Guia de Ejercicios I
JUAN ARIAS
16/4/2021
Ejercicio 1 Para una empresa se ha estimado un modelo que relaciona las ventas de 200 empresas, con su gasto en tv, radio, periódicos y la interacción entre tv y periódicos
Numeral 1 Calcule las matrices A, P, M
options(escipen=99999999)
load("C:/MEGA DOCS/UES/CICLO I - 2021/ECONOMETTRIA/EJERCICIIOS/GUIA 1/modelo_ventas.RData")
matriz_x<-model.matrix(modelo_ventas)
matriz_xx<-t(matriz_x)%*%matriz_x
#Calculo de la Matriz A
matriz_a<-solve(matriz_xx)%*%t(matriz_x)
print(matriz_a)## 1 2 3 4
## (Intercept) -1.128647e-02 1.410378e-02 3.506392e-02 4.283381e-04
## tv -6.704103e-05 3.094914e-05 -6.120193e-04 -2.120642e-04
## periodico 1.398182e-03 -1.907247e-03 -2.546882e-03 2.293243e-04
## radio -5.800213e-04 6.486665e-04 -1.093284e-04 -1.899710e-04
## tv:radio 1.481990e-05 1.945347e-06 3.260788e-05 1.485919e-05
## 5 6 7 8
## (Intercept) -2.802264e-02 4.966826e-02 6.721406e-03 1.368577e-02
## tv 1.568308e-03 -9.621560e-04 1.116638e-04 -3.266110e-04
## periodico 2.314279e-04 -3.270782e-03 -1.147087e-03 1.873821e-05
## radio 6.159562e-04 -3.308361e-04 7.724908e-04 -1.007450e-04
## tv:radio -3.937064e-05 4.642785e-05 -8.511094e-06 4.091601e-06
## 9 10 11 12
## (Intercept) 6.237349e-02 1.900575e-02 1.907749e-02 3.605589e-03
## tv -1.402153e-03 -1.946633e-04 1.318092e-05 -3.975640e-04
## periodico -1.235903e-03 2.251710e-04 -5.248900e-04 9.478699e-04
## radio -1.313443e-03 -7.359136e-04 -3.341352e-04 -6.782492e-05
## tv:radio 4.044251e-05 7.159682e-06 7.922246e-07 2.216420e-06
## 13 14 15 16
## (Intercept) 1.489911e-02 3.634140e-02 -1.184470e-02 -3.715741e-03
## tv 2.132861e-04 -8.584443e-04 1.960448e-04 -4.854365e-04
## periodico -2.038353e-03 -2.357826e-04 8.119328e-04 9.790399e-04
## radio 3.368152e-04 -8.947699e-04 6.785235e-05 -2.985399e-04
## tv:radio 5.251734e-06 2.304953e-05 -2.557309e-06 2.032708e-05
## 17 18 19 20
## (Intercept) 1.533281e-02 -1.698620e-02 1.357943e-02 3.694513e-03
## tv 3.888414e-05 -1.332124e-04 -1.024117e-04 -5.343781e-05
## periodico -1.236525e-03 1.950991e-03 -5.804288e-04 1.385062e-04
## radio -8.337856e-04 -4.469023e-04 1.455419e-04 1.519378e-04
## tv:radio 3.057413e-05 1.102821e-05 -8.453250e-07 -3.078161e-06
## 21 22 23 24
## (Intercept) -1.573570e-02 1.061403e-02 0.0039565024 -1.153284e-03
## tv 4.947903e-04 -5.292506e-05 0.0010010281 9.036244e-05
## periodico 7.937923e-04 5.982337e-04 -0.0020168690 7.584305e-04
## radio 6.684885e-05 -6.264755e-04 0.0008051669 -1.805957e-04
## tv:radio -8.570347e-06 2.653757e-06 -0.0000242403 -3.687696e-06
## 25 26 27 28
## (Intercept) 2.093213e-02 1.766200e-02 1.906480e-03 4.591668e-04
## tv -2.125199e-04 -2.941603e-04 -6.089947e-05 -2.752291e-05
## periodico -5.751502e-04 5.717586e-04 -4.463212e-05 8.924833e-04
## radio -2.223157e-04 -8.421747e-04 4.748021e-04 -2.705485e-04
## tv:radio 4.605371e-06 9.579634e-06 -6.627237e-06 -1.017345e-06
## 29 30 31 32
## (Intercept) -9.229297e-03 -7.425570e-04 -2.073713e-02 -1.693244e-03
## tv 2.560012e-05 6.484761e-04 3.024558e-04 5.302390e-04
## periodico 1.140034e-03 -6.316133e-04 1.724819e-03 -3.108545e-04
## radio 7.229892e-05 3.496591e-04 -9.787075e-05 2.549417e-04
## tv:radio -5.118001e-06 -1.618543e-05 -6.563958e-06 -1.343427e-05
## 33 34 35 36
## (Intercept) 8.864198e-03 1.027582e-02 4.236432e-02 3.033028e-02
## tv 3.493553e-04 -6.687179e-04 -1.063045e-03 -9.256622e-04
## periodico -4.168349e-05 1.195095e-03 6.961331e-05 8.200359e-04
## radio -3.351418e-04 -4.496078e-04 -1.364120e-03 -1.302987e-03
## tv:radio -7.465636e-06 1.074002e-05 3.137340e-05 2.639173e-05
## 37 38 39 40
## (Intercept) -3.691371e-02 1.189641e-02 8.312018e-03 -1.642179e-02
## tv 3.511957e-04 -3.451969e-04 2.824773e-04 5.537035e-05
## periodico 1.998789e-03 -1.249476e-03 -1.302071e-03 1.259943e-03
## radio 1.107036e-03 4.595454e-04 5.621722e-04 2.544078e-04
## tv:radio -2.740139e-05 1.270793e-05 -8.200132e-06 -4.675563e-06
## 41 42 43 44
## (Intercept) -7.098669e-03 -6.645943e-03 -7.827523e-03 5.624190e-03
## tv 2.225813e-04 1.553643e-04 -2.992073e-04 1.084722e-04
## periodico 7.473347e-04 2.683898e-04 1.648737e-03 5.100269e-04
## radio 2.979714e-05 2.826183e-04 5.696139e-05 -3.936878e-04
## tv:radio -7.123256e-06 -4.170304e-06 -3.001041e-06 -2.342030e-06
## 45 46 47 48
## (Intercept) 8.840056e-03 -2.874908e-03 1.009775e-03 -2.451540e-02
## tv 4.605731e-04 2.287565e-04 5.623451e-04 1.415854e-04
## periodico -1.710332e-03 2.657820e-04 -2.538277e-04 1.523566e-03
## radio 6.360170e-04 1.369731e-04 8.691167e-05 6.632482e-04
## tv:radio -1.057989e-05 -7.309017e-06 -1.413098e-05 -1.407076e-05
## 49 50 51 52
## (Intercept) -1.878765e-02 2.726160e-03 -1.787389e-03 3.598769e-02
## tv 9.599100e-04 5.869651e-04 6.024475e-04 -9.660068e-04
## periodico 5.354481e-04 -6.055750e-04 3.427554e-04 -5.860236e-05
## radio 2.640272e-04 2.173462e-04 -1.874531e-04 -9.057943e-04
## tv:radio -2.327068e-05 -1.482293e-05 -1.462919e-05 2.476176e-05
## 53 54 55 56
## (Intercept) -1.568181e-02 7.439684e-04 -1.116839e-02 2.541883e-05
## tv -6.715949e-05 -5.134907e-04 -6.223687e-05 -7.449449e-04
## periodico 1.345269e-03 7.278425e-04 1.418155e-03 1.258892e-03
## radio 1.036984e-04 -4.343122e-04 1.148652e-04 -6.898740e-04
## tv:radio 1.767024e-06 2.405979e-05 -5.442162e-06 3.168547e-05
## 57 58 59 60
## (Intercept) 1.831083e-02 1.065382e-02 -1.579016e-02 -5.853894e-03
## tv 3.797467e-04 -1.854524e-04 -2.119036e-04 -1.155820e-04
## periodico -2.664944e-03 2.526683e-05 1.251592e-03 8.915728e-04
## radio 8.511475e-04 -6.527219e-05 2.670703e-04 3.071536e-04
## tv:radio -8.906550e-06 1.426743e-06 4.245123e-06 -6.380628e-06
## 61 62 63 64
## (Intercept) 2.498756e-02 -1.302880e-02 -2.445181e-03 4.949873e-03
## tv -1.730577e-04 -2.816066e-04 1.286648e-04 -9.602718e-05
## periodico -4.346430e-04 1.736434e-03 8.874503e-04 -3.313392e-04
## radio -6.103788e-04 -4.342721e-04 -2.325456e-04 5.819573e-04
## tv:radio 6.783625e-06 1.501912e-05 -4.268503e-06 -7.163908e-06
## 65 66 67 68
## (Intercept) -8.217129e-03 4.273554e-02 2.294731e-02 1.820830e-02
## tv 6.580937e-05 -1.100340e-03 -3.618916e-04 -5.213747e-04
## periodico 1.079112e-05 -4.158651e-04 -1.271053e-03 3.742161e-04
## radio 7.277638e-04 -9.321364e-04 4.476366e-04 -5.045983e-04
## tv:radio -7.124280e-06 2.837397e-05 6.298279e-07 1.117128e-05
## 69 70 71 72
## (Intercept) -5.873309e-03 -1.941033e-02 -1.092974e-02 1.720050e-03
## tv -1.552554e-04 5.928086e-05 2.086633e-04 3.228599e-04
## periodico 1.142640e-03 1.140588e-03 7.513926e-04 2.223314e-05
## radio 1.226760e-04 5.709426e-04 1.526556e-04 9.188374e-06
## tv:radio -3.952340e-06 -8.096259e-06 -5.496981e-06 -8.621258e-06
## 73 74 75 76
## (Intercept) 1.415591e-02 4.183082e-03 9.649808e-05 4.133115e-02
## tv 1.080555e-04 3.870429e-04 -1.824780e-04 -7.169192e-04
## periodico -1.983762e-03 1.079693e-04 7.787717e-04 -2.599398e-03
## radio 1.013933e-03 -2.139304e-04 3.246395e-05 -6.477805e-04
## tv:radio -9.976884e-06 -9.149524e-06 -1.450933e-06 4.497655e-05
## 77 78 79 80
## (Intercept) 2.905222e-02 4.019870e-03 2.568588e-02 1.421552e-02
## tv -2.130880e-04 -5.458614e-05 -2.185503e-05 -4.918203e-05
## periodico -7.403821e-04 -2.232754e-04 -2.760304e-03 3.913355e-05
## radio -5.918943e-04 4.600174e-04 1.115097e-03 -4.235220e-04
## tv:radio 8.015092e-06 -5.969221e-06 -8.794800e-06 1.929415e-06
## 81 82 83 84
## (Intercept) 8.345105e-03 -0.0067821677 4.921868e-03 5.786402e-03
## tv 5.611272e-05 0.0007153471 2.982240e-04 -1.629653e-05
## periodico -8.027705e-04 0.0005249677 -6.138538e-04 -1.299317e-03
## radio 4.748634e-04 -0.0001189448 2.863517e-04 8.282945e-04
## tv:radio -5.880627e-06 -0.0000177861 -8.593964e-06 -1.622635e-06
## 85 86 87 88
## (Intercept) -1.519683e-02 -2.826804e-02 9.478257e-03 6.974223e-03
## tv -1.910786e-05 1.351945e-03 -3.594829e-05 -1.952482e-04
## periodico 1.025334e-03 4.564215e-04 -7.790619e-04 -4.284174e-04
## radio 3.629865e-04 4.660880e-04 5.200097e-04 -1.561016e-04
## tv:radio -2.475481e-06 -3.065541e-05 -5.520579e-06 1.652708e-05
## 89 90 91 92
## (Intercept) -1.345947e-02 9.330950e-03 0.0324700557 1.006202e-02
## tv 1.012771e-03 -4.235054e-04 -0.0008446069 5.505147e-04
## periodico -5.531002e-04 -6.062119e-04 0.0003259917 -6.964193e-04
## radio 4.064257e-04 9.972553e-05 -0.0011152082 -6.211493e-05
## tv:radio -1.719827e-05 1.793239e-05 0.0000238975 -1.293978e-05
## 93 94 95 96
## (Intercept) -1.256167e-02 -1.359268e-02 0.0226058265 -8.511490e-03
## tv 2.324576e-04 2.954089e-05 -0.0004968032 3.095457e-04
## periodico 8.750905e-04 1.487577e-03 -0.0001259276 2.884192e-04
## radio -1.285566e-04 -5.994048e-04 -0.0004127950 1.131399e-04
## tv:radio 1.429484e-06 1.306496e-05 0.0000108430 -3.180198e-06
## 97 98 99 100
## (Intercept) 3.711720e-02 9.731099e-04 -1.776733e-02 -3.069311e-04
## tv -1.091431e-03 -1.998235e-05 -2.292064e-04 -9.846864e-05
## periodico 5.648330e-04 5.432246e-04 2.089219e-03 -1.506631e-04
## radio -1.392184e-03 -3.980793e-05 -3.976146e-04 2.434359e-04
## tv:radio 3.115892e-05 -2.490315e-06 1.179114e-05 5.777537e-06
## 101 102 103 104
## (Intercept) -0.0225338310 -1.477603e-02 6.267206e-03 7.047658e-03
## tv 0.0014546750 2.311872e-05 -1.364109e-04 -1.868757e-04
## periodico 0.0002772215 1.917001e-03 9.649938e-04 5.500812e-04
## radio 0.0004411293 -1.223760e-03 -5.802535e-04 -2.564949e-04
## tv:radio -0.0000376632 2.504818e-05 3.477592e-06 2.322845e-06
## 105 106 107 108
## (Intercept) -1.558435e-02 6.061965e-03 1.589634e-02 2.129270e-02
## tv 8.587482e-06 -5.184297e-04 2.939545e-04 -7.684510e-05
## periodico 1.254319e-03 1.638959e-04 -1.228174e-03 -1.836395e-04
## radio 5.918937e-04 -3.298746e-04 1.506589e-04 -6.501441e-04
## tv:radio -1.338196e-05 2.443714e-05 -7.469916e-06 4.553308e-06
## 109 110 111 112
## (Intercept) 2.590811e-02 -5.860740e-03 -3.061337e-02 -1.873313e-02
## tv 9.901391e-05 -2.685841e-04 1.618507e-03 8.171129e-05
## periodico -1.145511e-03 1.438678e-03 5.116632e-04 1.331667e-03
## radio -3.291804e-04 3.386971e-05 5.634858e-04 4.395652e-04
## tv:radio -2.575464e-07 -2.297405e-06 -4.137368e-05 -9.291272e-06
## 113 114 115 116
## (Intercept) 2.231473e-02 6.912750e-03 3.504508e-03 5.788955e-03
## tv -7.895689e-04 -3.409355e-04 -3.798319e-05 1.746561e-04
## periodico 5.461166e-04 7.116478e-04 -1.147878e-03 -1.078270e-03
## radio -6.343376e-04 -1.994109e-04 8.721890e-04 3.540657e-04
## tv:radio 1.686494e-05 3.836647e-06 -1.865400e-06 9.186797e-07
## 117 118 119 120
## (Intercept) 7.621529e-03 3.207311e-02 3.488765e-03 2.374971e-02
## tv 8.459774e-05 -6.124680e-04 2.447478e-05 2.781209e-06
## periodico -8.596092e-06 3.257176e-05 -2.820461e-04 -1.641919e-03
## radio -1.120090e-04 -1.059557e-03 -3.787301e-04 2.358820e-04
## tv:radio -3.007049e-06 1.919778e-05 1.640435e-05 -1.574375e-06
## 121 122 123 124
## (Intercept) -8.371459e-03 5.790768e-03 0.0246214091 -2.274499e-03
## tv 4.332533e-04 7.734642e-04 -0.0005429257 7.232554e-05
## periodico 1.637105e-04 -1.934250e-03 0.0005456834 -2.942816e-04
## radio 2.300489e-04 7.332680e-04 -0.0010511815 8.323972e-04
## tv:radio -9.110407e-06 -1.741039e-05 0.0000166963 -1.233571e-05
## 125 126 127 128
## (Intercept) -1.607822e-02 1.148430e-02 2.429210e-02 4.260889e-02
## tv 4.033877e-04 1.025161e-04 3.911501e-05 -9.904250e-04
## periodico 9.978288e-04 -3.138293e-04 -2.941077e-03 -5.357818e-05
## radio -2.999755e-04 -1.218035e-04 7.410967e-04 -1.345943e-03
## tv:radio 2.109399e-06 -2.888536e-06 4.259761e-06 2.996835e-05
## 129 130 131 132
## (Intercept) -4.184895e-02 -3.402105e-03 2.635875e-02 -1.680636e-02
## tv 6.013395e-04 8.549938e-04 3.083029e-04 1.100018e-03
## periodico 1.497795e-03 -6.492798e-04 -4.348106e-03 6.659311e-04
## radio 1.657051e-03 3.888761e-04 2.080201e-03 8.961022e-05
## tv:radio -3.768111e-05 -2.141744e-05 -2.206911e-05 -2.816220e-05
## 133 134 135 136
## (Intercept) 2.919608e-02 -1.279917e-02 1.695420e-02 -4.564049e-03
## tv -2.252402e-04 1.673414e-04 -4.276786e-05 4.917033e-04
## periodico -2.477061e-03 9.475913e-04 -1.769446e-03 -2.008844e-03
## radio 9.033091e-04 4.893695e-05 1.462112e-04 2.058374e-03
## tv:radio -4.357890e-06 -2.109586e-06 1.305045e-05 -3.052679e-05
## 137 138 139 140
## (Intercept) 7.785945e-03 -2.259615e-02 1.455876e-02 -2.706945e-02
## tv 2.373260e-04 5.011279e-04 3.022135e-05 4.306249e-04
## periodico -2.125303e-03 1.495386e-03 -1.362978e-03 6.901625e-04
## radio 1.550631e-03 -1.393280e-04 5.639112e-04 1.502992e-03
## tv:radio -1.977492e-05 -6.599755e-06 -5.442513e-06 -3.119953e-05
## 141 142 143 144
## (Intercept) 2.021770e-02 -0.0082726940 -1.402242e-02 1.684741e-03
## tv -3.387613e-04 0.0001422678 1.372529e-04 5.605453e-04
## periodico -4.729170e-04 0.0007072714 1.111116e-03 -7.458885e-05
## radio -1.266876e-04 -0.0004324584 1.105908e-04 -6.142670e-05
## tv:radio 5.712816e-06 0.0000109961 -4.031128e-06 -1.374589e-05
## 145 146 147 148
## (Intercept) -1.988298e-03 3.763194e-02 2.629464e-02 -1.543522e-02
## tv 6.006327e-04 -9.518722e-04 -8.125497e-04 -3.641218e-04
## periodico -3.106293e-04 2.526885e-04 7.436004e-04 1.733909e-03
## radio 2.359902e-04 -1.300774e-03 -1.074400e-03 -1.204526e-04
## tv:radio -1.515365e-05 2.809328e-05 2.194616e-05 1.218465e-05
## 149 150 151 152
## (Intercept) 4.032549e-03 1.333848e-02 -1.215693e-02 -1.696418e-02
## tv 2.496545e-04 2.789553e-05 5.157614e-04 1.229439e-03
## periodico -1.813651e-03 -1.219077e-03 1.047340e-03 4.097211e-05
## radio 1.497146e-03 5.288003e-04 -1.047118e-04 4.129589e-04
## tv:radio -1.947075e-05 -5.332999e-06 -1.315815e-05 -3.126069e-05
## 153 154 155 156
## (Intercept) 1.417535e-03 -8.470400e-03 7.947807e-03 4.992102e-02
## tv -1.866535e-04 1.392983e-05 -3.570342e-04 -7.440677e-04
## periodico 7.397711e-04 4.560804e-04 6.032608e-04 -2.263069e-03
## radio -2.669888e-05 3.267175e-04 -1.563842e-04 -2.323027e-04
## tv:radio -5.660540e-07 -1.153531e-06 3.807189e-06 1.812879e-05
## 157 158 159 160
## (Intercept) 7.782880e-03 1.604421e-02 1.980209e-02 -8.384909e-04
## tv -2.111356e-04 -1.006840e-05 1.294380e-04 3.752240e-04
## periodico -7.708311e-04 1.415707e-04 -2.639098e-03 -7.396010e-05
## radio 2.225489e-04 -6.333972e-04 8.090011e-04 1.596440e-04
## tv:radio 1.127609e-05 2.441521e-06 -6.920975e-07 -1.006745e-05
## 161 162 163 164
## (Intercept) -1.790463e-03 4.687859e-03 6.411912e-04 -0.0113002582
## tv 2.439765e-04 1.313246e-04 7.568468e-05 0.0001188405
## periodico 3.713792e-04 -9.227419e-04 5.275872e-04 0.0003582426
## radio 4.212692e-06 3.693030e-04 -1.009962e-04 0.0009174504
## tv:radio -7.238300e-06 7.849008e-07 -3.640183e-06 -0.0000166088
## 165 166 167 168
## (Intercept) 2.587324e-02 -7.225834e-02 1.468504e-02 1.665351e-02
## tv -6.912295e-04 3.553814e-03 1.679935e-04 -2.788362e-04
## periodico -3.379496e-05 1.830439e-04 -2.467258e-03 5.314855e-04
## radio -5.019177e-04 1.896643e-03 1.273809e-03 -7.620664e-04
## tv:radio 1.503164e-05 -9.459444e-05 -1.194893e-05 8.659777e-06
## 169 170 171 172
## (Intercept) -0.0202275264 2.145996e-02 2.443398e-02 -1.151739e-02
## tv 0.0007922543 -8.219371e-04 -2.153381e-04 6.798238e-04
## periodico 0.0007450594 1.060729e-03 -8.789036e-04 1.939887e-04
## radio 0.0001652481 -9.954035e-04 -2.009754e-04 2.591503e-04
## tv:radio -0.0000160912 2.053574e-05 5.026328e-06 -1.576635e-05
## 173 174 175 176
## (Intercept) 2.357564e-02 2.514494e-02 2.775837e-02 -2.110395e-02
## tv -1.232980e-04 -5.956261e-04 -6.696104e-04 -3.127074e-04
## periodico -1.578420e-03 3.189468e-04 4.748640e-04 2.179846e-03
## radio 3.275548e-04 -8.565763e-04 -1.086497e-03 -1.114754e-04
## tv:radio -3.579651e-07 1.637958e-05 1.978627e-05 9.318024e-06
## 177 