Rango: SUPERIOR 475 INFERIOR 445

REPLICAS X S R# X1 X2 X3 X4 X5 X61 473 448 450 461 468 448 458.00 10.94 252 470 450 452 457 472 464 460.83 9.26 223 464 446 452 449 448 463 453.67 7.87 184 474 448 472 470 452 464 463.33 10.93 265 474 460 456 445 446 449 455.00 10.99 296 448 450 446 468 452 458 453.67 8.14 227 459 475 472 469 473 465 468.83 5.95 168 448 445 464 458 465 473 458.83 10.72 289 451 457 445 445 456 465 453.17 7.76 20

10 451 460 458 473 472 469 463.83 8.84 2211 447 471 457 458 448 468 458.17 9.91 2412 453 449 451 463 460 455 455.17 5.38 1413 463 470 473 464 474 453 466.17 7.88 2114 449 456 462 473 460 462 460.33 7.92 2415 463 454 463 469 465 466 463.33 5.09 1516 446 447 467 451 474 465 458.33 11.83 2817 451 461 468 451 475 465 461.83 9.56 2418 467 465 464 457 450 466 461.50 6.66 1719 463 450 445 470 459 467 459.00 9.78 2520 469 461 474 466 469 446 464.17 9.87 2821 469 446 445 475 458 450 457.17 12.51 3022 464 466 454 448 449 458 456.50 7.53 1823 459 471 468 455 475 446 462.33 10.95 2924 467 471 455 452 469 445 459.83 10.63 2625 450 469 458 472 462 445 459.33 10.54 2726 461 446 474 446 461 445 455.50 11.78 2927 456 450 473 449 466 466 460.00 9.78 2428 449 474 457 459 455 463 459.50 8.48 2529 453 450 461 459 445 473 456.83 9.85 2830 456 453 449 452 448 454 452.00 3.03 831 463 445 465 456 450 447 454.33 8.38 2032 457 470 450 461 445 457 456.67 8.69 2533 449 454 464 452 475 470 460.67 10.58 2634 447 467 470 459 462 466 461.83 8.23 2335 463 445 470 467 460 470 462.50 9.44 2536 446 455 467 448 467 461 457.33 9.18 2137 473 461 464 470 463 451 463.67 7.69 2238 474 448 455 448 468 467 460.00 11.15 2639 458 451 459 458 462 469 459.50 5.89 1840 458 467 462 475 471 474 467.83 6.79 17

459.51 8.91 22.88459.51 9.21

PROBLEMA # 01: Pruebas de pentracion trabajadas por la norma ASTM, fueron realizadas en muestras de grasa grado NLgI000, cuyo rango de variacion especificado es 445 y 475 decimas de milimetro. La informacion fue agrupada en un tabla de 40 muestras y con 6 replicas del ensayo.CALCULAR:a. Las medias, desviacion estandar y los rangos de cada fila. b. La gran media, la desvacion estandar media y el rango medio.c. Estimar la media y la desviacion estandar del universo.

XMIN = 445 R = 30XMAX = 475 k= 51 17 grupos de 3

h= 0.58823529 0.6

K L XE ne nk Xmk Nk*Wk dk2 nk*dk2

1A 445 9

17 445.56 7574.6 1.0561E+10 1.7954E+11

102986.801

B 446 0C 446 8

2A 447 0

17 447.79 7612.4 1.0553E+10 1.7941E+11B 447 6C 448 11

3A 449 0

9 449.20 4042.8 1.13E+10 1.017E+11B 449 9C 450 0

4A 450 6

14 450.74 6310.4 1.0823E+10 1.5152E+11B 451 8C 452 0

5A 452 5

15 453.00 6795 1.0722E+10 1.6083E+11B 453 0C 453 10

6A 454 9

12 454.30 5451.6 1.1002E+10 1.3202E+11B 455 0C 455 3

7A 456 0

25 456.69 11417.2 9786195195 2.4465E+11B 456 13C 457 12

8A 458 0

10 458.20 4582 1.1185E+10 1.1185E+11B 458 10C 459 0

9A 459 9

11 459.51 5054.6 1.1086E+10 1.2194E+11B 460 2C 461 0

10A 461 11

20 461.74 9234.8 1.0223E+10 2.0445E+11B 462 0C 462 9

11A 463 3

13 463.92 6031 1.0881E+10 1.4145E+11B 464 0C 464 10

12A 465 0

10 465.52 4655.2 1.117E+10 1.117E+11B 465 8C 466 2

13A 467 0

2 467.20 934.4 1.197E+10 2.394E+10B 467 2C 468 0

14A 468 8

22 468.78 10313.2 1.0006E+10 2.2013E+11B 469 14C 470 0

15A 470 4

12 471.00 5652 1.096E+10 1.3152E+11B 471 0C 471 8

16A 472 8

16 472.60 7561.6 1.0564E+10 1.6902E+11B 473 0C 473 8

17A 474 0

15 474.64 7119.6 1.0655E+10 1.5982E+11B 474 9C 475 6

datos cada uno

σ'w

Con los datos anteriores preparar una tabla de tal manera que se agrupen lo resultados de las penetraciones de la grasa en 17 grupos con tres datos en forma consecutiva, cada resultado debera tener su peso o frecuencia de aparicion de acuerdo con este ordenamiento, emplear EL CRITERIO DE PONDERACION para determinar:a. Promedios de penetracion por grupo.b. La gran media ponderada. c. La desviacion estandar ponderada del universo.

240 110342.4 2.5455E+12

LA GRAN MEDIA PONDERADA = 459.76La desviacion estandar del universo = 102986.8

R= 30K= 17h= 1.764706

1.8EXACTITUD PRECISION

Intervalo Intervalo fk Xmk fk * Xmk dk^2 fk * dk^2Inferior Superior445 447 10 446 4459 1.12E+10 1.12E+11

103276.9

447 449 14 448 6267.8 1.08E+10 1.52E+11449 450 16 450 7192 1.07E+10 1.7E+11450 452 13 451 5866.9 1.09E+10 1.42E+11452 454 18 453 8155.8 1.05E+10 1.88E+11454 456 9 455 4094.1 1.13E+10 1.02E+11456 458 17 457 7763.9 1.05E+10 1.79E+11458 459 20 459 9170 1.03E+10 2.05E+11459 461 14 460 6444.2 1.08E+10 1.51E+11461 463 18 462 8317.8 1.04E+10 1.88E+11463 465 6 464 2783.4 1.16E+10 6.95E+10465 467 17 466 7916.9 1.05E+10 1.79E+11467 468 19 468 8882.5 1.03E+10 1.96E+11468 470 18 469 8447.4 1.04E+10 1.87E+11470 472 15 471 7066.5 1.07E+10 1.6E+11472 474 4 473 1891.6 1.18E+10 4.71E+10474 476 12 475 5696.4 1.1E+10 1.32E+11

240 110416.2 2.56E+12

Σ(ni Xi) /Σ(ni) =

σ'

Con la tabla del ejercicio anterior prepare una tabla de frecuencia para determinar:a) El tipo de distribucion de frecuencia.b) Los parametros del universo.

PROBLEMA # 01: Pruebas de pentracion trabajadas por la norma ASTM, fueron realizadas en muestras de grasa grado NLgI000, cuyo rango de variacion especificado es 445 y 475 decimas de milimetro. La informacion fue agrupada en un tabla de 40 muestras y con 6 replicas del ensayo.CALCULAR:a. Las medias, desviacion estandar y los rangos de cada fila. b. La gran media, la desvacion estandar media y el rango medio.c. Estimar la media y la desviacion estandar del universo.

