kjfksdn
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Ejercicio 7 Dados los siguientes datos a) Ajuste una recta usando m´ ınimos cuadrados. b) Construya un intervalo de confianza del 95% para el coeficiente de regresi´ on α . c) Deter mine el coefici ente de corre laci´ on. d) Elabore un diagrama de dispersi´ on y grafique la recta que se obtuvo con m´ ınimos cuadrados. Datos: [1.21342, −8.12689 ]; [82.3759, −178.306 ]; [96.2051, −279.798 ]; [9.6192, −86.4361] ; [173.676, −491.862]; [174.376, −491.342]; [164.731, −413.597 ]; [1.33124, −109.954 ]; [61 .6784, −153.059 ]; [54.1137, −152.419]; [185.981, −406.76] ; [71 .1982, −247.925]; [153.197, −432.918]; [112.422, −340.231]; [104.041, −281.44]; [81.7275, −242.559]; [162.961, −350.406 ]; [12 2.902, −276.521 ]; [38 .4988, −187.242 ]; [34.9162, −83.0511]; [86.0269, −291.212]; [141.194, −321.566 ]; [41.7013, −157.733]; [158.382, −333.12] ; [12 2.547, −350.745]; [98.3834, −334.724]; [197.136, −403.748 ]; [18 2.684, −374.875 ]; [0.227456, −93.9409] ; [119.904, −365.479]; [124.082, −329.887]; [145.811, −340.566 ]; [53.6274, −209.071]; [130.932, −358.486 ]; [11 9.493, −260.576]; [139.259, −327.472 ]; [61 .539, −233.87] ; [33 .2543, −187.139 ]; [14 7.763, −322.216 ]; [4.34994, −117.482]; [171.994, −430.6]; [74 .2983, −289.496]; [147.216, −421.533 ]; [17 0.94, −410.784]; [198.165, −472.974]; [33.5976, −142.256]; [154.847, −317.958 ]; [43.0648, −175.159 ]; [11 .251, −22.038 ]; [51 .4498, −146.755]; [81.0212, −298.977]; [179.153, −493.994 ]; [19 5.114, −442.031]; [106.38, −279.354]; [143.242, −406.982]; [97.3895, −278.59] ; [14 0.811, −398.161 ]; [42.8239, −96.756 8]; [3.24503, −35.0885] ; [145.404, −306.941]; [33.2055, −139.831 ]; [85 .2706, −173.738 ]; [11 1.739, −298.822]; [188.393, −422.455 ]; [92.1813, −211.506]; [59.6468, −263.333]; [179.37, −361.894 ]; [21.8156, −124.461]; [192.028, −419.873]; [172.88, −479.386]; [191.793, −480.806]; [143.861, −366.926 ]; [13 4.795, −361.746]; [119.457, −268.006 ]; [84.422, −200.273]; [34.4569, −150.934]; [128.105, −279.654 ]; [2.65688, −36.4559] ; [80.59, −278.402 ]; [75 .0962, −218.033]; [177.85, −403.477]; [114.119, −298.88] ; [76 .1437, −229.615 ]; [14 4.848, −361.579 ]; [30 .7762, −187.334]; [114.866, −322.304]; [151.546, −387.781 ]; [14 2.772, −415.088 ]; [49 .9654, −127.435 ]; [13 4.148, −293.324]; [71.7396, −274.135]; [185.123, −414.559 ]; [10 6.358, −273.803]; [109.574, −345.328 ]; [10 4.169, −269.995]; [153.928, −432.178]; [118.687, −236.568 ]; [11 0.253, −284.128 ]; [31 .1153, −118.25] ; [60 .4179, −249.377]; [121.913, −353.171]; [187.685, −401.64]; [91.7258, −228.619 ]; [60 .6388, −150.429]; [135.598, −392.457]; [109.884, −243.736]; [134.846, −283.68] ; [45.7226, −118.914 ]; [84 .2015, −189.397]; [172.76, −363.884]; [168.785, −395.364 ]; [29 .5709, −178.007 ]; [19 3.533, −402.481]; [196.25, −447.791 ]; [8.59538, −129.719]; [116.154, −327.375 ]; [36 .8174, −150.827 ]; [10 5.97, −233.656 ]; [58 .0198, −223.583 ]; [61 .5283, −252.306]; [179.547, −402.83] ; [84 .8101, −196.898]; [187.992, −455.832 ]; [80 .1192, −237.272 ]; [3.79395, −144.873]; [21.9765, −70.0679] ; [53.403, −190.535 ]; [6.20999, −58.7219] ; [106.968, −285.794 ]; [76 .5407, −208.789]; [146.634, −296.85] ; [13 .8374, −65.4577] ; [26.6257, −147.98] ; [19 3.06, −502.569]; [128.708, −402.624]; [77.3514, −163.556]; [124.759, −339.603 ]; [48.5074, −156.567]; [107.571, −280.421 ]; [11 3.276, −343.076]; [79.2499, −158.506]; [154.392, −351.385 ]; [17 3.024, −406.545 ]; [46 .2326, −175.755 ]; [14 7.657, −378.338]; [163.771, −340.685]; [148.539, −297.687 ]; [90.501, −325.43] ; [7.29155, −131.951]; [174.973, −397.232]; a) ¯ x = 103.96366824 ¯ y = −277.5788579333 150 i=1 x i = 15594.550236 150 i=1 y i = −41636.82869 150 i=1 x i y i = −5258950.4739483912 150 i=1 x 2 i = 2105444.1928578941 150 i=1 y 2 i = 13609336.080169903 S xx = 150 i=1 x 2 i − ( 150 i=1 xi) 2 150 = 484177.5457703758 S xy = 150 i=1 x i y i − ( 150 i=1 x i )( 150 i=1 y i ) = −930233.0294555137 1
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Transcript of kjfksdn
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Ejercicio 7
Dados los siguientes datosa) Ajuste una recta usando mnimos cuadrados.b) Construya un intervalo de confianza del 95% para el coeficiente de regresion .c) Determine el coeficiente de correlacion.d) Elabore un diagrama de dispersion y grafique la recta que se obtuvo con mnimos cuadrados.