178 179 180
## (Intercept) -1.266988e-02 -1.813647e-03 1.259792e-02 1.576661e-02
## tv 1.151397e-05 5.642261e-04 -5.266763e-05 -3.026122e-04
## periodico 1.330664e-03 1.672257e-04 5.600144e-04 3.789482e-04
## radio 1.699640e-04 -5.098358e-05 -7.132863e-04 -5.678584e-04
## tv:radio -6.420500e-06 -1.404644e-05 3.337299e-06 7.731302e-06
## 181 182 183 184
## (Intercept) 0.0375360999 6.249895e-03 1.182661e-02 -1.048364e-02
## tv -0.0009729864 1.664214e-04 3.134397e-04 -5.236678e-04
## periodico 0.0002714128 4.775732e-04 -5.206422e-04 2.277583e-03
## radio -0.0012900129 -4.447875e-04 -1.375444e-04 -1.088559e-03
## tv:radio 0.0000283698 -3.254349e-06 -7.157360e-06 3.015597e-05
## 185 186 187 188
## (Intercept) -8.785427e-03 -2.403901e-02 1.211205e-02 -4.594159e-03
## tv 1.827114e-04 1.806029e-04 1.331399e-04 -1.596352e-05
## periodico 1.083958e-03 1.153629e-03 1.389030e-04 6.161788e-04
## radio -7.791804e-05 8.700013e-04 -5.052878e-04 2.699566e-04
## tv:radio -6.285980e-06 -1.563611e-05 -1.664489e-06 -5.867028e-06
## 189 190 191 192
## (Intercept) 1.849131e-02 2.342024e-02 1.703599e-03 3.410062e-02
## tv -8.144124e-04 1.870478e-05 3.273062e-04 -8.016730e-04
## periodico 1.127997e-03 -1.399889e-03 -1.886755e-03 -3.617666e-04
## radio -8.439192e-04 5.865675e-05 1.728106e-03 -6.874994e-04
## tv:radio 1.843973e-05 -8.807575e-07 -2.479561e-05 1.995866e-05
## 193 194 195 196
## (Intercept) 1.595371e-02 -2.143367e-02 -8.586354e-03 3.609475e-02
## tv 4.487800e-04 3.311492e-04 8.016567e-05 -5.975327e-04
## periodico -1.218500e-03 4.979461e-04 2.356738e-04 -6.265249e-04
## radio 4.599813e-05 1.343107e-03 8.890881e-04 -8.052848e-04
## tv:radio -1.048754e-05 -2.656952e-05 -1.558263e-05 1.780196e-05
## 197 198 199 200
## (Intercept) 3.769835e-02 2.808613e-02 -1.282058e-02 0.0246735133
## tv -9.029173e-04 -8.561509e-04 -3.777848e-04 -0.0007715129
## periodico -8.300596e-05 5.274169e-04 2.132624e-03 0.0007233832
## radio -1.073063e-03 -9.693913e-04 -8.426392e-04 -0.0009870685
## tv:radio 2.548349e-05 2.210282e-05 2.311277e-05 0.0000202718#Cálculo de la Matriz P
matriz_p<-matriz_x%*%matriz_a
print(matriz_p)## 1 2 3 4 5
## 1 3.181459e-02 0.0037034602 0.0175878610 2.250872e-02 5.917854e-03
## 2 3.703460e-03 0.0246048049 0.0344728495 1.212022e-02 -4.597074e-04
## 3 1.758786e-02 0.0344728495 0.0676682205 2.641047e-02 -1.414709e-02
## 4 2.250872e-02 0.0121202208 0.0264104733 2.031981e-02 -1.677629e-03
## 5 5.917854e-03 -0.0004597074 -0.0141470892 -1.677629e-03 4.837246e-02
## 6 1.974129e-02 0.0415471420 0.0850681470 3.138114e-02 -2.300480e-02
## 7 -3.964913e-03 0.0151013072 0.0121764407 3.373267e-03 1.419930e-03
## 8 -1.607113e-03 0.0024432890 -0.0003834528 6.504267e-04 -3.653982e-03
## 9 -5.829162e-03 0.0063462287 0.0220657545 9.492958e-04 -2.413265e-02
## 10 1.421804e-03 -0.0036631551 -0.0033947436 -1.311471e-03 7.110009e-03
## 11 -2.168503e-03 0.0024857405 0.0022926063 -1.747623e-03 9.967185e-03
## 12 2.759271e-04 -0.0032037695 -0.0111934245 4.375016e-04 -6.719194e-03
## 13 1.107980e-02 0.0258646152 0.0428880590 1.626574e-02 8.010246e-03
## 14 -1.804019e-03 0.0008626337 0.0069060350 4.952366e-04 -1.195906e-02
## 15 1.554083e-02 0.0035749666 0.0042721338 1.126839e-02 9.198107e-03
## 16 2.621480e-02 0.0088688054 0.0227034141 2.278002e-02 -9.839149e-03
## 17 3.915388e-02 0.0256493572 0.0655093769 3.416510e-02 1.193130e-02
## 18 2.886666e-02 -0.0007202930 0.0064928948 1.950186e-02 2.531157e-03
## 19 -3.044620e-03 0.0071457201 0.0050758153 8.189455e-04 1.149745e-03
## 20 7.491250e-04 0.0032402654 -0.0015379015 1.968809e-03 2.059947e-03
## 21 1.615551e-02 0.0022716014 0.0017427388 9.949161e-03 1.871645e-02
## 22 3.433394e-03 -0.0054681525 -0.0078040763 -8.765953e-04 1.014826e-02
## 23 -4.316663e-03 0.0168062511 0.0144227775 -1.078210e-04 2.980589e-02
## 24 5.388466e-03 -0.0028238544 -0.0078571873 1.795623e-03 9.631299e-03
## 25 -2.842055e-03 0.0047916106 0.0053003997 -1.953947e-04 1.605219e-03
## 26 3.165795e-03 -0.0057765720 -0.0055901992 -6.057810e-04 4.805308e-03
## 27 -2.681876e-03 0.0056091483 -0.0020158956 1.115757e-03 -1.277872e-03
## 28 5.390598e-03 -0.0039360203 -0.0088022958 1.728407e-03 6.801279e-03
## 29 7.082428e-03 -0.0024483251 -0.0098140645 3.979545e-03 4.524996e-03
## 30 1.053252e-03 0.0069889995 0.0028884407 8.445642e-04 2.254848e-02
## 31 1.744206e-02 -0.0046387344 -0.0091074919 8.964771e-03 1.397943e-02
## 32 2.625373e-03 0.0051955492 0.0011305214 1.646147e-03 1.954280e-02
## 33 -7.829225e-05 -0.0022167758 -0.0064433622 -3.348367e-03 2.040057e-02
## 34 1.510274e-03 -0.0060880287 -0.0114263483 6.446965e-04 -1.144240e-02
## 35 8.416577e-04 -0.0028577552 0.0065243581 9.256259e-04 -1.376413e-02
## 36 4.178794e-03 -0.0073185847 -0.0020501923 1.300105e-03 -1.057639e-02
## 37 1.732765e-03 -0.0053479204 -0.0303344305 1.262853e-04 4.053882e-03
## 38 1.100707e-02 0.0239175299 0.0378695407 1.826930e-02 -1.140309e-02
## 39 -1.115782e-03 0.0150694185 0.0154985910 4.154417e-03 8.911453e-03
## 40 1.264104e-02 0.0008899392 -0.0040621941 9.336971e-03 2.863736e-03
## 41 7.313660e-03 -0.0007424149 -0.0060140321 3.768510e-03 1.136973e-02
## 42 9.811140e-03 0.0068675687 0.0063238146 9.004553e-03 6.311546e-03
## 43 2.207548e-03 -0.0072554645 -0.0201607339 2.723174e-04 -5.310161e-03
## 44 3.394473e-03 -0.0038024488 -0.0076354001 -5.124565e-04 1.280932e-02
## 45 -7.196211e-04 0.0180678107 0.0203916189 4.848410e-03 1.387028e-02
## 46 4.887768e-03 0.0026344608 -0.0015122830 3.422348e-03 1.078242e-02
## 47 6.364770e-04 0.0021011897 -0.0033398654 -1.340547e-03 2.260230e-02
## 48 7.218179e-03 -0.0011585876 -0.0148485246 5.349817e-03 1.695566e-03
## 49 8.581239e-03 -0.0007964303 -0.0091883803 1.954072e-03 3.235259e-02
## 50 -5.966116e-04 0.0051694004 0.0005973611 -9.760684e-04 2.219122e-02
## 51 2.124699e-03 -0.0043484704 -0.0119877971 -3.289900e-03 2.656568e-02
## 52 -1.623302e-03 0.0001020848 0.0056863913 8.084888e-04 -1.534792e-02
## 53 1.794312e-02 0.0024873711 0.0025554716 1.382880e-02 -1.551011e-05
## 54 2.781336e-02 0.0107309188 0.0285241240 2.436240e-02 -9.370305e-03
## 55 5.972562e-03 -0.0043581066 -0.0143310569 3.022021e-03 1.299242e-03
## 56 3.310110e-02 0.0085691126 0.0292305850 2.779753e-02 -1.470564e-02
## 57 -5.429990e-03 0.0253858461 0.0305803883 4.858263e-03 9.685108e-03
## 58 -3.563637e-04 0.0025162950 -0.0004207625 1.023629e-03 3.442756e-04
## 59 1.840577e-02 0.0056895900 0.0069264375 1.625436e-02 -6.457950e-03
## 60 7.718026e-04 -0.0010323673 -0.0117697000 1.148181e-03 -1.809726e-03
## 61 -1.921627e-03 0.0006979854 0.0025139247 -1.996278e-03 6.960573e-03
## 62 2.873016e-02 0.0018831118 0.0114454927 2.097276e-02 -2.291898e-03
## 63 6.115473e-03 -0.0041175800 -0.0095268177 1.582491e-03 1.131323e-02
## 64 -5.758882e-03 0.0073465166 -0.0008618847 -7.101528e-05 -3.165671e-03
## 65 5.449429e-03 0.0108369324 0.0071867691 8.676384e-03 -8.682326e-04
## 66 -3.613872e-03 0.0024431192 0.0100832760 7.278373e-04 -1.906002e-02
## 67 -1.161771e-02 0.0121155014 0.0085973604 -1.728730e-03 -9.352013e-03
## 68 5.469009e-04 -0.0014442658 -0.0020694491 7.813228e-04 -5.816314e-03
## 69 2.934147e-03 -0.0031759488 -0.0129470052 1.700562e-03 -1.368084e-03
## 70 1.030267e-02 0.0032133517 -0.0042415718 9.177453e-03 -1.750268e-04
## 71 1.150713e-02 0.0025518083 0.0000402868 8.201520e-03 9.130784e-03
## 72 2.349486e-03 0.0015927828 -0.0027003456 5.687564e-04 1.552351e-02
## 73 -9.978274e-03 0.0205623129 0.0179995065 1.548324e-03 -4.663288e-04
## 74 1.333042e-03 -0.0018627594 -0.0069135842 -2.118511e-03 2.009795e-02
## 75 2.111718e-03 -0.0013298794 -0.0084317867 1.664044e-03 -1.078586e-03
## 76 2.743539e-02 0.0362243559 0.0808056666 3.321476e-02 -1.269759e-02
## 77 -3.463964e-03 0.0026867197 0.0057266833 -2.190870e-03 5.719769e-03
## 78 -2.917267e-03 0.0067346299 0.0002880732 