N= 400 PESO NOMINAL = 15 X 113 = 1695K= 20 TOLERANCIA PNI = 1610.25 PNS= 1779.75

N X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X201 1724.4 1610.5 1662.6 1770.7 1685.8 1720.8 1611.6 1746.3 1749.5 1779.6 1638.3 1668.8 1643.8 1778.2 1766.4 1744.4 1713.2 1675.1 1636.5 1752.02 1655.5 1648.0 1740.3 1632.7 1685.1 1733.4 1666.0 1653.2 1617.6 1659.9 1728.2 1753.2 1644.9 1726.9 1674.5 1625.8 1707.8 1768.5 1618.2 1711.63 1653.8 1719.7 1738.3 1733.7 1726.1 1703.7 1628.4 1747.3 1675.1 1678.7 1665.1 1613.7 1613.1 1612.1 1737.2 1665.5 1766.1 1629.4 1658.4 1764.44 1640.8 1678.1 1641.9 1657.3 1646.8 1672.4 1772.5 1739.1 1727.2 1769.8 1722.5 1772.0 1644.1 1685.1 1651.1 1747.1 1723.9 1647.7 1709.5 1758.65 1719.3 1646.9 1734.8 1666.5 1753.8 1739.4 1708.3 1631.8 1617.2 1767.3 1697.2 1685.7 1611.3 1617.3 1747.3 1719.4 1619.5 1739.6 1680.9 1754.86 1745.7 1734.4 1713.4 1689.5 1615.6 1726.4 1694.6 1644.4 1706.8 1764.3 1635.5 1637.5 1628.6 1705.3 1766.9 1672.9 1614.0 1718.1 1675.4 1721.47 1624.5 1613.3 1701.8 1767.0 1634.3 1656.2 1764.7 1749.8 1774.3 1641.7 1755.3 1677.5 1765.2 1663.2 1776.6 1719.2 1685.5 1664.5 1763.3 1613.68 1614.6 1724.1 1739.3 1734.8 1778.9 1725.0 1623.1 1707.4 1774.7 1621.9 1697.8 1623.9 1651.4 1725.6 1723.8 1716.0 1735.1 1761.2 1662.2 1735.89 1678.2 1716.1 1751.2 1724.9 1757.6 1653.9 1721.3 1644.9 1703.1 1639.6 1770.8 1666.8 1761.3 1648.6 1648.4 1728.8 1668.4 1661.0 1624.2 1688.3

10 1753.7 1741.2 1705.5 1759.0 1710.2 1773.5 1733.6 1770.6 1673.3 1655.4 1733.0 1693.4 1755.8 1771.2 1673.8 1662.8 1633.3 1624.4 1682.5 1764.711 1730.6 1729.9 1622.2 1773.1 1691.8 1691.7 1613.5 1653.3 1764.1 1762.7 1636.1 1713.5 1734.0 1634.8 1740.5 1637.8 1742.4 1779.1 1671.0 1658.412 1748.1 1611.7 1723.4 1726.8 1697.4 1708.7 1770.8 1725.0 1636.9 1772.5 1754.7 1697.4 1660.2 1715.5 1635.6 1689.9 1700.1 1729.8 1683.8 1722.613 1726.0 1629.9 1660.8 1633.6 1702.1 1766.0 1764.2 1639.2 1754.3 1768.4 1643.7 1765.7 1677.6 1633.8 1687.4 1652.1 1733.4 1667.0 1766.5 1770.714 1751.5 1681.0 1610.6 1719.3 1656.0 1748.3 1704.2 1778.6 1738.3 1771.3 1687.3 1661.6 1678.4 1635.5 1682.7 1699.0 1723.0 1723.8 1763.4 1632.815 1645.5 1673.9 1622.4 1711.1 1662.4 1646.0 1722.6 1657.3 1755.5 1671.6 1723.1 1628.7 1654.2 1718.1 1708.4 1629.0 1643.9 1712.5 1720.0 1708.016 1616.4 1659.3 1758.6 1761.9 1717.2 1735.1 1773.4 1779.6 1735.9 1617.2 1641.6 1735.4 1682.9 1657.4 1622.3 1725.3 1702.7 1629.0 1778.6 1716.617 1645.5 1642.9 1619.5 1711.4 1627.6 1723.6 1679.6 1702.8 1701.0 1679.9 1678.6 1707.3 1643.7 1700.9 1750.3 1725.6 1623.5 1672.2 1632.5 1631.318 1741.6 1753.9 1770.2 1766.0 1643.5 1668.4 1770.0 1669.2 1643.9 1718.1 1634.2 1653.8 1679.2 1720.9 1629.7 1649.2 1644.3 1747.3 1657.4 1648.719 1657.2 1731.3 1649.2 1627.7 1636.0 1628.7 1665.3 1643.3 1636.7 1721.4 1775.2 1641.4 1722.4 1758.2 1640.8 1732.2 1729.3 1763.3 1676.5 1734.020 1735.1 1740.8 1761.6 1693.1 1659.9 1682.1 1700.3 1675.0 1629.8 1624.9 1740.3 1629.7 1647.5 1612.0 1719.0 1684.8 1745.8 1762.4 1707.3 1656.8

media especificada = Xe = 1695 r= 169.5

desviacion estandar especificada 28.25 k= 20

media observada= Xo = 1696.1 h= 8.475σe =

Problema #02:La distribucion de frecuencias de los paquetes de cobre refinado fabricados en una planta, tipo asarco, cada paquete consta de 15 barras de 113 kg de peso nominal, la norma ASTM B5, especifica que el peso promedio de los paquetes sea 1965 kg con una tolerancia de +/- 5% para que las barras no caucen atascamiento en los rodillos iniciales durante laminado en caliente.A) Encontrar el numero de clases o celdas necesarias para agrupar los 400 datos extraidos del universo y determinar los extremos de cada intervalo entre el limite inferior y el limite superior especificados por la norma.B) Determinar los parametros (la media y la desviacion estandar poblacional de la especificacion y la media y desviacion estandar de la distribucion de observada), ajustar las distribuciones con la distribucion probabilistica normal y determinar la bondad del ajuste a un nivel de significacion del 5 %.C) Determinar la desviacion estandar de la media observada con respecto a la media de la especificada como fraccion de la desviacion estandar observada.

desviacion estandar observada = σo = 16.089limites Frecuencia especifica Frecuencia teorica

N inf. sup. fk xmk frk frk*xmk σ fre fke frt fkt xi^2 ρ1 1610.3 1618.7 21 1614.5 0.0525 84.761 2596284 136305

1608.9

0.00185356912 4.59740375264 1.70237219E-13 8.16149501E-10 5E+11

0.0658

2 1618.7 1627.2 20 1623.0 0.05 81.148 2607938 130397 0.00277906082 6.8928989401 2.69279879E-11 1.29097879E-07 3E+093 1627.2 1635.7 18 1631.4 0.045 73.415 2632976 118484 0.00398330961 9.87979480243 2.445404E-09 1.17237304E-05 3E+074 1635.7 1644.1 19 1639.9 0.0475 77.896 2618453 124377 0.00545816708 13.5378808184 1.27495443E-07 0.00061123732 5905675 1644.1 1652.6 16 1648.4 0.04 65.935 2657304 106292 0.00715000485 17.7341426103 3.8162431E-06 0.01829579291 139606 1652.6 1661.1 20 1656.9 0.05 82.843 2602467 130123 0.00895411349 22.2088696431 6.55805009E-05 0.31440535421 1232.67 1661.1 1669.6 17 1665.3 0.0425 70.777 2641543 112266 0.01072002014 26.588844352 0.00064700964 3.10188689603 62.2718 1669.6 1678 22 1673.8 0.055 92.06 2572815 141505 0.01226945738 30.4319104143 0.00366474791 17.5694962731 1.11729 1678 1686.5 23 1682.3 0.0575 96.732 2557850 147076 0.01342492474 33.2978137794 0.01191721531 57.1333894792 20.392