Datos:
[1.21342,8.12689]; [82.3759,178.306]; [96.2051,279.798]; [9.6192,86.4361]; [173.676,491.862];[174.376,491.342]; [164.731,413.597]; [1.33124,109.954]; [61.6784,153.059]; [54.1137,152.419];[185.981,406.76]; [71.1982,247.925]; [153.197,432.918]; [112.422,340.231]; [104.041,281.44];[81.7275,242.559]; [162.961,350.406]; [122.902,276.521]; [38.4988,187.242]; [34.9162,83.0511];[86.0269,291.212]; [141.194,321.566]; [41.7013,157.733]; [158.382,333.12]; [122.547,350.745];[98.3834,334.724]; [197.136,403.748]; [182.684,374.875]; [0.227456,93.9409]; [119.904,365.479];[124.082,329.887]; [145.811,340.566]; [53.6274,209.071]; [130.932,358.486]; [119.493,260.576];[139.259,327.472]; [61.539,233.87]; [33.2543,187.139]; [147.763,322.216]; [4.34994,117.482];[171.994,430.6]; [74.2983,289.496]; [147.216,421.533]; [170.94,410.784]; [198.165,472.974];[33.5976,142.256]; [154.847,317.958]; [43.0648,175.159]; [11.251,22.038]; [51.4498,146.755];[81.0212,298.977]; [179.153,493.994]; [195.114,442.031]; [106.38,279.354]; [143.242,406.982];[97.3895,278.59]; [140.811,398.161]; [42.8239,96.7568]; [3.24503,35.0885]; [145.404,306.941];[33.2055,139.831]; [85.2706,173.738]; [111.739,298.822]; [188.393,422.455]; [92.1813,211.506];[59.6468,263.333]; [179.37,361.894]; [21.8156,124.461]; [192.028,419.873]; [172.88,479.386];[191.793,480.806]; [143.861,366.926]; [134.795,361.746]; [119.457,268.006]; [84.422,200.273];[34.4569,150.934]; [128.105,279.654]; [2.65688,36.4559]; [80.59,278.402]; [75.0962,218.033];[177.85,403.477]; [114.119,298.88]; [76.1437,229.615]; [144.848,361.579]; [30.7762,187.334];[114.866,322.304]; [151.546,387.781]; [142.772,415.088]; [49.9654,127.435]; [134.148,293.324];[71.7396,274.135]; [185.123,414.559]; [106.358,273.803]; [109.574,345.328]; [104.169,269.995];[153.928,432.178]; [118.687,236.568]; [110.253,284.128]; [31.1153,118.25]; [60.4179,249.377];[121.913,353.171]; [187.685,401.64]; [91.7258,228.619]; [60.6388,150.429]; [135.598,392.457];[109.884,243.736]; [134.846,283.68]; [45.7226,118.914]; [84.2015,189.397]; [172.76,363.884];[168.785,395.364]; [29.5709,178.007]; [193.533,402.481]; [196.25,447.791]; [8.59538,129.719];[116.154,327.375]; [36.8174,150.827]; [105.97,233.656]; [58.0198,223.583]; [61.5283,252.306];[179.547,402.83]; [84.8101,196.898]; [187.992,455.832]; [80.1192,237.272]; [3.79395,144.873];[21.9765,70.0679]; [53.403,190.535]; [6.20999,58.7219]; [106.968,285.794]; [76.5407,208.789];[146.634,296.85]; [13.8374,65.4577]; [26.6257,147.98]; [193.06,502.569]; [128.708,402.624];[77.3514,163.556]; [124.759,339.603]; [48.5074,156.567]; [107.571,280.421]; [113.276,343.076];[79.2499,158.506]; [154.392,351.385]; [173.024,406.545]; [46.2326,175.755]; [147.657,378.338];[163.771,340.685]; [148.539,297.687]; [90.501,325.43]; [7.29155,131.951]; [174.973,397.232];
a)x = 103.96366824y = 277.5788579333150
i=1 xi = 15594.550236150i=1 yi = 41636.82869150i=1 xiyi = 5258950.4739483912150i=1 x
2i = 2105444.1928578941150
i=1 y2i = 13609336.080169903
Sxx =150
i=1 x2i (
150i=1 xi)
2
150 = 484177.5457703758
Sxy =150
i=1 xiyi (150
i=1 xi)(150
i=1 yi) = 930233.02945551371
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2Syy =150
i=1 y2i (
150i=1 yi)
2
150 = 2051832.7244338430
b =SxySxx
= 1.9212642915a = y bx = 77.8371745260y = a+ bx = 1.9212642915x+77.8371745260
b)
S2e =Syy(S2xy/Sxx)
n2 = 1787.9001495079
Se =
1787.9001495079 = 42.2835683157
Para el intervalo del 95%, como n 30 :
= a Z1.96 Se
( 1n ) x2
Sxx
1 = 77.3342418086
2 = 78.3401072435
c) Para calcular el coeficiente de correlacion r:
r =SxySxxSyy
r = 0.9332939647
d) Diagrama de dispersion