1.272770e-03 -8.449312e-04
## 79 -1.768365e-02 0.0242281819 0.0217083151 -1.853458e-03 -4.702395e-03
## 80 7.147327e-04 -0.0008202598 -0.0021312910 -7.675508e-04 8.490997e-03
## 81 -2.945595e-03 0.0107661079 0.0078586718 2.180415e-03 2.685843e-03
## 82 3.301367e-03 -0.0052594894 -0.0143612386 -3.106977e-03 2.926354e-02
## 83 3.371442e-04 0.0080091104 0.0056872082 2.074552e-03 1.209165e-02
## 84 3.008872e-03 0.0212144913 0.0254307236 1.108387e-02 -4.004360e-03
## 85 1.338641e-02 0.0044826317 0.0018014995 1.166449e-02 -7.270034e-04
## 86 1.280438e-02 0.0014341410 -0.0064509846 4.448956e-03 4.227214e-02
## 87 -5.010777e-03 0.0104062858 0.0060499645 1.101041e-03 -5.368574e-04
## 88 2.132525e-02 0.0168712816 0.0348646588 2.110973e-02 -1.216796e-03
## 89 1.477712e-02 0.0119540647 0.0155312148 1.078879e-02 3.209347e-02
## 90 1.730354e-02 0.0196293652 0.0359622466 2.078517e-02 -1.083455e-02
## 91 1.582923e-03 -0.0037024430 0.0017972966 7.708485e-04 -9.621315e-03
## 92 -3.428544e-03 0.0022714935 -0.0022748569 -4.445140e-03 2.439605e-02
## 93 2.174365e-02 0.0045044969 0.0103322401 1.537059e-02 1.181572e-02
## 94 3.284429e-02 0.0028105239 0.0163342165 2.246580e-02 9.089004e-03
## 95 -1.796909e-03 0.0018859775 0.0025491337 3.619854e-04 -5.651231e-03
## 96 1.524119e-02 0.0072582994 0.0106996491 1.192185e-02 1.250268e-02
## 97 2.952671e-03 -0.0057179048 0.0019451929 1.502198e-03 -1.471907e-02
## 98 3.576789e-03 -0.0002569184 -0.0051082293 2.193005e-03 4.813121e-03
## 99 2.835628e-02 -0.0011039459 0.0050339774 1.954114e-02 -1.059394e-03
## 100 1.386391e-02 0.0134925461 0.0210193258 1.515811e-02 -1.727939e-03
## 101 2.413055e-03 -0.0034638990 -0.0187006193 -5.084294e-03 4.700460e-02
## 102 4.845143e-02 0.0025058317 0.0281586535 3.201733e-02 1.388520e-02
## 103 5.316900e-03 -0.0064891634 -0.0097834932 5.771213e-04 6.675879e-03
## 104 2.653151e-03 -0.0016227621 -0.0051715226 1.310801e-03 1.925084e-03
## 105 9.995288e-05 -0.0026092937 -0.0187224118 2.366563e-04 -9.499388e-04
## 106 2.526116e-02 0.0147343483 0.0342491339 2.418343e-02 -1.024973e-02
## 107 -4.749254e-03 0.0090616684 0.0079997782 -1.454019e-03 1.413553e-02
## 108 -7.485001e-04 -0.0015631086 -0.0010986470 -2.450001e-03 1.028630e-02
## 109 -5.672610e-03 0.0050670562 0.0061879253 -3.708917e-03 1.319585e-02
## 110 2.618834e-03 -0.0057525446 -0.0168470426 8.908024e-04 -4.070336e-03
## 111 5.771231e-03 -0.0034843573 -0.0194326500 -3.153845e-03 5.049834e-02
## 112 8.662951e-03 -0.0003918361 -0.0100643251 6.388678e-03 2.104422e-03
## 113 -1.175903e-04 -0.0026527589 -0.0027944289 7.764986e-04 -1.296498e-02
## 114 1.545444e-03 -0.0020989660 -0.0070448430 1.167366e-03 -3.551416e-03
## 115 3.597274e-03 0.0208242719 0.0242968873 1.156126e-02 -5.278239e-03
## 116 9.832110e-03 0.0179950102 0.0270385248 1.290082e-02 6.482524e-03
## 117 1.186060e-03 0.0016157498 -0.0013020365 5.203164e-04 9.344844e-03
## 118 5.756822e-04 -0.0028243277 0.0023639602 -5.306074e-04 -2.609638e-03
## 119 2.754303e-02 0.0158507594 0.0373582172 2.369485e-02 7.535961e-03
## 120 -7.546088e-03 0.0132788805 0.0144917051 -5.249320e-04 4.285915e-03
## 121 1.009288e-02 0.0057642174 0.0047557273 7.492325e-03 1.578081e-02
## 122 -1.256304e-03 0.0185165393 0.0196801293 3.474396e-03 2.294746e-02
## 123 3.049405e-03 -0.0059078442 -0.0030689587 -1.193038e-04 -8.682083e-04
## 124 -4.575825e-03 0.0087758902 -0.0010304012 1.086659e-03 -6.374068e-04
## 125 2.806683e-02 0.0044417069 0.0140972012 1.868722e-02 1.844232e-02
## 126 -5.171007e-04 0.0029373475 0.0008912172 -3.336806e-04 1.028551e-02
## 127 1.157018e-03 0.0321442097 0.0472168338 1.306949e-02 -6.729220e-04
## 128 4.007523e-04 -0.0023952609 0.0070207827 4.954016e-04 -1.155764e-02
## 129 -3.063197e-03 -0.0008164906 -0.0300466960 -1.564617e-03 6.720754e-03
## 130 9.101935e-05 0.0057275248 -0.0004660127 -1.081664e-03 2.884528e-02
## 131 -2.749573e-02 0.0376788482 0.0325690011 -3.453268e-03 -3.180179e-03
## 132 3.753654e-03 -0.0066637251 -0.0198491583 -4.475979e-03 3.923051e-02
## 133 -1.838769e-02 0.0210523137 0.0181502824 -3.028304e-03 -8.904895e-03
## 134 1.605427e-02 0.0027870035 0.0031460750 1.144497e-02 8.395455e-03
## 135 1.455353e-02 0.0255002355 0.0457574120 1.928658e-02 1.440959e-03
## 136 -1.697786e-02 0.0235072770 0.0082063393 -1.706439e-03 1.213916e-03
## 137 -1.587288e-02 0.0222763337 0.0127398327 -1.384722e-03 -1.496246e-03
## 138 2.259996e-02 -0.0016164633 -0.0013490171 1.268489e-02 2.029286e-02
## 139 -6.392195e-03 0.0142620123 0.0125490053 1.251770e-03 1.398814e-03
## 140 -6.815004e-03 0.0032980248 -0.0210629548 -2.415945e-03 3.536289e-03
## 141 -3.521477e-03 0.0051679782 0.0047001842 2.214570e-04 -3.431624e-03
## 142 2.961916e-02 0.0079934056 0.0232914067 2.184108e-02 1.142445e-02
## 143 1.366700e-02 0.0009246100 -0.0019237993 9.390502e-03 6.978404e-03
## 144 5.481730e-04 -0.0005880946 -0.0067065339 -2.650943e-03 2.412517e-02
## 145 1.992701e-03 0.0042853267 -0.0006231371 5.364973e-04 2.207252e-02
## 146 1.662813e-03 -0.0039965892 0.0036727348 7.749480e-04 -1.102708e-02
## 147 3.293329e-03 -0.0059438071 -0.0026066580 1.167379e-03 -9.327458e-03
## 148 2.500593e-02 0.0030381808 0.0086854932 1.980499e-02 -7.948305e-03
## 149 -1.311176e-02 0.0207572750 0.0112517037 -1.254037e-04 -8.951488e-04
## 150 -5.633951e-03 0.0132476482 0.0112425775 1.372099e-03 1.588896e-03
## 151 8.303315e-03 -0.0054408202 -0.0133350243 1.275566e-03 2.204423e-02
## 152 2.857885e-03 -0.0002684596 -0.0118643771 -2.756187e-03 4.010683e-02
## 153 2.360179e-03 -0.0013594731 -0.0076637006 1.713795e-03 -5.853487e-04
## 154 1.190548e-02 0.0076965145 0.0080635833 1.148842e-02 1.027533e-03
## 155 6.204743e-04 -0.0012784462 -0.0062521988 9.613227e-04 -4.408604e-03
## 156 -1.294278e-02 0.0158301580 0.0243132109 -1.267765e-03 -1.380081e-02
## 157 1.404482e-02 0.0189762695 0.0320652195 1.760593e-02 -4.975580e-03
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## 16 17 18 19 20
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## 200 4.133526e-03 -0.0057813367 4.979911e-03 6.099116e-03 6.161945e-03
## 21 22 23 24 25
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## 25 -0.0001151089 0.0081666766 7.267461e-03 4.731310e-03 9.724786e-03
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## 26 27 28 29 30
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## 8 7.468359e-03 8.410255e-03 6.386626e-03 0.0063695481 1.615869e-03
## 9 1.836383e-02 2.614513e-03 4.145275e-03 -0.0035904520 -2.425530e-03
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## 19 5.068960e-03 7.534912e-03 4.112657e-03 0.0036836833 5.083373e-03
## 20 4.636249e-03 8.414174e-03 6.033217e-03 0.0072957949 3.390148e-03
## 21 3.087262e-03 1.200211e-03 6.055112e-03 0.0070906034 8.261421e-03
## 22 1.474925e-02 1.544657e-03 9.466693e-03 0.0053780675 6.444902e-03
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## 24 8.826180e-03 4.708863e-03 8.548827e-03 0.0080676621 5.200165e-03
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## 26 1.649318e-02 1.392853e-03 9.615916e-03 0.0048540604 4.442518e-03
## 27 1.392853e-03 1.193472e-02 5.196972e-03 0.0084226747 2.223717e-03
## 28 9.615916e-03 5.196972e-03 9.112153e-03 0.0087336070 3.714407e-03
## 29 4.854060e-03 8.422675e-03 8.733607e-03 0.0116867157 1.601300e-03
## 30 4.442518e-03 2.223717e-03 3.714407e-03 0.0016013005 1.411203e-02
## 31 5.068045e-03 3.655200e-03 9.469031e-03 0.0120623597 3.862780e-03
## 32 4.891569e-03 2.835077e-03 4.626500e-03 0.0031458237 1.198571e-02
## 33 1.349390e-02 6.500463e-05 7.749716e-03 0.0023611749 1.244438e-02
## 34 1.073634e-02 1.056789e-02 1.056304e-02 0.0120302513 -4.642016e-03
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## 50 6.654126e-03 1.934209e-03 4.499966e-03 0.0014134117 1.411693e-02