10 1686.5 1695 20 1690.8 0.05 84.538 2597001 129850 0.0140428453 34.8304408873 0.02224860536 106.664032005 70.41411 1695 1703.5 15 1699.2 0.0375 63.721 2664527 99920 0.0140428453 34.8304408873 0.02384669113 114.325558195 86.29412 1703.5 1711.9 21 1707.7 0.0525 89.655 2580535 135478 0.01342492474 33.2978137794 0.01467407681 70.3503061782 34.61913 1711.9 1720.4 22 1716.2 0.055 94.39 2565344 141094 0.01226945738 30.4319104143 0.00518406904 24.8534097894 0.327614 1720.4 1728.9 21 1724.7 0.0525 90.545 2577677 135328 0.01072002014 26.5888443521 0.00105144871 5.04084445555 50.52615 1728.9 1737.4 21 1733.1 0.0525 90.99 2576249 135253 0.00895411349 22.2088696431 0.0001224342 0.58697275044 709.916 1737.4 1745.8 22 1741.6 0.055 95.789 2560866 140848 0.00715000485 17.7341426103 8.18492505E-06 0.03924008241 1229017 1745.8 1754.3 30 1750.1 0.075 131.26 2448608 183646 0.00545816708 13.5378808184 3.14140554E-07 0.00150604937 59753018 1754.3 1762.8 19 1758.6 0.0475 83.532 2600245 123512 0.00398330961 9.87979480244 6.92198463E-09 3.31853066E-05 1E+07

19 1762.8 1771.3 19 1767.0 0.0475 83.934 2598947 123450 0.00277906082 6.8928989401 8.75658128E-11 4.19807107E-07 9E+08

20 1771.3 1779.7 14 1775.5 0.035 62.143 2669683 93439 0.00185356912 4.59740375264 6.35968877E-13 3.04895537E-09 6E+10

400 1 1696 2588641 desv. 0.1612709451 0.0834343309media estand.observ. observ.

FUNCIONES:

el X es X

fke = (N/sumatoria(fre))*fre

d2k frk*d2

k

f(Xmk) = (1/(σ*raiz(2*pi)))*e^-(Xmk-X)^2/(2*σ)^2

f(fre) = (1/(σe*raiz(2*pi)))*e^-(Xmk-Xe)^2/(2*σe)^2

f(frt) = (1/(σo*raiz(2*pi)))*e^-(Xmk-Xo)^2/(2*σo)^2

1600.0 1650.0 1700.0 1750.0 1800.00

0.005

0.01

0.015

0.02

0.025

0.03

frt fre

1600.0 1650.0 1700.0 1750.0 1800.00

20

40

60

80

100

120

140

fkt fke

fkt = (N/sumatoria(frt))*frt

1600.0 1650.0 1700.0 1750.0 1800.00

0.005

0.01

0.015

0.02

0.025

0.03

frt fre

1600.0 1650.0 1700.0 1750.0 1800.00

20

40

60

80

100

120

140

fkt fke

MuestraVARIABLES GEOMETRICA EXPONENCIAL HIPERBOLICA

X Y ln(y) ln(x) ln(x).ln(y) [ln(x)]^2 x ln(y) x^2 1/y x/y1 14580 2.73 1.00 9.59 9.63 91.92 1.94 14642.72 2.13E+08 1.55 0.37 5340.66 2.012 11940 1.76 0.57 9.39 5.31 88.13 2.51 6749.85 1.43E+08 2.45 0.57 6784.09 2.483 11750 2.68 0.99 9.37 9.24 87.83 2.56 11583.35 1.38E+08 2.53 0.37 4384.33 2.524 11510 3.74 1.32 9.35 12.33 87.44 2.63 15182.68 1.32E+08 2.63 0.27 3077.54 2.585 10370 4.67 1.54 9.25 14.25 85.50 3.01 15981.82 1.08E+08 3.20 0.21 2220.56 2.896 9430 1.26 0.23 9.15 2.12 83.75 3.41 2179.38 8.89E+07 3.77 0.79 7484.13 3.207 9110 4.16 1.43 9.12 13.00 83.12 3.56 12986.44 8.30E+07 3.98 0.24 2189.90 3.338 7460 5.46 1.70 8.92 15.14 79.52 4.61 12662.97 5.57E+07 5.28 0.18 1366.30 4.169 7210 5.31 1.67 8.88 14.83 78.91 4.82 12037.76 5.20E+07 5.51 0.19 1357.82 4.32

10 6150 6.96 1.94 8.72 16.93 76.11 5.92 11932.10 3.78E+07 6.62 0.14 883.62 5.1811 5640 5.77 1.75 8.64 15.14 74.61 6.62 9885.07 3.18E+07 7.22 0.17 977.47 5.7212 5610 4.99 1.61 8.63 13.88 74.52 6.67 9017.72 3.15E+07 7.26 0.20 1124.25 5.7613 5480 4.73 1.55 8.61 13.38 74.11 6.87 8515.51 3.00E+07 7.42 0.21 1158.56 5.9214 5420 7.68 2.04 8.60 17.53 73.92 6.97 11049.32 2.94E+07 7.50 0.13 705.73 6.0015 5380 13.1 2.57 8.59 22.10 73.80 7.04 13840.65 2.89E+07 7.55 0.08 410.69 6.0516 5300 8.59 2.15 8.58 18.44 73.54 7.18 11398.17 2.81E+07 7.66 0.12 617.00 6.1617 5220 3.77 1.33 8.56 11.36 73.28 7.32 6927.33 2.72E+07 7.76 0.27 1384.62 6.2718 4990 3.57 1.27 8.52 10.84 72.51 7.76 6350.10 2.49E+07 8.08 0.28 1397.76 6.6219 4710 9.25 2.22 8.46 18.81 71.53 8.36 10477.98 2.22E+07 8.47 0.11 509.19 7.0920 4140 4.95 1.60 8.33 13.32 69.36 9.88 6621.46 1.71E+07 9.35 0.20 836.36 8.3121 4060 13.9 2.63 8.31 21.87 69.04 10.13 10685.47 1.65E+07 9.48 0.07 292.09 8.5222 4050 19.2 2.95 8.31 24.54 69.00 10.16 11967.39 1.64E+07 9.49 0.05 210.94 8.5423 4030 12.5 2.53 8.30 20.97 68.92 10.23 10178.69 1.62E+07 9.52 0.08 322.40 8.6024 3540 19.2 2.95 8.17 24.15 66.78 12.09 10460.38 1.25E+07 10.36 0.05 184.38 10.1525 3520 10.8 2.38 8.17 19.43 66.69 12.18 8376.00 1.24E+07 10.40 0.09 325.93 10.2226 2620 18.4 2.91 7.87 22.92 61.95 17.84 7630.36 6.86E+06 12.14 0.05 142.39 15.34Σ 173220 199.13 46.84 226.37 401.44 1975.77 182.28 2.69E+05 1.40E+09 177.18 5.50 45688.68 157.94

Promedio 6662.307692 7.658846154 1.80 8.71 15.44 75.99 7.01 10358.49 5.40E+07 6.81 0.21 1757.26 6.07467959.2840 19.0367001787565 -0.029758102473754

yg yexp yhip

ag= ae= ah=

En un estudio experimental de resistencia a la abrasion, encontraron una cierta relacion inversa, no definida matematicamente, entre la relacion a la compresion (X), dada en lb/pulg2, y la pérdida por abrasion (Y). De una serie de ladrillos de refractarios de la clase de silico-aluminosos, alta alumina, magnesita-cromo, cromo magnesita, fosterita, carburo de silicio, circonia y silica; cuyos resultados han sido ordenados en la siguiente tabla. La importancia de este experimento estriba en la posibilidad de estimar una de las variables conociendo la otra. Muchas de las industrias dedicadas a la fabricacion de productos ceramicos y refractarios no cuentan con los equipos adecuados para determinar ambas variables en forma independiente y mucho menos en forma simultanea, por lo que, mediante este experimento y la utilizacion de las tecnicas de regresion y correlacion estadistica es posible determinar formulas matematicas adecuadas que permitan estimar el valor esperado de dichas variables de acuerdo a la infraestructura con que se cuente y, de esta forma, solucionar cualquier incoveniente al respecto. Si este es el caso: Encontrar la formula mas apropiada para estimar la perdida por abrasion de un material refractario cualquiera conociendo su resistencia a la compresion segun se muestra en la tabla. Determina el error tipico de la estima y el coeficiente de correccion lineal para todos los ajustes posibles y aquellos correspondientes a los ajustes no lineales. Mostrar los resultados graficamente.

