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

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