## 51 1.241888e-02 5.160082e-05 8.733363e-03 0.0043280289 1.384222e-02
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## 93 2.119956e-03 2.546840e-04 5.075333e-03 0.0067040616 4.987314e-03
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## 98 6.792857e-03 6.783954e-03 7.535621e-03 0.0081581992 3.599084e-03
## 99 2.246862e-03 3.385895e-03 8.071542e-03 0.0130121844 -3.846733e-03
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## 103 1.339358e-02 3.305766e-03 1.012650e-02 0.0078150686 3.820193e-03
## 104 9.265358e-03 6.286489e-03 8.119356e-03 0.0076552616 2.611416e-03
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## 108 1.562581e-02 2.016275e-04 7.496995e-03 0.0012689932 8.799299e-03
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## 81 82 83 84 85
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## 86 87 88 89 90
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## 41 1.082152e-02 3.115837e-03 1.857885e-03 6.306648e-03 7.455343e-04
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## 46 9.878857e-03 4.525371e-03 2.641765e-03 7.156929e-03 1.911375e-03
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## 96 97 98 99 100
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## 101 102 103 104 105
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## 14 -8.079471e-03 -3.944601e-03 1.042585e-02 9.215685e-03 4.105078e-04
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## 16 -1.336659e-02 3.421927e-02 1.763952e-03 3.110249e-03 7.432914e-03
## 17 5.763761e-03 7.154346e-02 -3.948586e-03 -7.076034e-03 -3.309795e-02
## 18 -3.536735e-04 4.017641e-02 6.907654e-03 5.017520e-03 9.369368e-03
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## 111 112 113 114 115
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## 200 -7.925671e-03 0.0029071784 0.0185699756 1.205482e-02 -0.0048462531
## 116 117 118 119 120
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## 2 1.799501e-02 1.615750e-03 -2.824328e-03 1.585076e-02 1.327888e-02
## 3 2.703852e-02 -1.302036e-03 2.363960e-03 3.735822e-02 1.449171e-02
## 4 1.290082e-02 5.203164e-04 -5.306074e-04 2.369485e-02 -5.249320e-04
## 5 6.482524e-03 9.344844e-03 -2.609638e-03 7.535961e-03 4.285915e-03
## 6 3.180769e-02 -2.601125e-03 4.968035e-03 4.493668e-02 1.789710e-02
## 7 9.491255e-03 3.516413e-03 -1.891368e-03 9.579008e-04 1.096383e-02
## 8 7.303542e-04 5.610335e-03 8.995916e-03 -3.643754e-03 6.373981e-03
## 9 1.533380e-03 7.423331e-03 2.943223e-02 1.398534e-03 1.636333e-02
## 10 -9.667932e-04 8.866910e-03 1.773738e-02 9.374508e-04 6.930846e-03
## 11 2.925035e-03 8.523146e-03 1.408067e-02 1.761337e-03 1.084365e-02
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## 33 1.174729e-02 9.351140e-03 7.005350e-03 -3.904820e-03 7.904232e-03
## 34 9.015069e-03 1.467482e-02 1.775113e-02 7.459635e-03 1.740919e-02
## 35 2.477805e-02 2.898993e-02 2.563292e-02 3.703492e-03 2.466458e-02
## 36 2.031493e-02 2.544962e-02 2.435557e-02 8.616494e-03 2.403445e-02
## 37 -1.417949e-02 -1.034386e-02 -4.170540e-04 7.613247e-03 3.958037e-04
## 38 -1.413527e-05 -2.634468e-04 -1.275989e-03 1.181677e-02 -2.946878e-03
## 39 3.975805e-03 3.991780e-04 -1.806504e-03 -5.379200e-03 -2.457031e-03
## 40 -5.379539e-03 -2.690818e-03 2.147554e-03 1.705747e-02 2.781250e-03
## 41 1.399233e-03 1.816670e-03 3.744873e-03 8.139229e-03 4.575367e-03
## 42 -1.629401e-03 -1.564801e-03 1.639116e-04 1.075797e-02 4.206450e-04
## 43 6.313392e-04 5.901644e-03 1.171250e-02 8.456022e-03 1.192778e-02
## 44 9.421081e-03 9.428050e-03 9.046062e-03 2.764068e-03 9.841313e-03
## 45 4.010498e-03 -1.322951e-03 -4.819278e-03 -6.987069e-03 -5.393243e-03
## 46 2.435476e-03 1.937177e-03 2.829959e-03 4.477087e-03 3.307859e-03
## 47 6.441091e-03 2.967649e-03 1.326991e-03 -3.875067e-03 2.191046e-03
## 48 -9.246851e-03 -5.898517e-03 1.223112e-03 1.244258e-02 1.783342e-03
## 49 -1.682784e-03 -5.448410e-03 -4.720105e-03 4.799662e-03 -2.731904e-03
## 50 6.271230e-03 2.083174e-03 -1.295644e-04 -5.944055e-03 4.781771e-04
## 51 7.690785e-03 4.918011e-03 3.841501e-03 -1.713128e-03 5.340175e-03
## 52 2.012431e-02 2.413899e-02 2.210507e-02 1.347911e-03 2.086100e-02
## 53 -5.910656e-03 -2.598434e-03 2.177385e-03 2.344497e-02 2.784526e-03
## 54 -1.189063e-03 2.471569e-03 4.166947e-03 3.396559e-02 4.094757e-03
## 55 -1.102155e-03 2.430436e-03 7.330008e-03 1.056744e-02 7.874086e-03
## 56 -1.621917e-03 4.079829e-03 6.841677e-03 4.193539e-02 6.851338e-03
## 57 5.992234e-03 -6.460610e-04 -5.984526e-03 -1.352160e-02 -7.442149e-03
## 58 8.117947e-03 9.133538e-03 9.268229e-03 2.466565e-04 8.924368e-03
## 59 -7.997415e-03 -3.889005e-03 1.610456e-03 2.511751e-02 1.752034e-03
## 60 1.377004e-04 3.109953e-03 7.295266e-03 4.389435e-03 7.251740e-03
## 61 1.738405e-02 1.664814e-02 1.304380e-02 -4.326975e-03 1.291604e-02
## 62 -4.557998e-03 1.777621e-06 4.250486e-03 3.612766e-02 5.178435e-03
## 63 4.996647e-03 5.896381e-03 7.320902e-03 7.067351e-03 8.246775e-03
## 64 2.893973e-03 3.525318e-03 5.079964e-03 -5.332599e-03 4.143320e-03
## 65 -4.897986e-03 -4.296119e-03 -1.313656e-03 7.172358e-03 -1.774256e-03
## 66 2.239014e-02 2.634758e-02 2.339024e-02 -9.702761e-04 2.169655e-02
## 67 9.981624e-03 9.905198e-03 8.562241e-03 -1.286984e-02 6.663549e-03
## 68 1.256076e-02 1.558591e-02 1.563361e-02 3.103285e-03 1.518312e-02
## 69 9.203270e-04 4.396976e-03 8.664494e-03 7.149415e-03 8.846647e-03
## 70 -8.224687e-03 -5.390167e-03 3.964784e-04 1.506782e-02 6.936449e-04
## 71 -2.055454e-03 -1.421223e-03 1.116046e-03 1.317201e-02 1.855845e-03
## 72 5.938284e-03 4.253722e-03 3.643252e-03 7.568608e-05 4.260833e-03
## 73 3.812616e-03 3.609556e-04 -1.708940e-03 -1.443131e-02 -3.513069e-03
## 74 9.086122e-03 6.954027e-03 5.508030e-03 -1.865877e-03 6.472774e-03
## 75 3.542998e-03 6.273998e-03 9.112472e-03 5.204443e-03 9.115111e-03
## 76 1.158195e-02 8.920932e-03 1.232099e-04 2.543245e-02 -1.943756e-03
## 77 1.870394e-02 1.756234e-02 1.318401e-02 -6.508350e-03 1.278663e-02
## 78 2.966965e-03 3.429119e-03 4.735469e-03 -2.563344e-03 4.062614e-03
## 79 8.082761e-03 3.848808e-03 6.104208e-05 -2.376769e-02 -2.560535e-03
## 80 1.236571e-02 1.219806e-02 1.057775e-02 -4.658005e-04 1.081410e-02
## 81 4.475134e-03 3.106172e-03 2.494978e-03 -4.817113e-03 1.719997e-03
## 82 5.731123e-03 2.815571e-03 2.350825e-03 -4.876554e-04 4.122238e-03
## 83 4.992763e-03 2.445129e-03 1.124730e-03 -2.856864e-03 1.110399e-03
## 84 -1.331465e-03 -2.954739e-03 -3.342601e-03 1.851768e-03 -4.764306e-03
## 85 -6.451328e-03 -3.725482e-03 1.033587e-03 1.804685e-02 1.312873e-03
## 86 -5.983139e-03 -1.182288e-02 -1.126339e-02 7.210844e-03 -8.675354e-03
## 87 4.703455e-03 3.959111e-03 3.783700e-03 -6.276611e-03 2.785111e-03
## 88 1.290122e-03 1.128125e-03 -2.271618e-04 2.251976e-02 -5.711478e-04
## 89 -3.061161e-03 -9.312211e-03 -1.130130e-02 8.733731e-03 -9.851419e-03
## 90 1.639766e-04 1.220692e-03 8.557859e-04 1.988417e-02 -2.774461e-04
## 91 2.038595e-02 2.427483e-02 2.228821e-02 4.475725e-03 2.168748e-02
## 92 1.147580e-02 6.947977e-03 3.323301e-03 -9.839203e-03 4.017135e-03
## 93 -3.105735e-03 -2.763574e-03 -9.832738e-04 2.371699e-02 1.882938e-04
## 94 -3.430136e-03 -1.342442e-03 8.405232e-04 3.744694e-02 2.420491e-03
## 95 1.381920e-02 1.576789e-02 1.462080e-02 -6.832004e-04 1.385745e-02
## 96 -1.791537e-03 -2.778341e-03 -1.975717e-03 1.524478e-02 -1.218565e-03
## 97 2.278808e-02 2.817049e-02 2.626918e-02 7.430230e-03 2.554904e-02
## 98 4.551415e-03 5.786632e-03 7.280060e-03 4.906501e-03 7.549799e-03
## 99 -5.921436e-03 -8.388031e-04 4.511740e-03 3.641856e-02 5.696831e-03
## 100 -1.615125e-03 -1.143814e-03 -2.577863e-04 1.562071e-02 -6.566708e-04
## 101 -6.433378e-04 -7.395234e-03 -7.814687e-03 -5.356544e-03 -5.187640e-03
## 102 -3.136733e-03 -9.961165e-04 1.944791e-05 5.388402e-02 2.462691e-03
## 103 9.749317e-03 1.181750e-02 