-1.29268084500161 0.999828168486864 0.00004

Muestra

1 24.29352441 32.71 37.27 31.96 0.624122985 1.382911229 0.525425832

2 34.79638595 26.49 27.17 26.81 0.564834714 0.470831319 0.520157513

3 24.78890902 25.96 26.33 26.36 0.013414859 0.023299232 0.024225284

4 15.35735518 25.25 25.25 25.78 1.224336021 1.22373452 1.343200987

5 8.933201331 21.58 19.85 22.75 2.743610743 2.149881506 3.171359281

6 40.9452321 18.07 15.16 19.84 4.61165751 6.277108534 3.781590625

7 12.24192441 16.78 13.55 18.75 0.35642189 0.033022812 0.69164662

8 4.834924408 9.28 5.65 12.27 0.717241431 0.03151375 1.701604704

9 5.517078254 8.05 4.60 11.16 0.239208746 0.04176626 0.983767611

10 0.488385947 3.02 1.09 6.16 1.079330611 0.118230703 3.178812694

11 3.567739793 1.07 0.19 3.74 0.726222306 2.108802649 0.002027538

12 7.122739793 0.98 0.16 3.60 2.815683862 5.150634522 0.594186564 r=13 8.578139793 0.62 0.06 3.02 4.593243477 7.254960551 1.419860598

14 0.000447485 0.47 0.03 2.76 0.501688339 0.032241274 2.82632043 TIPO DE REGRESION COEFICIENTE DE CORRELACION (r)15 29.60615518 0.38 0.01 2.58 36.73840914 30.77835148 49.68182651 GEOMETRICA 0.7116 0.867047485 0.23 0.00 2.25 1.99820179 0.871015301 5.907077067 EXPONENCIAL 0.5617 15.12312441 0.12 0.01 1.92 12.59478777 15.94171045 6.257847888 HIPERGEOMETRICA 0.6418 16.71866287 0.01 0.17 1.08 17.53852921 20.30105779 9.287651917

19 2.531770562 0.49 0.66 0.32 0.793538983 0.60256951 4.648273629

20 7.337847485 4.92 2.85 0.43 24.26546015 19.32289902 11.30523049

21 38.95200133 6.10 3.30 0.74 14.22589173 19.57927788 28.96990314

22 133.1982321 6.26 3.36 0.78 81.71045391 94.25596417 113.5501489 TIPO DE REGRESION23 23.43677056 6.59 3.48 0.88 5.171771459 8.855823437 15.23138838 GEOMETRICA 3.2124 133.1982321 19.65 7.30 6.19 50.53102876 78.13082897 81.9641903 EXPONENCIAL 3.6925 9.866847485 20.44 7.49 6.57 1.905407387 0.162807256 0.334338618 HIPERGEOMETRICA 3.71

bg= be= bh=

(y-yprom)2 (Yg - yprom)2 (yexp-yprom)2 (yhip - yprom)2 (Y-Yg)^2 (Y-Yexp)^2 (Y-Yhip)^2

σ =

ERROR TIPICO DE LA ESTIMA (σ)

𝑎_𝑔=exp((∑▒〖 ln(𝑥).〗 ∑▒〖〖 [ln 〗 (𝑥) ln (𝑦)]−∑▒ln(𝑦) ∑▒〖 [ln 〖 ( )𝑥 ]〗〗^2 〗 )/([∑▒〖 ln 〖 ( )]𝑥 〗〗 ^2 −𝑛∑▒〖〖 [ln 〗〖 ( )]𝑥 〗〗 ^2 ))𝑏_𝑔=(∑▒〖 ln(𝑦) − 〗 𝑛 ln(𝑎))/(∑▒〖 ln(𝑥) 〗 )

〖𝑦=𝑎𝑥 〗 ^𝑏𝑎_𝑒=exp((∑▒ 〖 〗𝑥∑▒〖𝑥 .ln(𝑦) −∑▒〗 〖 ln(𝑦) ∑〗▒𝑥^2)/(〖 (∑▒〖𝑦′ ) 〗〗 ^2−𝑛∑▒〖𝑥 ^2 〗 ))𝑏_𝑒=exp((∑▒ln(𝑦)−𝑛ln(𝑎))/(∑▒𝑥))

〖𝑦=𝑎𝑏 〗 ^𝑥 𝑎_(ℎ)=(∑▒𝑥∑▒ 〖𝑥 /𝑦−∑▒ 〖 1/𝑦∑▒𝑥^2〗〗 )/( 〖 (∑▒ 〖𝑥 )〗〗^2−𝑛∑▒𝑥^2)𝑏_ℎ=(∑▒1/𝑦−𝑎𝑛)/(∑▒𝑥)

〖𝑦=1/( +𝑎 𝑏𝑥)〗^

2000 4000 6000 8000 10000 12000 14000 160000

5

10

15

20

25

DATOS GEOMETRICAEXPONENCIAL HIPERGEOMETRICA

√((∑▒〖 (𝑦〗 _𝑒𝑠𝑝𝑒𝑟𝑎𝑑𝑜−𝑦))/(∑▒〖 (𝑦 −〗 𝑦 )))

±√((∑▒〖 (𝑦−𝑦_𝑒𝑠𝑝𝑒𝑟𝑎𝑑𝑜)〗 ^2)/𝑁)

26 115.3723859 103.69 20.04 58.93 0.311734053 39.24450534 9.391310133

Σ 717.68 359.21 225.02 297.65 268.60 354.35 357.29

Muestra

1 5.15 -1.27 5.25 -2.14 5.71 -1.702 5.73 -0.70 6.14 -1.25 6.19 -1.233 5.78 -0.65 6.22 -1.16 6.23 -1.184 5.85 -0.58 6.33 -1.06 6.29 -1.135 6.23 -0.20 6.90 -0.49 6.60 -0.826 6.62 0.19 7.46 0.07 6.91 -0.507 6.78 0.35 7.67 0.29 7.04 -0.388 7.83 1.40 8.97 1.59 7.86 0.459 8.04 1.61 9.21 1.82 8.03 0.61

10 9.14 2.71 10.31 2.92 8.88 1.4711 9.84 3.41 10.91 3.53 9.43 2.0212 9.88 3.45 10.95 3.57 9.47 2.0513 10.09 3.66 11.12 3.73 9.63 2.2114 10.19 3.76 11.19 3.81 9.71 2.2915 10.25 3.82 11.24 3.86 9.76 2.3416 10.39 3.96 11.35 3.97 9.87 2.4517 10.53 4.10 11.45 4.07 9.98 2.5618 10.97 4.54 11.77 4.38 10.32 2.9119 11.57 5.15 12.17 4.78 10.80 3.3920 13.09 6.66 13.04 5.65 12.02 4.6121 13.34 6.91 13.17 5.78 12.22 4.8122 13.37 6.95 13.18 5.80 12.25 4.8423 13.44 7.01 13.22 5.83 12.30 4.8924 15.31 8.88 14.05 6.67 13.85 6.4425 15.39 8.97 14.09 6.70 13.93 6.5126 21.06 14.63 15.83 8.44 19.04 11.63

LS Yg LI Yg LS Yexp LI Y exp LS Yhip LI Yhip

GEOMETRICA

DATOS GEOMETRICALIM. SUPERIOR LIM. INFERIOR

EXPONENCIAL

DATOS EXPONENCIALLIM. SUPERIOR LIM. INFERIOR

HIPERGEOMETRICA

DATOS HIPERGEOMETRICALIM. SUPERIOR LIM. INFERIOR

Muestra

yg x*yg y lin geo y exp x * y exp y lin exp y hip x * y hip y lin hip1 1.94 28284.99 -1.11 1.55 22657.72 -0.19 2.01 29234.90 -0.462 2.51 29987.97 1.60 2.45 29207.29 2.15 2.48 29625.76 1.723 2.56 30129.09 1.79 2.53 29696.47 2.31 2.52 29661.17 1.874 2.63 30311.62 2.04 2.63 30314.75 2.53 2.58 29707.71 2.075 3.01 31251.19 3.21 3.20 33222.91 3.54 2.89 29960.68 3.016 3.41 32132.51 4.17 3.77 35507.87 4.37 3.20 30219.67 3.797 3.56 32458.83 4.50 3.98 36242.11 4.65 3.33 30321.24 4.058 4.61 34413.72 6.19 5.28 39407.29 6.11 4.16 31000.36 5.429 4.82 34758.76 6.45 5.51 39758.59 6.33 4.32 31133.86 5.62

