 |
Oct-03 | 70 | 21.313,80 |
Nov-03 | 71 | 21.613,70 |
Dic-03 | 72 | 21.836,83 |
NRO. DE REFERENCIA (x) | IPM (y) | x*y | x⼢> | y⼯b>
| |
1 | 8.482,70 | 8.482,70 | 1 | 71.956.199,29 | |
2 | 8.584,30 | 17.168,60 | 4 | 73.690.206,49 | |
3 | 8.761,70 | 26.285,10 | 9 | 76.767.386,89 | |
4 | 8.963,70 | 35.854,80 | 16 | 80.347.917,69 | |
5 | 9.136,90 | 45.684,50 | 25 | 83.482.941,61 | |
6 | 9.325,00 | 55.950,00 | 36 | 86.955.625,00 | |
7 | 9.515,00 | 66.605,00 | 49 | 90.535.225,00 | |
8 | 9.706,30 | 77.650,40 | 64 | 94.212.259,69 | |
9 | 9.859,50 | 88.735,50 | 81 | 97.209.740,25 | |
10 | 10.035,40 | 100.354,00 | 100 | 100.709.253,16 | |
11 | 10.152,90 | 111.681,90 | 121 | 103.081.378,41 | |
12 | 10.714,60 | 128.575,20 | 144 | 114.802.653,16 | |
13 | 10.322,60 | 134.193,80 | 169 | 106.556.070,76 | |
14 | 10.436,50 | 146.111,00 | 196 | 108.920.532,25 | |
15 | 10.571,70 | 158.575,50 | 225 | 111.760.840,89 | |
16 | 10.748,80 | 171.980,80 | 256 | 115.536.701,44 | |
17 | 10.938,80 | 185.959,60 | 289 | 119.657.345,44 | |
18 | 11.106,70 | 199.920,60 | 324 | 123.358.784,89 | |
19 | 11.118,00 | 211.242,00 | 361 | 123.609.924,00 | |
20 | 11.241,40 | 224.828,00 | 400 | 126.369.073,96 | |
21 | 11.362,10 | 238.604,10 | 441 | 129.097.316,41 | |
22 | 11.598,70 | 255.171,40 | 484 | 134.529.841,69 | |
23 | 11.730,70 | 269.806,10 | 529 | 137.609.322,49 | |
24 | 11.893,50 | 285.444,00 | 576 | 141.455.342,25 | |
25 | 12.072,00 | 301.800,00 | 625 | 145.733.184,00 | |
26 | 12.246,70 | 318.414,20 | 676 | 149.981.660,89 | |
27 | 12.345,10 | 333.317,70 | 729 | 152.401.494,01 | |
28 | 12.538,50 | 351.078,00 | 784 | 157.213.982,25 | |
29 | 12.622,80 | 366.061,20 | 841 | 159.335.079,84 | |
30 | 12.731,20 | 381.936,00 | 900 | 162.083.453,44 | |
31 | 12.882,30 | 399.351,30 | 961 | 165.953.653,29 | |
32 | 13.113,80 | 419.641,60 | 1024 | 171.971.750,44 | |
33 | 13.452,00 | 443.916,00 | 1089 | 180.956.304,00 | |
34 | 13.612,20 | 462.814,80 | 1156 | 185.291.988,84 | |
35 | 13.716,10 | 480.063,50 | 1225 | 188.131.399,21 | |
36 | 13.884,50 | 499.842,00 | 1296 | 192.779.340,25 | |
37 | 13.945,30 | 515.976,10 | 1369 | 194.471.392,09 | |
38 | 14.023,10 | 532.877,80 | 1444 | 196.647.333,61 | |
39 | 14.129,70 | 551.058,30 | 1521 | 199.648.422,09 | |
40 | 14.282,70 | 571.308,00 | 1600 | 203.995.519,29 | |
41 | 14.463,20 | 592.991,20 | 1681 | 209.184.154,24 | |
42 | 14.894,20 | 625.556,40 | 1764 | 221.837.193,64 | |
43 | 15.007,40 | 645.318,20 | 1849 | 225.222.054,76 | |
44 | 14.941,20 | 657.412,80 | 1936 | 223.239.457,44 | |
45 | 15.184,30 | 683.293,50 | 2025 | 230.562.966,49 | |
46 | 15.162,60 | 697.479,60 | 2116 | 229.904.438,76 | |
47 | 15.269,80 | 717.680,60 | 2209 | 233.166.792,04 | |
48 | 15.304,30 | 734.606,40 | 2304 | 234.221.598,49 | |
49 | 15.569,50 | 762.905,50 | 2401 | 242.409.330,25 | |
50 | 15.900,30 | 795.015,00 | 2500 | 252.819.540,09 | |
51 | 16.321,60 | 832.401,60 | 2601 | 266.394.626,56 | |
52 | 16.740,40 | 870.500,80 | 2704 | 280.240.992,16 | |
53 | 16.915,00 | 896.495,00 | 2809 | 286.117.225,00 | |
54 | 17.194,90 | 928.524,60 | 2916 | 295.664.586,01 | |
55 | 17.481,60 | 961.488,00 | 3025 | 305.606.338,56 | |
56 | 17.732,80 | 993.036,80 | 3136 | 314.452.195,84 | |
57 | 18.085,70 | 1.030.884,90 | 3249 | 327.092.544,49 | |
58 | 18.314,00 | 1.062.212,00 | 3364 | 335.402.596,00 | |
59 | 18.568,90 | 1.095.565,10 | 3481 | 344.804.047,21 | |
60 | 18.906,90 | 1.134.414,00 | 3600 | 357.470.867,61 | |
61 | 19.164,00 | 1.169.004,00 | 3721 | 367.258.896,00 | |
62 | 19.360,90 | 1.200.375,80 | 3844 | 374.844.448,81 | |
63 | 19.544,70 | 1.231.316,10 | 3969 | 381.995.298,09 | |
64 | 19.866,50 | 1.271.456,00 | 4096 | 394.677.822,25 | |
65 | 20.111,40 | 1.307.241,00 | 4225 | 404.468.409,96 | |
66 | 20.381,00 | 1.345.146,00 | 4356 | 415.385.161,00 | |
67 | 20.628,40 | 1.382.102,80 | 4489 | 425.530.886,56 | |
68 | 20.776,30 | 1.412.788,40 | 4624 | 431.654.641,69 | |
69 | 21.052,90 | 1.452.650,10 | 4761 | 443.224.598,41 | |
70 | 21.313,80 | 1.491.966,00 | 4900 | 454.278.070,44 | |
71 | 21.613,70 | 1.534.572,70 | 5041 | 467.152.027,69 | |
72 | 21.836,83 | 1.572.251,47 | 5184 | 476.846.970,78 | |
x | y | x*y | x⼯em>
| y⼯em>
| |
2.628,00 | 1.023.031,83 | 43.262.973,47 | 127.020,00 | 15.811.938.617,97 | |
Valores totales | |||||
Nuevamente se puede observar que la relación de observancia entre la variable dependiente y la independiente es de 94%.
Se obtiene m y B:
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