1.255673e-02 7.142597e-03 1.328136e-02
## 104 7.818964e-03 9.705121e-03 1.064555e-02 4.389209e-03 1.076087e-02
## 105 -4.426292e-03 -9.787455e-04 5.234013e-03 4.621624e-03 5.387286e-03
## 106 1.804682e-04 2.805999e-03 3.228548e-03 3.001155e-02 2.739297e-03
## 107 1.079481e-02 6.805831e-03 3.013540e-03 -1.040399e-02 2.732980e-03
## 108 1.666354e-02 1.588397e-02 1.267498e-02 -3.123288e-03 1.291282e-02
## 109 1.733750e-02 1.397547e-02 8.802557e-03 -1.128935e-02 8.569469e-03
## 110 1.374763e-03 5.993681e-03 1.101364e-02 8.080099e-03 1.120025e-02
## 111 -4.416974e-03 -1.142137e-02 -1.092778e-02 -1.789757e-03 -7.925671e-03
## 112 -6.332870e-03 -3.369004e-03 2.370094e-03 1.326194e-02 2.907178e-03
## 113 1.408324e-02 1.877767e-02 1.935624e-02 4.220338e-03 1.856998e-02
## 114 7.074442e-03 1.022932e-02 1.221369e-02 4.781992e-03 1.205482e-02
## 115 -2.611680e-03 -3.737883e-03 -3.431092e-03 3.164513e-03 -4.846253e-03
## 116 1.361305e-03 -1.484169e-03 -3.547617e-03 7.280349e-03 -4.026660e-03
## 117 8.155674e-03 7.555194e-03 6.832261e-03 -6.247819e-05 7.054076e-03
## 118 2.092848e-02 2.299820e-02 1.985900e-02 1.234412e-03 1.950529e-02
## 119 1.119271e-03 -2.535255e-04 -2.510590e-03 2.762080e-02 -2.107428e-03
## 120 1.210189e-02 8.938961e-03 4.850944e-03 -1.240546e-02 3.682984e-03
## 121 -7.623594e-04 -2.508467e-03 -1.905940e-03 8.816007e-03 -1.111654e-03
## 122 3.588390e-03 -3.804403e-03 -8.234336e-03 -9.939868e-03 -8.395585e-03
## 123 1.823937e-02 2.102873e-02 1.934921e-02 4.867422e-03 1.941917e-02
## 124 -1.062938e-03 -9.540518e-04 1.428652e-03 -4.328242e-03 6.470179e-04
## 125 -3.930177e-03 -4.518001e-03 -3.388553e-03 2.933668e-02 -1.619808e-03
## 126 9.915759e-03 8.559054e-03 6.818691e-03 -2.878812e-03 6.907248e-03
## 127 5.439258e-03 -1.190773e-04 -5.957615e-03 -5.146056e-03 -8.085890e-03
## 128 2.508403e-02 2.866106e-02 2.485081e-02 2.470889e-03 2.394137e-02
## 129 -1.796013e-02 -1.582550e-02 -5.660804e-03 9.810847e-04 -5.115503e-03
## 130 3.807550e-03 -1.719234e-03 -3.899144e-03 -6.574401e-03 -2.922127e-03
## 131 4.137626e-03 -4.003556e-03 -9.291546e-03 -3.810081e-02 -1.298511e-02
## 132 2.328551e-03 -2.115358e-03 -2.085173e-03 -1.542494e-03 3.508179e-04
## 133 1.038184e-02 7.597399e-03 4.189562e-03 -2.305756e-02 1.486281e-03
## 134 -3.214817e-03 -2.096011e-03 7.305307e-04 1.863227e-02 1.617438e-03
## 135 4.123548e-03 6.785578e-04 -3.831900e-03 1.142843e-02 -4.894610e-03
## 136 -6.988472e-03 -1.119262e-02 -9.804430e-03 -2.166381e-02 -1.178674e-02
## 137 -3.636299e-04 -4.093926e-03 -4.655179e-03 -2.055398e-02 -6.772509e-03
## 138 -5.168151e-03 -4.976423e-03 -1.936560e-03 2.450912e-02 1.098194e-04
## 139 6.425761e-03 4.129821e-03 2.226498e-03 -9.644611e-03 1.000212e-03
## 140 -1.191357e-02 -1.076046e-02 -3.358538e-03 -4.584451e-03 -3.483451e-03
## 141 1.177158e-02 1.249242e-02 1.115813e-02 -3.704641e-03 1.027131e-02
## 142 -1.972771e-03 -1.942403e-03 -1.676481e-03 3.159115e-02 -4.539410e-04
## 143 -3.480500e-03 -1.750956e-03 1.866835e-03 1.683383e-02 2.710096e-03
## 144 7.924247e-03 4.655080e-03 2.928069e-03 -3.908181e-03 4.005257e-03
## 145 4.039069e-03 4.186259e-04 -8.275408e-04 -2.369074e-03 -2.950711e-05
## 146 2.303812e-02 2.711409e-02 2.434929e-02 4.539596e-03 2.365196e-02
## 147 1.787811e-02 2.253239e-02 2.192672e-02 7.359953e-03 2.159187e-02
## 148 -7.105927e-03 -1.672307e-03 4.033447e-03 3.349377e-02 4.507054e-03
## 149 -1.760705e-03 -4.974445e-03 -4.819840e-03 -1.694479e-02 -6.679730e-03
## 150 6.142709e-03 4.118839e-03 2.513245e-03 -8.519564e-03 1.394203e-03
## 151 1.861074e-03 1.144601e-03 2.792903e-03 7.710840e-03 4.479536e-03
## 152 2.452471e-04 -5.825531e-03 -6.591445e-03 -4.103461e-03 -4.506511e-03
## 153 4.336289e-03 6.928131e-03 9.410032e-03 5.230031e-03 9.434620e-03
## 154 -3.662001e-03 -2.378456e-03 4.263950e-04 1.459666e-02 4.857306e-04
## 155 7.221291e-03 1.029228e-02 1.215676e-02 3.712665e-03 1.186525e-02
## 156 2.251969e-02 2.152354e-02 1.511031e-02 -1.639596e-02 1.248109e-02
## 157 4.100796e-04 1.336570e-04 -6.941688e-04 1.484860e-02 -1.625540e-03
## 158 1.476229e-02 1.432914e-02 1.204660e-02 -8.265488e-04 1.258912e-02
## 159 4.489160e-03 -8.120714e-04 -5.667438e-03 -6.872365e-03 -7.530079e-03
## 160 3.854142e-03 1.866089e-03 1.501728e-03 8.288652e-04 2.054584e-03
## 161 4.044893e-03 3.521478e-03 4.132994e-03 3.882513e-03 4.803273e-03
## 162 8.937973e-04 -1.358271e-03 -2.801525e-03 7.544691e-03 -3.299627e-03
## 163 5.135749e-03 5.732473e-03 6.722761e-03 4.741988e-03 7.228391e-03
## 164 -4.391094e-03 -3.026393e-03 1.589560e-03 -1.944009e-03 1.181509e-03
## 165 1.498786e-02 1.808368e-02 1.724365e-02 -3.449861e-05 1.621487e-02
## 166 -1.963698e-02 -3.615782e-02 -3.516245e-02 -1.567961e-02 -2.965379e-02
## 167 2.355172e-03 -2.119203e-03 -4.685481e-03 -1.683171e-02 -6.853935e-03
## 168 1.446739e-02 1.615993e-02 1.510019e-02 3.818298e-03 1.544370e-02
## 169 -3.842164e-03 -6.412134e-03 -5.041279e-03 1.341917e-02 -3.133927e-03
## 170 1.554433e-02 2.102893e-02 2.174193e-02 9.386951e-03 2.149889e-02
## 171 1.429568e-02 1.337909e-02 1.023595e-02 -6.699207e-03 9.430911e-03
## 172 -5.076786e-04 -3.485054e-03 -3.211776e-03 5.481202e-03 -1.954418e-03
## 173 1.107181e-02 8.857058e-03 5.607704e-03 -1.207440e-02 4.142301e-03
## 174 1.701631e-02 1.986704e-02 1.842421e-02 3.413224e-03 1.809585e-02
## 175 1.911696e-02 2.240219e-02 2.062438e-02 4.920083e-03 2.043247e-02
## 176 -8.789158e-03 -2.668765e-03 4.314646e-03 3.500677e-02 5.123925e-03
## 177 -2.096902e-03 9.088202e-04 5.634827e-03 1.131120e-02 6.242499e-03
## 178 6.337738e-03 3.571351e-03 2.627698e-03 -1.393650e-03 3.846531e-03
## 179 1.365846e-02 1.424080e-02 1.299410e-02 2.712689e-03 1.375934e-02
## 180 1.276425e-02 1.451560e-02 1.385951e-02 3.042924e-03 1.390666e-02
## 181 2.284714e-02 2.709255e-02 2.447452e-02 4.744268e-03 2.373657e-02
## 182 1.036419e-02 9.921744e-03 9.097706e-03 1.715641e-03 1.002858e-02
## 183 1.132083e-02 8.357199e-03 5.463235e-03 -6.377245e-03 5.858535e-03
## 184 -2.888532e-03 3.230155e-03 6.989230e-03 5.105409e-02 8.374721e-03
## 185 1.364813e-03 2.577639e-03 5.159809e-03 1.020090e-02 6.188788e-03
## 186 -1.035848e-02 -7.743512e-03 -9.563446e-04 1.039988e-02 -6.970136e-04
## 187 1.305049e-02 1.199587e-02 9.943856e-03 -1.382094e-03 1.066165e-02
## 188 5.677723e-04 2.343396e-03 5.352154e-03 5.087110e-03 5.406410e-03
## 189 1.364423e-02 1.943281e-02 2.096651e-02 9.166342e-03 2.064303e-02
## 190 1.321126e-02 1.024528e-02 6.114453e-03 -1.102395e-02 5.263005e-03
## 191 -2.990985e-03 -6.463162e-03 -5.756553e-03 -2.110224e-02 -7.724849e-03
## 192 1.876344e-02 2.152134e-02 1.913349e-02 -1.577109e-03 1.785920e-02
## 193 1.252097e-02 7.578515e-03 3.032662e-03 -1.263643e-02 3.141098e-03
## 194 -9.466564e-03 -8.394604e-03 -2.031127e-03 -4.277370e-03 -2.317405e-03
## 195 -3.194970e-03 -1.912919e-03 2.284372e-03 -3.253962e-03 1.749381e-03
## 196 2.101662e-02 2.193810e-02 1.782144e-02 -3.763698e-03 1.690727e-02
## 197 2.193810e-02 2.533300e-02 2.239450e-02 1.594227e-03 2.140903e-02
## 198 1.782144e-02 2.239450e-02 2.165793e-02 5.598310e-03 2.102198e-02
## 199 -3.763698e-03 1.594227e-03 5.598310e-03 4.542387e-02 6.952453e-03
## 200 1.690727e-02 2.140903e-02 2.102198e-02 6.952453e-03 2.068263e-02n<-nrow(matriz_x)
#Calculo de la Matriz M
matriz_m<-diag(n)-matriz_p
print(matriz_m)## 1 2 3 4 5