10 5.92 36414.71 7.54 6.62 40689.34 7.27 5.18 31839.03 6.5011 6.62 37349.13 8.06 7.22 40733.05 7.72 5.72 32288.84 6.9212 6.67 37407.48 8.09 7.26 40725.80 7.75 5.76 32318.28 6.9413 6.87 37665.06 8.22 7.42 40680.80 7.86 5.92 32450.25 7.0514 6.97 37786.62 8.29 7.50 40652.39 7.91 6.00 32513.68 7.1015 7.04 37868.63 8.33 7.55 40630.71 7.95 6.05 32556.89 7.1316 7.18 38035.04 8.41 7.66 40580.61 8.02 6.16 32645.63 7.2017 7.32 38204.73 8.49 7.76 40521.33 8.09 6.27 32737.59 7.2718 7.76 38711.93 8.73 8.08 40297.59 8.29 6.62 33021.65 7.4619 8.36 39371.79 9.01 8.47 39911.35 8.54 7.09 33412.81 7.6920 9.88 40886.63 9.60 9.35 38691.54 9.05 8.31 34413.03 8.1621 10.13 41120.81 9.68 9.48 38469.12 9.12 8.52 34581.58 8.2222 10.16 41150.50 9.69 9.49 38440.37 9.12 8.54 34603.24 8.2323 10.23 41210.16 9.71 9.52 38382.23 9.14 8.60 34646.95 8.2524 12.09 42803.85 10.21 10.36 36677.36 9.58 10.15 35918.94 8.6525 12.18 42874.88 10.23 10.40 36595.70 9.59 10.22 35980.66 8.6726 17.84 46745.17 11.16 12.14 31794.90 10.39 15.34 40178.95 9.41Σ 182.28 959335.79 177.18 960489.18 157.94 846973.35

a= 13.84 a= 12.71 a= 11.57b= -0.001026 b= -0.000884 b= -0.000826

Linealizacion de la regresion geometrica

Linealizacion de la regresion Exponencial

Linealizacion de la regresion Hiperbolica

HIPERGEOMETRICA

DATOS HIPERGEOMETRICALIM. SUPERIOR LIM. INFERIOR

DATOS Geo linealExpon. lineal Hipergeo. lineal

Muestra

1 1.06 1.89 2.54 1.80 0.12 0.32 0.10

2 2.16 1.24 1.30 1.27 0.13 0.11 0.12

3 1.10 1.20 1.23 1.23 0.00 0.00 0.00

4 0.51 1.14 1.14 1.18 0.12 0.12 0.14

5 0.24 0.87 0.76 0.95 0.19 0.14 0.23

6 3.26 0.66 0.50 0.76 0.99 1.20 0.87

7 0.37 0.59 0.43 0.69 0.02 0.00 0.05

8 0.11 0.26 0.14 0.37 0.03 0.00 0.07

9 0.13 0.21 0.11 0.33 0.01 0.00 0.04

10 0.01 0.07 0.02 0.15 0.03 0.00 0.09

11 0.08 0.02 0.00 0.08 0.02 0.05 0.00

12 0.18 0.02 0.00 0.08 0.08 0.14 0.02

13 0.23 0.01 0.00 0.07 0.14 0.20 0.05

14 0.00 0.01 0.00 0.06 0.01 0.00 0.06

15 0.29 0.01 0.00 0.06 0.39 0.30 0.60

16 0.01 0.00 0.00 0.05 0.03 0.01 0.11

17 0.50 0.00 0.00 0.04 0.44 0.52 0.26

18 0.58 0.00 0.00 0.02 0.60 0.67 0.38

19 0.04 0.01 0.01 0.01 0.01 0.01 0.07

20 0.19 0.06 0.04 0.01 0.48 0.40 0.27

21 0.36 0.08 0.05 0.01 0.10 0.15 0.24

22 0.84 0.08 0.05 0.01 0.40 0.50 0.66

23 0.24 0.08 0.05 0.01 0.04 0.07 0.14

24 0.84 0.21 0.09 0.08 0.21 0.38 0.41

25 0.12 0.22 0.09 0.08 0.01 0.00 0.00

26 0.77 0.72 0.21 0.48 0.00 0.17 0.03

(ln y-ln y)2 (lnyg-lny)2 (lnye-lny)2 (lnyh-lny)2 (lny-lnyg)2 (lny-lnye)2 (lny-lnyh)2

𝑎=(∑▒𝑥∑▒ − ∑▒ ∑▒〖𝑥𝑦 𝑦 𝑥 ^2〗 )/(〖 (∑▒𝑥)〗^2−𝑛∑▒𝑥^2)𝑏=(∑▒ −〖 〗𝑦 𝑛𝑎 )/(∑▒𝑥)

Σ 14.25 9.64 8.77 9.89 4.61 5.48 5.01

geometrica exponencial hipergeometrica

r 0.82 0.78 0.83σ 0.42 0.46 0.44

Si r € [0.9,1], entonces no correjimos; sino tomamos los primeros 18 valores y los demas los arreglamos

manualmente hasta cumplir la condicion.

MuestraVARIABLES GEOMETRICA EXPONENCIAL HIPERBOLICA

X Y ln(y) ln(x) ln(x).ln(y) [ln(x)]^2 x ln(y) x^2 1/y x/y1 14580 2.73 1.00 9.59 9.63 91.92 2.40 14642.72 2.13E+08 1.92 0.37 5340.66 2.072 11940 1.76 0.57 9.39 5.31 88.13 2.88 6749.85 1.43E+08 2.70 0.57 6784.09 2.543 11750 2.68 0.99 9.37 9.24 87.83 2.93 11583.35 1.38E+08 2.77 0.37 4384.33 2.584 11510 3.74 1.32 9.35 12.33 87.44 2.98 15182.68 1.32E+08 2.86 0.27 3077.54 2.635 10370 4.67 1.54 9.25 14.25 85.50 3.28 15981.82 1.08E+08 3.31 0.21 2220.56 2.936 9430 1.26 0.23 9.15 2.12 83.75 3.58 2179.38 8.89E+07 3.75 0.79 7484.13 3.237 9110 4.16 1.43 9.12 13.00 83.12 3.69 12986.44 8.30E+07 3.90 0.24 2189.90 3.358 7460 5.46 1.70 8.92 15.14 79.52 4.43 12662.97 5.57E+07 4.84 0.18 1366.30 4.119 7210 5.31 1.67 8.88 14.83 78.91 4.57 12037.76 5.20E+07 5.00 0.19 1357.82 4.25

10 6150 6.96 1.94 8.72 16.93 76.11 5.28 11932.10 3.78E+07 5.74 0.14 883.62 5.0111 5640 5.77 1.75 8.64 15.14 74.61 5.72 9885.07 3.18E+07 6.13 0.17 977.47 5.4812 5610 4.99 1.61 8.63 13.88 74.52 5.74 9017.72 3.15E+07 6.15 0.20 1124.25 5.5113 5480 4.73 1.55 8.61 13.38 74.11 5.87 8515.51 3.00E+07 6.26 0.21 1158.56 5.6514 5420 7.68 2.04 8.60 17.53 73.92 5.93 11049.32 2.94E+07 6.31 0.13 705.73 5.7215 5380 7 1.95 8.59 16.72 73.80 5.97 10469.00 2.89E+07 6.34 0.14 768.57 5.7616 5300 8.59 2.15 8.58 18.44 73.54 6.05 11398.17 2.81E+07 6.41 0.12 617.00 5.8517 5220 7 1.95 8.56 16.66 73.28 6.13 10157.65 2.72E+07 6.47 0.14 745.71 5.9418 4990 7 1.95 8.52 16.57 72.51 6.39 9710.09 2.49E+07 6.67 0.14 712.86 6.2319 4710 7 1.95 8.46 16.46 71.53 6.74 9165.24 2.22E+07 6.92 0.14 672.86 6.6220 4140 7 1.95 8.33 16.21 69.36 7.58 8056.07 1.71E+07 7.45 0.14 591.43 7.5821 4060 8 2.08 8.31 17.28 69.04 7.71 8442.53 1.65E+07 7.53 0.13 507.50 7.7322 4050 8 2.08 8.31 17.27 69.00 7.73 8421.74 1.64E+07 7.54 0.13 506.25 7.7523 4030 8 2.08 8.30 17.26 68.92 7.77 8380.15 1.62E+07 7.56 0.13 503.75 7.8024 3540 8 2.08 8.17 16.99 66.78 8.74 7361.22 1.25E+07 8.06 0.13 442.50 8.9425 3520 8 2.08 8.17 16.98 66.69 8.79 7319.63 1.24E+07 8.08 0.13 440.00 9.0026 2620 8 2.08 7.87 16.37 61.95 11.51 5448.14 6.86E+06 9.08 0.13 327.50 12.36Σ 173220 153.49 43.69 226.37 375.89 1975.77 150.37 2.59E+05 1.40E+09 149.74 5.63 45890.88 146.62

Promedio 6662.307692 5.903461538 1.68 8.71 14.46 75.99 5.78 9951.40 5.40E+07 5.76 0.22 1765.03 5.6415147.4830 12.764227676628 -0.00709861420593232

yg yexp yhip

ag= ae= ah=

En un estudio experimental de resistencia a la abrasion, encontraron una cierta relacion inversa, no definida matematicamente, entre la relacion a la compresion (X), dada en lb/pulg2, y la pérdida por abrasion (Y). De una serie de ladrillos de refractarios de la clase de silico-aluminosos, alta alumina, magnesita-cromo, cromo magnesita, fosterita, carburo de silicio, circonia y silica; cuyos resultados han sido ordenados en la siguiente tabla. La importancia de este experimento estriba en la posibilidad de estimar una de las variables conociendo la otra. Muchas de las industrias dedicadas a la fabricacion de productos ceramicos y refractarios no cuentan con los equipos adecuados para determinar ambas variables en forma independiente y mucho menos en forma simultanea, por lo que, mediante este experimento y la utilizacion de las tecnicas de regresion y correlacion estadistica es posible determinar formulas matematicas adecuadas que permitan estimar el valor esperado de dichas variables de acuerdo a la infraestructura con que se cuente y, de esta forma, solucionar cualquier incoveniente al respecto. Si este es el caso: Encontrar la formula mas apropiada para estimar la perdida por abrasion de un material refractario cualquiera conociendo su resistencia a la compresion segun se muestra en la tabla. Determina el error tipico de la estima y el coeficiente de correccion lineal para todos los ajustes posibles y aquellos correspondientes a los ajustes no lineales. Mostrar los resultados graficamente.

-0.912569969104201 0.99986997823231 0.00003

Muestra

1 10.07085814 12.26 15.89 14.68 0.107412097 0.660830434 0.433283529

2 17.16827352 9.13 10.25 11.33 1.260296019 0.887839873 0.605419921

3 10.39070429 8.87 9.82 11.05 0.060091926 0.008072166 0.010023939

4 4.680565828 8.54 9.28 10.68 0.576465371 0.77854611 1.221730821

5 1.521427367 6.89 6.70 8.84 1.936562385 1.838041908 3.026408065

6 21.56173506 5.42 4.66 7.15 5.360918012 6.175968469 3.877513296

7 3.039658136 4.90 4.00 6.54 0.221087365 0.065397026 0.663799127

8 0.196658136 2.18 1.13 3.23 1.065282655 0.386163984 1.831326921

9 0.352196598 1.78 0.82 2.72 0.550899429 0.097060954 1.116337279

10 1.116273521 0.39 0.03 0.79 2.818605769 1.495388591 3.79225294

11 0.017811982 0.04 0.05 0.18 0.002996719 0.1299593 0.082057807

12 0.834411982 0.03 0.06 0.15 0.567222813 1.355966836 0.274590886 r=13 1.377011982 0.00 0.13 0.06 1.293553331 2.33899925 0.846524146

14 3.156088905 0.00 0.16 0.04 3.074447755 1.881275003 3.86062827 TIPO DE REGRESION COEFICIENTE DE CORRELACION (r)15 1.202396598 0.00 0.19 0.02 1.067527031 0.433884349 1.539135748 GEOMETRICA 1.0316 7.217488905 0.02 0.25 0.00 6.457065067 4.76282537 7.508010966 EXPONENCIAL 0.9117 1.202396598 0.05 0.33 0.00 0.750879811 0.276031818 1.116484919 HIPERGEOMETRICA 1.1518 1.202396598 0.24 0.59 0.11 0.370949908 0.108127042 0.593796901

19 1.202396598 0.69 1.03 0.51 0.069288581 0.006636364 0.146582315

20 1.202396598 2.81 2.39 2.80 0.334487217 0.203220778 0.333157765

21 4.395473521 3.28 2.64 3.35 0.081508226 0.222113306 0.070383954

22 4.395473521 3.34 2.67 3.43 0.07188595 0.212975804 0.060098717 TIPO DE REGRESION23 4.395473521 3.47 2.74 3.58 0.054338564 0.195242759 0.041834613 GEOMETRICA 1.2724 4.395473521 8.06 4.63 9.24 0.551038311 0.003066383 0.889245828 EXPONENCIAL 0.9925 4.395473521 8.32 4.72 9.57 0.6203732 0.005829482 0.994120729 HIPERGEOMETRICA 1.44

bg= be= bh=

(y-yprom)2 (Yg - yprom)2 (yexp-yprom)2 (yhip - yprom)2 (Y-Yg)^2 (Y-Yexp)^2 (Y-Yhip)^2

σ =

ERROR TIPICO DE LA ESTIMA (σ)

𝑎_𝑔=exp((∑▒〖 ln(𝑥). ∑▒〗 〖〖 [ln 〗(𝑥)ln(𝑦)]−∑▒ln(𝑦)∑▒〖 [ln〖 (𝑥)]〗〗^2〗 )/([∑▒〖 ln〖 (𝑥)]〗〗^2−𝑛∑▒〖〖 [ln 〗〖 (𝑥)]〗〗^2))𝑏_𝑔=(∑▒〖 ln(𝑦) − 〗 𝑛 ln(𝑎))/(∑▒〖 ln(𝑥) 〗 )

〖𝑦=𝑎𝑥 〗 ^𝑏𝑎_𝑒=exp((∑▒ 〖 〗𝑥∑▒〖𝑥 .ln(𝑦) −∑▒〗 〖 ln(𝑦) ∑〗▒𝑥^2)/(〖 (∑▒〖𝑦′ ) 〗〗 ^2−𝑛∑▒〖𝑥 ^2 〗 ))𝑏_𝑒=exp((∑▒ln(𝑦)−𝑛ln(𝑎))/(∑▒𝑥))

〖𝑦=𝑎𝑏 〗 ^𝑥 𝑎_(ℎ)=(∑▒𝑥∑▒ 〖𝑥 /𝑦−∑▒ 〖 1/𝑦∑▒𝑥^2〗〗 )/( 〖 (∑▒ 〖𝑥 )〗〗^2−𝑛∑▒𝑥^2)𝑏_ℎ=(∑▒1/𝑦−𝑎𝑛)/(∑▒𝑥)

〖𝑦=1/(𝑎+𝑏𝑥)〗^

2000 4000 6000 8000 10000 12000 14000 1600002468

101214

DATOS GEOMETRICAEXPONENCIAL HIPERGEOMETRICA

√((∑▒〖 (𝑦〗 _𝑒𝑠𝑝𝑒𝑟𝑎𝑑𝑜−𝑦))/(∑▒〖 (𝑦 − 〗 𝑦 )))

±√((∑▒〖 (𝑦−𝑦_𝑒𝑠𝑝𝑒𝑟𝑎𝑑𝑜)〗 ^2)/𝑁)

26 4.395473521 31.38 10.08 41.67 12.28776378 1.164305883 18.99901715

Σ 115.09 122.09 95.26 151.73 41.61 25.69 53.93

Muestra

1 3.67 1.14 2.91 0.92 3.51 0.632 4.15 1.62 3.70 1.71 3.98 1.103 4.19 1.66 3.76 1.78 4.02 1.144 4.25 1.72 3.85 1.86 4.07 1.195 4.54 2.01 4.31 2.32 4.37 1.496 4.84 2.31 4.74 2.75 4.67 1.797 4.95 2.42 4.90 2.91 4.79 1.908 5.69 3.16 5.83 3.84 5.55 2.679 5.83 3.30 5.99 4.00 5.69 2.81

10 6.55 4.02 6.73 4.74 6.45 3.5711 6.98 4.45 7.12 5.14 6.92 4.0412 7.01 4.48 7.15 5.16 6.95 4.0713 7.13 4.60 7.25 5.27 7.09 4.2114 7.19 4.66 7.30 5.31 7.16 4.2715 7.23 4.70 7.34 5.35 7.20 4.3216 7.31 4.78 7.40 5.41 7.29 4.4117 7.40 4.87 7.47 5.48 7.38 4.5018 7.66 5.13 7.67 5.68 7.67 4.7919 8.00 5.47 7.91 5.92 8.06 5.1820 8.84 6.31 8.44 6.46 9.02 6.1421 8.98 6.45 8.52 6.53 9.17 6.2922 9.00 6.47 8.53 6.54 9.20 6.3123 9.03 6.50 8.55 6.56 9.24 6.3624 10.01 7.48 9.05 7.06 10.38 7.5025 10.05 7.52 9.07 7.08 10.44 7.5626 12.77 10.24 10.07 8.08 13.80 10.92

LS Yg LI Yg LS Yexp LI Y exp LS Yhip LI Yhip

GEOMETRICA

DATOS GEOMETRICALIM. SUPERIOR LIM. INFERIOR

EXPONENCIAL

DATOS EXPONENCIALLIM. SUPERIOR LIM. INFERIOR

HIPERGEOMETRICA

DATOS HIPERGEOMETRICALIM. SUPERIOR LIM. INFERIOR

Muestra

yg x*yg y lin geo y exp x * y exp y lin exp y hip x * y hip y lin hip1 2.40 35024.98 0.75 1.92 27951.10 0.96 2.07 30206.22 0.172 2.88 34418.59 2.43 2.70 32264.90 2.56 2.54 30304.76 1.993 2.93 34370.35 2.55 2.77 32545.68 2.67 2.58 30313.59 2.124 2.98 34308.40 2.70 2.86 32891.52 2.82 2.63 30325.17 2.295 3.28 33996.96 3.43 3.31 34368.83 3.51 2.93 30387.65 3.086 3.58 33715.70 4.02 3.75 35316.76 4.08 3.23 30450.79 3.737 3.69 33614.08 4.23 3.90 35567.91 4.27 3.35 30475.33 3.958 4.43 33031.95 5.28 4.84 36095.80 5.28 4.11 30636.24 5.099 4.57 32933.65 5.44 5.00 36038.85 5.43 4.25 30667.24 5.26

10 5.28 32478.95 6.11 5.74 35283.41 6.07 5.01 30827.67 5.9911 5.72 32234.05 6.43 6.13 34576.01 6.38 5.48 30927.18 6.3512 5.74 32219.03 6.45 6.15 34526.52 6.40 5.51 30933.62 6.3713 5.87 32153.05 6.53 6.26 34301.40 6.48 5.65 30962.37 6.4614 5.93 32122.12 6.57 6.31 34191.55 6.51 5.72 30976.12 6.5015 5.97 32101.32 6.60 6.34 34116.20 6.54 5.76 30985.47 6.5316 6.05 32059.30 6.65 6.41 33960.33 6.59 5.85 31004.60 6.5817 6.13 32016.70 6.70 6.47 33797.48 6.63 5.94 31024.35 6.6418 6.39 31890.81 6.85 6.67 33289.15 6.77 6.23 31084.79 6.8019 6.74 31730.20 7.02 6.92 32586.31 6.94 6.62 31166.73 6.9920 7.58 31374.36 7.39 7.45 30846.31 7.29 7.58 31369.60 7.3821 7.71 31320.88 7.44 7.53 30566.57 7.34 7.73 31402.88 7.4422 7.73 31314.13 7.44 7.54 30530.95 7.34 7.75 31407.14 7.4523 7.77 31300.58 7.46 7.56 30459.29 7.36 7.80 31415.72 7.4624 8.74 30947.81 7.77 8.06 28516.03 7.65 8.94 31658.21 7.8025 8.79 30932.48 7.78 8.08 28428.76 7.66 9.00 31669.64 7.8126 11.51 30144.12 8.35 9.08 23787.06 8.21 12.36 32380.02 8.43Σ 150.37 843754.56 149.74 846804.69 146.62 804963.13

a= 10.02 a= 9.80 a= 10.25b= -0.000636 b= -0.000606 b= -0.000691

Linealizacion de la regresion geometrica

Linealizacion de la regresion Exponencial

Linealizacion de la regresion Hiperbolica

HIPERGEOMETRICA

DATOS HIPERGEOMETRICALIM. SUPERIOR LIM. INFERIOR

DATOS Geo linealExpon. lineal Hipergeo. lineal

Muestra

1 0.59 0.81 1.27 1.10 0.02 0.12 0.08

2 1.46 0.51 0.61 0.71 0.24 0.18 0.13

3 0.62 0.49 0.57 0.69 0.01 0.00 0.00

4 0.21 0.47 0.53 0.65 0.05 0.07 0.12

5 0.05 0.35 0.33 0.49 0.13 0.12 0.22

6 2.39 0.25 0.21 0.36 1.09 1.19 0.89

7 0.12 0.22 0.17 0.32 0.01 0.00 0.05

8 0.01 0.08 0.04 0.13 0.04 0.01 0.08

9 0.01 0.07 0.03 0.11 0.02 0.00 0.05

10 0.03 0.01 0.00 0.03 0.08 0.04 0.11

11 0.00 0.00 0.00 0.01 0.00 0.00 0.00

12 0.03 0.00 0.00 0.00 0.02 0.04 0.01

13 0.05 0.00 0.00 0.00 0.05 0.08 0.03

14 0.07 0.00 0.00 0.00 0.07 0.04 0.09

15 0.03 0.00 0.01 0.00 0.03 0.01 0.04

16 0.14 0.00 0.01 0.00 0.12 0.09 0.15

17 0.03 0.00 0.01 0.00 0.02 0.01 0.03

18 0.03 0.01 0.01 0.00 0.01 0.00 0.01

19 0.03 0.02 0.03 0.01 0.00 0.00 0.00

20 0.03 0.06 0.05 0.06 0.01 0.00 0.01

21 0.09 0.07 0.06 0.07 0.00 0.00 0.00

22 0.09 0.07 0.06 0.07 0.00 0.00 0.00

23 0.09 0.08 0.06 0.08 0.00 0.00 0.00

24 0.09 0.15 0.10 0.17 0.01 0.00 0.01

25 0.09 0.16 0.10 0.18 0.01 0.00 0.01

26 0.09 0.45 0.19 0.55 0.13 0.02 0.19

(ln y-ln y)2 (lnyg-lny)2 (lnye-lny)2 (lnyh-lny)2 (lny-lnyg)2 (lny-lnye)2 (lny-lnyh)2

𝑎=(∑▒𝑥∑▒ − ∑▒ ∑▒〖𝑥𝑦 𝑦 𝑥 ^2〗 )/(〖 (∑▒𝑥)〗^2−𝑛∑▒𝑥^2)𝑏=(∑▒ −〖 〗𝑦 𝑛𝑎 )/(∑▒𝑥)

Σ 6.49 4.33 4.44 5.80 2.16 2.05 2.31

geometrica exponencial hipergeometrica

r 0.82 0.83 0.95σ 0.29 0.28 0.30

Si r € [0.9,1], entonces no correjimos; sino tomamos los primeros 18 valores y los demas los arreglamos

manualmente hasta cumplir la condicion.

MuestraVARIABLES CUADRATICA

X Y xy1 14580 2.73 2.13E+08 3.10E+12 4.52E+16 39803.40 5.80E+08 5.142 11940 1.76 1.43E+08 1.70E+12 2.03E+16 21014.40 2.51E+08 2.093 11750 2.68 1.38E+08 1.62E+12 1.91E+16 31490.00 3.70E+08 1.994 11510 3.74 1.32E+08 1.52E+12 1.76E+16 43047.40 4.95E+08 1.895 10370 4.67 1.08E+08 1.12E+12 1.16E+16 48427.90 5.02E+08 1.786 9430 1.26 8.89E+07 8.39E+11 7.91E+15 11881.80 1.12E+08 2.137 9110 4.16 8.30E+07 7.56E+11 6.89E+15 37897.60 3.45E+08 2.348 7460 5.46 5.57E+07 4.15E+11 3.10E+15 40731.60 3.04E+08 4.169 7210 5.31 5.20E+07 3.75E+11 2.70E+15 38285.10 2.76E+08 4.55

10 6150 6.96 3.78E+07 2.33E+11 1.43E+15 42804.00 2.63E+08 6.4911 5640 5.77 3.18E+07 1.79E+11 1.01E+15 32542.80 1.84E+08 7.6112 5610 4.99 3.15E+07 1.77E+11 9.90E+14 27993.90 1.57E+08 7.6813 5480 4.73 3.00E+07 1.65E+11 9.02E+14 25920.40 1.42E+08 7.9814 5420 7.68 2.94E+07 1.59E+11 8.63E+14 41625.60 2.26E+08 8.1315 5380 13.1 2.89E+07 1.56E+11 8.38E+14 70478.00 3.79E+08 8.2216 5300 8.59 2.81E+07 1.49E+11 7.89E+14 45527.00 2.41E+08 8.4217 5220 3.77 2.72E+07 1.42E+11 7.42E+14 19679.40 1.03E+08 8.6218 4990 3.57 2.49E+07 1.24E+11 6.20E+14 17814.30 8.89E+07 9.2019 4710 9.25 2.22E+07 1.04E+11 4.92E+14 43567.50 2.05E+08 9.9520 4140 4.95 1.71E+07 7.10E+10 2.94E+14 20493.00 8.48E+07 11.5821 4060 13.9 1.65E+07 6.69E+10 2.72E+14 5.64E+04 2.29E+08 11.8222 4050 19.2 1.64E+07 6.64E+10 2.69E+14 7.78E+04 3.15E+08 11.8523 4030 12.5 1.62E+07 6.55E+10 2.64E+14 5.04E+04 2.03E+08 11.9124 3540 19.2 1.25E+07 4.44E+10 1.57E+14 6.80E+04 2.41E+08 13.4525 3520 10.8 1.24E+07 4.36E+10 1.54E+14 3.80E+04 1.34E+08 13.5226 2620 18.4 6.86E+06 1.80E+10 4.71E+13 4.82E+04 1.26E+08 16.64Σ 173220 199.13 1402703200 1.34121E+13 1.44419E+17 1039786.1 6557515837 199.13

Promedio6662.307692 7.658846154 5.40E+07 5.16E+11 5.55E+15 4.00E+04 2.52E+08 7.66E+00

=

26 173220 1.40E+09 199.13173220 1.40E+09 1.34E+13 1.04E+06

1.40E+09 1.34E+13 1.44E+17 6.56E+09

27.8332749= -0.0048664

2.2701E-07

x2 x3 x4 x2y y cuadratica

■8(𝑛&∑▒𝑥&∑ ^2 ▒𝑥@∑▒𝑥&∑ ^2 ▒𝑥&∑ ^3 ▒𝑥 @∑ ^2 ▒𝑥&∑ ^▒𝑥 3 &∑ ^▒𝑥 4 )■8(∑▒𝑦@∑▒𝑥𝑦@∑▒〖𝑥 ^2𝑦〗 )-1■8(𝑎@𝑏@𝑐)

-1

■8(𝑎@𝑏@𝑐) 𝑌=𝑎+𝑏𝑥+𝑐𝑥^2+𝑑𝑥^3

MuestraCubica

1 6.59E+20 9.61E+24 8.46E+12 2.24E+002 2.43E+20 2.90E+24 3.00E+12 3.37E+003 2.24E+20 2.63E+24 4.35E+12 3.35E+004 2.02E+20 2.33E+24 5.70E+12 3.32E+005 1.20E+20 1.24E+24 5.21E+12 3.14E+006 7.46E+19 7.03E+23 1.06E+12 3.06E+007 6.27E+19 5.72E+23 3.15E+12 3.08E+008 2.31E+19 1.72E+23 2.27E+12 3.84E+009 1.95E+19 1.40E+23 1.99E+12 4.09E+00

10 8.80E+18 5.41E+22 1.62E+12 5.65E+0011 5.71E+18 3.22E+22 1.04E+12 6.75E+0012 5.56E+18 3.12E+22 8.81E+11 6.82E+0013 4.94E+18 2.71E+22 7.78E+11 7.14E+0014 4.68E+18 2.54E+22 1.22E+12 7.30E+0015 4.51E+18 2.42E+22 2.04E+12 7.40E+0016 4.18E+18 2.22E+22 1.28E+12 7.62E+0017 3.88E+18 2.02E+22 5.36E+11 7.84E+0018 3.09E+18 1.54E+22 4.44E+11 8.52E+0019 2.32E+18 1.09E+22 9.67E+11 9.42E+0020 1.22E+18 5.04E+21 3.51E+11 1.15E+0121 1.10E+18 4.48E+21 9.30E+11 1.19E+0122 1.09E+18 4.41E+21 1.28E+12 1.19E+0123 1.06E+18 4.28E+21 8.18E+11 1.20E+0124 5.56E+17 1.97E+21 8.52E+11 1.42E+0125 5.40E+17 1.90E+21 4.71E+11 1.43E+0126 1.23E+17 3.23E+20 3.31E+11 1.93E+01Σ 1.68E+21 2.06E+25 5.10E+13

Promedio 6.46E+19 7.91E+23 1.96E+12

=

26 173220 1402703200 1.3412E+13 199.13 4.15E+01 = 173220 1402703200 1.3412E+13 1.44E+17 1039786.1 -1.09E-02

x5 x6 x3y y cubico

■8(𝑎@𝑏@𝑐)

■8(𝑛&∑▒𝑥&∑ ^2 ▒𝑥@∑▒𝑥&∑ ^2 ▒𝑥 &∑ ^3 ▒𝑥@█(∑ ^2 ▒𝑥@∑ ^3 ▒𝑥 )&█(∑ ^3 ▒𝑥@∑ ^4 ▒𝑥 )&█(∑ ^4 ▒𝑥@∑ ^▒𝑥 5 ))■8(█(∑ ^3 ▒𝑥@∑ ^4 ▒𝑥 )@∑ ^▒𝑥 5 @∑ ^▒𝑥 6 )

■8(∑▒𝑦@∑▒𝑥𝑦@█(∑▒〖𝑥 ^2𝑦〗@ (∑█ ▒〖𝑥 ^3 𝑦〗@)))■8(𝑎@𝑏@█(𝑐@𝑑))-1

-1■8(a@b@█(c@d))

1402703200 1.3412E+13 1.44E+17 1.68E+21 6557515837 = 1.03E-061.3412E+13 1.44E+17 1.68E+21 2.06E+25 5.10E+13 -3.15E-11

■8(a@b@█(c@d))

2000 4000 6000 8000 10000 12000 14000 160000.00

5.00

10.00

15.00

20.00

25.00

■8(∑▒𝑦@∑▒𝑥𝑦@∑▒〖𝑥 ^2𝑦〗 )

■8(∑▒𝑦@∑▒𝑥𝑦@█(∑▒〖𝑥 ^2𝑦〗@ (∑█ ▒〖𝑥 ^3 𝑦〗@)))