## 1 9.681854e-01 -0.0037034602 -0.0175878610 -2.250872e-02 -5.917854e-03
## 2 -3.703460e-03 0.9753951951 -0.0344728495 -1.212022e-02 4.597074e-04
## 3 -1.758786e-02 -0.0344728495 0.9323317795 -2.641047e-02 1.414709e-02
## 4 -2.250872e-02 -0.0121202208 -0.0264104733 9.796802e-01 1.677629e-03
## 5 -5.917854e-03 0.0004597074 0.0141470892 1.677629e-03 9.516275e-01
## 6 -1.974129e-02 -0.0415471420 -0.0850681470 -3.138114e-02 2.300480e-02
## 7 3.964913e-03 -0.0151013072 -0.0121764407 -3.373267e-03 -1.419930e-03
## 8 1.607113e-03 -0.0024432890 0.0003834528 -6.504267e-04 3.653982e-03
## 9 5.829162e-03 -0.0063462287 -0.0220657545 -9.492958e-04 2.413265e-02
## 10 -1.421804e-03 0.0036631551 0.0033947436 1.311471e-03 -7.110009e-03
## 11 2.168503e-03 -0.0024857405 -0.0022926063 1.747623e-03 -9.967185e-03
## 12 -2.759271e-04 0.0032037695 0.0111934245 -4.375016e-04 6.719194e-03
## 13 -1.107980e-02 -0.0258646152 -0.0428880590 -1.626574e-02 -8.010246e-03
## 14 1.804019e-03 -0.0008626337 -0.0069060350 -4.952366e-04 1.195906e-02
## 15 -1.554083e-02 -0.0035749666 -0.0042721338 -1.126839e-02 -9.198107e-03
## 16 -2.621480e-02 -0.0088688054 -0.0227034141 -2.278002e-02 9.839149e-03
## 17 -3.915388e-02 -0.0256493572 -0.0655093769 -3.416510e-02 -1.193130e-02
## 18 -2.886666e-02 0.0007202930 -0.0064928948 -1.950186e-02 -2.531157e-03
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## 60 -1.377004e-04 -3.109953e-03 -7.295266e-03 -4.389435e-03 -7.251740e-03
## 61 -1.738405e-02 -1.664814e-02 -1.304380e-02 4.326975e-03 -1.291604e-02
## 62 4.557998e-03 -1.777621e-06 -4.250486e-03 -3.612766e-02 -5.178435e-03
## 63 -4.996647e-03 -5.896381e-03 -7.320902e-03 -7.067351e-03 -8.246775e-03
## 64 -2.893973e-03 -3.525318e-03 -5.079964e-03 5.332599e-03 -4.143320e-03
## 65 4.897986e-03 4.296119e-03 1.313656e-03 -7.172358e-03 1.774256e-03
## 66 -2.239014e-02 -2.634758e-02 -2.339024e-02 9.702761e-04 -2.169655e-02
## 67 -9.981624e-03 -9.905198e-03 -8.562241e-03 1.286984e-02 -6.663549e-03
## 68 -1.256076e-02 -1.558591e-02 -1.563361e-02 -3.103285e-03 -1.518312e-02
## 69 -9.203270e-04 -4.396976e-03 -8.664494e-03 -7.149415e-03 -8.846647e-03
## 70 8.224687e-03 5.390167e-03 -3.964784e-04 -1.506782e-02 -6.936449e-04
## 71 2.055454e-03 1.421223e-03 -1.116046e-03 -1.317201e-02 -1.855845e-03
## 72 -5.938284e-03 -4.253722e-03 -3.643252e-03 -7.568608e-05 -4.260833e-03
## 73 -3.812616e-03 -3.609556e-04 1.708940e-03 1.443131e-02 3.513069e-03
## 74 -9.086122e-03 -6.954027e-03 -5.508030e-03 1.865877e-03 -6.472774e-03
## 75 -3.542998e-03 -6.273998e-03 -9.112472e-03 -5.204443e-03 -9.115111e-03
## 76 -1.158195e-02 -8.920932e-03 -1.232099e-04 -2.543245e-02 1.943756e-03
## 77 -1.870394e-02 -1.756234e-02 -1.318401e-02 6.508350e-03 -1.278663e-02
## 78 -2.966965e-03 -3.429119e-03 -4.735469e-03 2.563344e-03 -4.062614e-03
## 79 -8.082761e-03 -3.848808e-03 -6.104208e-05 2.376769e-02 2.560535e-03
## 80 -1.236571e-02 -1.219806e-02 -1.057775e-02 4.658005e-04 -1.081410e-02
## 81 -4.475134e-03 -3.106172e-03 -2.494978e-03 4.817113e-03 -1.719997e-03
## 82 -5.731123e-03 -2.815571e-03 -2.350825e-03 4.876554e-04 -4.122238e-03
## 83 -4.992763e-03 -2.445129e-03 -1.124730e-03 2.856864e-03 -1.110399e-03
## 84 1.331465e-03 2.954739e-03 3.342601e-03 -1.851768e-03 4.764306e-03
## 85 6.451328e-03 3.725482e-03 -1.033587e-03 -1.804685e-02 -1.312873e-03
## 86 5.983139e-03 1.182288e-02 1.126339e-02 -7.210844e-03 8.675354e-03
## 87 -4.703455e-03 -3.959111e-03 -3.783700e-03 6.276611e-03 -2.785111e-03
## 88 -1.290122e-03 -1.128125e-03 2.271618e-04 -2.251976e-02 5.711478e-04
## 89 3.061161e-03 9.312211e-03 1.130130e-02 -8.733731e-03 9.851419e-03
## 90 -1.639766e-04 -1.220692e-03 -8.557859e-04 -1.988417e-02 2.774461e-04
## 91 -2.038595e-02 -2.427483e-02 -2.228821e-02 -4.475725e-03 -2.168748e-02
## 92 -1.147580e-02 -6.947977e-03 -3.323301e-03 9.839203e-03 -4.017135e-03
## 93 3.105735e-03 2.763574e-03 9.832738e-04 -2.371699e-02 -1.882938e-04
## 94 3.430136e-03 1.342442e-03 -8.405232e-04 -3.744694e-02 -2.420491e-03
## 95 -1.381920e-02 -1.576789e-02 -1.462080e-02 6.832004e-04 -1.385745e-02
## 96 1.791537e-03 2.778341e-03 1.975717e-03 -1.524478e-02 1.218565e-03
## 97 -2.278808e-02 -2.817049e-02 -2.626918e-02 -7.430230e-03 -2.554904e-02
## 98 -4.551415e-03 -5.786632e-03 -7.280060e-03 -4.906501e-03 -7.549799e-03
## 99 5.921436e-03 8.388031e-04 -4.511740e-03 -3.641856e-02 -5.696831e-03
## 100 1.615125e-03 1.143814e-03 2.577863e-04 -1.562071e-02 6.566708e-04
## 101 6.433378e-04 7.395234e-03 7.814687e-03 5.356544e-03 5.187640e-03
## 102 3.136733e-03 9.961165e-04 -1.944791e-05 -5.388402e-02 -2.462691e-03
## 103 -9.749317e-03 -1.181750e-02 -1.255673e-02 -7.142597e-03 -1.328136e-02
## 104 -7.818964e-03 -9.705121e-03 -1.064555e-02 -4.389209e-03 -1.076087e-02
## 105 4.426292e-03 9.787455e-04 -5.234013e-03 -4.621624e-03 -5.387286e-03
## 106 -1.804682e-04 -2.805999e-03 -3.228548e-03 -3.001155e-02 -2.739297e-03
## 107 -1.079481e-02 -6.805831e-03 -3.013540e-03 1.040399e-02 -2.732980e-03
## 108 -1.666354e-02 -1.588397e-02 -1.267498e-02 3.123288e-03 -1.291282e-02
## 109 -1.733750e-02 -1.397547e-02 -8.802557e-03 1.128935e-02 -8.569469e-03
## 110 -1.374763e-03 -5.993681e-03 -1.101364e-02 -8.080099e-03 -1.120025e-02
## 111 4.416974e-03 1.142137e-02 1.092778e-02 1.789757e-03 7.925671e-03
## 112 6.332870e-03 3.369004e-03 -2.370094e-03 -1.326194e-02 -2.907178e-03
## 113 -1.408324e-02 -1.877767e-02 -1.935624e-02 -4.220338e-03 -1.856998e-02
## 114 -7.074442e-03 -1.022932e-02 -1.221369e-02 -4.781992e-03 -1.205482e-02
## 115 2.611680e-03 3.737883e-03 3.431092e-03 -3.164513e-03 4.846253e-03
## 116 -1.361305e-03 1.484169e-03 3.547617e-03 -7.280349e-03 4.026660e-03
## 117 -8.155674e-03 -7.555194e-03 -6.832261e-03 6.247819e-05 -7.054076e-03
## 118 -2.092848e-02 -2.299820e-02 -1.985900e-02 -1.234412e-03 -1.950529e-02
## 119 -1.119271e-03 2.535255e-04 2.510590e-03 -2.762080e-02 2.107428e-03
## 120 -1.210189e-02 -8.938961e-03 -4.850944e-03 1.240546e-02 -3.682984e-03
## 121 7.623594e-04 2.508467e-03 1.905940e-03 -8.816007e-03 1.111654e-03
## 122 -3.588390e-03 3.804403e-03 8.234336e-03 9.939868e-03 8.395585e-03
## 123 -1.823937e-02 -2.102873e-02 -1.934921e-02 -4.867422e-03 -1.941917e-02
## 124 1.062938e-03 9.540518e-04 -1.428652e-03 4.328242e-03 -6.470179e-04
## 125 3.930177e-03 4.518001e-03 3.388553e-03 -2.933668e-02 1.619808e-03
## 126 -9.915759e-03 -8.559054e-03 -6.818691e-03 2.878812e-03 -6.907248e-03
## 127 -5.439258e-03 1.190773e-04 5.957615e-03 5.146056e-03 8.085890e-03
## 128 -2.508403e-02 -2.866106e-02 -2.485081e-02 -2.470889e-03 -2.394137e-02
## 129 1.796013e-02 1.582550e-02 5.660804e-03 -9.810847e-04 5.115503e-03
## 130 -3.807550e-03 1.719234e-03 3.899144e-03 6.574401e-03 2.922127e-03
## 131 -4.137626e-03 4.003556e-03 9.291546e-03 3.810081e-02 1.298511e-02
## 132 -2.328551e-03 2.115358e-03 2.085173e-03 1.542494e-03 -3.508179e-04
## 133 -1.038184e-02 -7.597399e-03 -4.189562e-03 2.305756e-02 -1.486281e-03
## 134 3.214817e-03 2.096011e-03 -7.305307e-04 -1.863227e-02 -1.617438e-03
## 135 -4.123548e-03 -6.785578e-04 3.831900e-03 -1.142843e-02 4.894610e-03
## 136 6.988472e-03 1.119262e-02 9.804430e-03 2.166381e-02 1.178674e-02
## 137 3.636299e-04 4.093926e-03 4.655179e-03 2.055398e-02 6.772509e-03
## 138 5.168151e-03 4.976423e-03 1.936560e-03 -2.450912e-02 -1.098194e-04
## 139 -6.425761e-03 -4.129821e-03 -2.226498e-03 9.644611e-03 -1.000212e-03
## 140 1.191357e-02 1.076046e-02 3.358538e-03 4.584451e-03 3.483451e-03
## 141 -1.177158e-02 -1.249242e-02 -1.115813e-02 3.704641e-03 -1.027131e-02
## 142 1.972771e-03 1.942403e-03 1.676481e-03 -3.159115e-02 4.539410e-04
## 143 3.480500e-03 1.750956e-03 -1.866835e-03 -1.683383e-02 -2.710096e-03
## 144 -7.924247e-03 -4.655080e-03 -2.928069e-03 3.908181e-03 -4.005257e-03
## 145 -4.039069e-03 -4.186259e-04 8.275408e-04 2.369074e-03 2.950711e-05
## 146 -2.303812e-02 -2.711409e-02 -2.434929e-02 -4.539596e-03 -2.365196e-02
## 147 -1.787811e-02 -2.253239e-02 -2.192672e-02 -7.359953e-03 -2.159187e-02
## 148 7.105927e-03 1.672307e-03 -4.033447e-03 -3.349377e-02 -4.507054e-03
## 149 1.760705e-03 4.974445e-03 4.819840e-03 1.694479e-02 6.679730e-03
## 150 -6.142709e-03 -4.118839e-03 -2.513245e-03 8.519564e-03 -1.394203e-03
## 151 -1.861074e-03 -1.144601e-03 -2.792903e-03 -7.710840e-03 -4.479536e-03
## 152 -2.452471e-04 5.825531e-03 6.591445e-03 4.103461e-03 4.506511e-03
## 153 -4.336289e-03 -6.928131e-03 -9.410032e-03 -5.230031e-03 -9.434620e-03
## 154 3.662001e-03 2.378456e-03 -4.263950e-04 -1.459666e-02 -4.857306e-04
## 155 -7.221291e-03 -1.029228e-02 -1.215676e-02 -3.712665e-03 -1.186525e-02
## 156 -2.251969e-02 -2.152354e-02 -1.511031e-02 1.639596e-02 -1.248109e-02
## 157 -4.100796e-04 -1.336570e-04 6.941688e-04 -1.484860e-02 1.625540e-03
## 158 -1.476229e-02 -1.432914e-02 -1.204660e-02 8.265488e-04 -1.258912e-02
## 159 -4.489160e-03 8.120714e-04 5.667438e-03 6.872365e-03 7.530079e-03
## 160 -3.854142e-03 -1.866089e-03 -1.501728e-03 -8.288652e-04 -2.054584e-03
## 161 -4.044893e-03 -3.521478e-03 -4.132994e-03 -3.882513e-03 -4.803273e-03
## 162 -8.937973e-04 1.358271e-03 2.801525e-03 -7.544691e-03 3.299627e-03
## 163 -5.135749e-03 -5.732473e-03 -6.722761e-03 -4.741988e-03 -7.228391e-03
## 164 4.391094e-03 3.026393e-03 -1.589560e-03 1.944009e-03 -1.181509e-03
## 165 -1.498786e-02 -1.808368e-02 -1.724365e-02 3.449861e-05 -1.621487e-02
## 166 1.963698e-02 3.615782e-02 3.516245e-02 1.567961e-02 2.965379e-02
## 167 -2.355172e-03 2.119203e-03 4.685481e-03 1.683171e-02 6.853935e-03
## 168 -1.446739e-02 -1.615993e-02 -1.510019e-02 -3.818298e-03 -1.544370e-02
## 169 3.842164e-03 6.412134e-03 5.041279e-03 -1.341917e-02 3.133927e-03
## 170 -1.554433e-02 -2.102893e-02 -2.174193e-02 -9.386951e-03 -2.149889e-02
## 171 -1.429568e-02 -1.337909e-02 -1.023595e-02 6.699207e-03 -9.430911e-03
## 172 5.076786e-04 3.485054e-03 3.211776e-03 -5.481202e-03 1.954418e-03
## 173 -1.107181e-02 -8.857058e-03 -5.607704e-03 1.207440e-02 -4.142301e-03
## 174 -1.701631e-02 -1.986704e-02 -1.842421e-02 -3.413224e-03 -1.809585e-02
## 175 -1.911696e-02 -2.240219e-02 -2.062438e-02 -4.920083e-03 -2.043247e-02
## 176 8.789158e-03 2.668765e-03 -4.314646e-03 -3.500677e-02 -5.123925e-03
## 177 2.096902e-03 -9.088202e-04 -5.634827e-03 -1.131120e-02 -6.242499e-03
## 178 -6.337738e-03 -3.571351e-03 -2.627698e-03 1.393650e-03 -3.846531e-03
## 179 -1.365846e-02 -1.424080e-02 -1.299410e-02 -2.712689e-03 -1.375934e-02
## 180 -1.276425e-02 -1.451560e-02 -1.385951e-02 -3.042924e-03 -1.390666e-02
## 181 -2.284714e-02 -2.709255e-02 -2.447452e-02 -4.744268e-03 -2.373657e-02
## 182 -1.036419e-02 -9.921744e-03 -9.097706e-03 -1.715641e-03 -1.002858e-02
## 183 -1.132083e-02 -8.357199e-03 -5.463235e-03 6.377245e-03 -5.858535e-03
## 184 2.888532e-03 -3.230155e-03 -6.989230e-03 -5.105409e-02 -8.374721e-03
## 185 -1.364813e-03 -2.577639e-03 -5.159809e-03 -1.020090e-02 -6.188788e-03
## 186 1.035848e-02 7.743512e-03 9.563446e-04 -1.039988e-02 6.970136e-04
## 187 -1.305049e-02 -1.199587e-02 -9.943856e-03 1.382094e-03 -1.066165e-02
## 188 -5.677723e-04 -2.343396e-03 -5.352154e-03 -5.087110e-03 -5.406410e-03
## 189 -1.364423e-02 -1.943281e-02 -2.096651e-02 -9.166342e-03 -2.064303e-02
## 190 -1.321126e-02 -1.024528e-02 -6.114453e-03 1.102395e-02 -5.263005e-03
## 191 2.990985e-03 6.463162e-03 5.756553e-03 2.110224e-02 7.724849e-03
## 192 -1.876344e-02 -2.152134e-02 -1.913349e-02 1.577109e-03 -1.785920e-02
## 193 -1.252097e-02 -7.578515e-03 -3.032662e-03 1.263643e-02 -3.141098e-03
## 194 9.466564e-03 8.394604e-03 2.031127e-03 4.277370e-03 2.317405e-03
## 195 3.194970e-03 1.912919e-03 -2.284372e-03 3.253962e-03 -1.749381e-03
## 196 9.789834e-01 -2.193810e-02 -1.782144e-02 3.763698e-03 -1.690727e-02
## 197 -2.193810e-02 9.746670e-01 -2.239450e-02 -1.594227e-03 -2.140903e-02
## 198 -1.782144e-02 -2.239450e-02 9.783421e-01 -5.598310e-03 -2.102198e-02
## 199 3.763698e-03 -1.594227e-03 -5.598310e-03 9.545761e-01 -6.952453e-03
## 200 -1.690727e-02 -2.140903e-02 -2.102198e-02 -6.952453e-03 9.793174e-01Numeral 2 Compruebe que los residuos en el objeto “modelo_ventas” son iguales al producto de M*y, donde “y” es la variable endógena en el modelo (“ventas”)
#Comprobacion de los residuos
library(magrittr)
residuos_modelo_ventas<-modelo_ventas$residuals
datos_modelo<-modelo_ventas$model
residuos_matrices<-matriz_m%*%datos_modelo$ventas
cbind(residuos_matrices,residuos_modelo_ventas,residuos_modelo_ventas-residuos_matrices)%>%round(digits = 2) %>% as.data.frame()->comparacion
names(comparacion)<-c("Por matrices","En el modelo", "Diferencias")
comparacion## Por matrices En el modelo Diferencias
## 1 -15.93 -15.93 0
## 2 19.33 19.33 0
## 3 38.02 38.02 0
## 4 -15.43 -15.43 0
## 5 5.16 5.16 0
## 6 80.22 80.22 0
## 7 -16.35 -16.35 0
## 8 -22.89 -22.89 0
## 9 -34.40 -34.40 0
## 10 46.09 46.09 0
## 11 -40.56 -40.56 0
## 12 9.25 9.25 0
## 13 5.82 5.82 0
## 14 -19.64 -19.64 0
## 15 -2.74 -2.74 0
## 16 -20.58 -20.58 0
## 17 -4.89 -4.89 0
## 18 -0.83 -0.83 0
## 19 -36.61 -36.61 0
## 20 -8.11 -8.11 0
## 21 11.00 11.00 0
## 22 56.50 56.50 0
## 23 -7.55 -7.55 0
## 24 31.71 31.71 0
## 25 -40.48 -40.48 0
## 26 86.80 86.80 0
## 27 -1.44 -1.44 0
## 28 35.92 35.92 0
## 29 24.51 24.51 0
## 30 -38.94 -38.94 0
## 31 25.44 25.44 0
## 32 -17.24 -17.24 0
## 33 -44.11 -44.11 0
## 34 47.62 47.62 0
## 35 -38.06 -38.06 0
## 36 104.56 104.56 0
## 37 -22.01 -22.01 0
## 38 6.26 6.26 0
## 39 -20.85 -20.85 0
## 40 -8.14 -8.14 0
## 41 3.52 3.52 0
## 42 7.13 7.13 0
## 43 39.33 39.33 0
## 44 29.22 29.22 0
## 45 -13.40 -13.40 0
## 46 8.21 8.21 0
## 47 -42.24 -42.24 0
## 48 -15.16 -15.16 0
## 49 36.15 36.15 0
## 50 -42.33 -42.33 0
## 51 29.60 29.60 0
## 52 -27.94 -27.94 0
## 53 -25.78 -25.78 0
## 54 -16.15 -16.15 0
## 55 20.52 20.52 0
## 56 -34.10 -34.10 0
## 57 32.84 32.84 0
## 58 -8.84 -8.84 0
## 59 -25.90 -25.90 0
## 60 4.38 4.38 0
## 61 -56.13 -56.13 0
## 62 -5.97 -5.97 0
## 63 34.06 34.06 0
## 64 -22.00 -22.00 0
## 65 -22.92 -22.92 0
## 66 -33.91 -33.91 0
## 67 -25.98 -25.98 0
## 68 -24.10 -24.10 0
## 69 15.18 15.18 0
## 70 -12.96 -12.96 0
## 71 -2.78 -2.78 0
## 72 -39.34 -39.34 0
## 73 9.10 9.10 0
## 74 -23.58 -23.58 0
## 75 16.53 16.53 0
## 76 41.92 41.92 0
## 77 -61.13 -61.13 0
## 78 -11.80 -11.80 0
## 79 42.30 42.30 0
## 80 -28.28 -28.28 0
## 81 -18.10 -18.10 0
## 82 55.90 55.90 0
## 83 -32.84 -32.84 0
## 84 1.99 1.99 0
## 85 -7.85 -7.85 0
## 86 2.06 2.06 0
## 87 -18.80 -18.80 0
## 88 -12.42 -12.42 0
## 89 -34.44 -34.44 0
## 90 -0.71 -0.71 0
## 91 -19.86 -19.86 0
## 92 -71.04 -71.04 0
## 93 5.47 5.47 0
## 94 -1.83 -1.83 0
## 95 -22.68 -22.68 0
## 96 -9.60 -9.60 0
## 97 30.46 30.46 0
## 98 2.80 2.80 0
## 99 -1.39 -1.39 0
## 100 -6.92 -6.92 0
## 101 47.13 47.13 0
## 102 13.67 13.67 0
## 103 74.24 74.24 0
## 104 8.29 8.29 0
## 105 5.20 5.20 0
## 106 -23.16 -23.16 0
## 107 -39.16 -39.16 0
## 108 -36.55 -36.55 0
## 109 -51.39 -51.39 0
## 110 14.93 14.93 0
## 111 31.77 31.77 0
## 112 0.85 0.85 0
## 113 3.55 3.55 0
## 114 20.05 20.05 0
## 115 1.25 1.25 0
## 116 -6.04 -6.04 0
## 117 -5.24 -5.24 0
## 118 -59.49 -59.49 0
## 119 -9.08 -9.08 0
## 120 -15.33 -15.33 0
## 121 -22.74 -22.74 0
## 122 -6.98 -6.98 0
## 123 52.60 52.60 0
## 124 -7.38 -7.38 0
## 125 6.99 6.99 0
## 126 -36.29 -36.29 0
## 127 51.55 51.55 0
## 128 -45.71 -45.71 0
## 129 -38.99 -38.99 0
## 130 -49.74 -49.74 0
## 131 137.77 137.77 0
## 132 68.15 68.15 0
## 133 29.49 29.49 0
## 134 4.04 4.04 0
## 135 2.44 2.44 0
## 136 24.96 24.96 0
## 137 14.83 14.83 0
## 138 18.65 18.65 0
## 139 -13.45 -13.45 0
## 140 -17.13 -17.13 0
## 141 -36.00 -36.00 0
## 142 -7.79 -7.79 0
## 143 -5.46 -5.46 0
## 144 -38.02 -38.02 0
## 145 -33.90 -33.90 0
## 146 -7.02 -7.02 0
## 147 57.02 57.02 0
## 148 -24.42 -24.42 0
## 149 5.76 5.76 0
## 150 -21.33 -21.33 0
## 151 60.96 60.96 0
## 152 -37.40 -37.40 0
## 153 3.70 3.70 0
## 154 -11.53 -11.53 0
## 155 5.57 5.57 0
## 156 20.34 20.34 0
## 157 -6.39 -6.39 0
## 158 0.10 0.10 0
## 159 35.21 35.21 0
## 160 -12.86 -12.86 0
## 161 -0.28 -0.28 0
## 162 -5.49 -5.49 0
## 163 7.07 7.07 0
## 164 -11.48 -11.48 0
## 165 -17.07 -17.07 0
## 166 43.48 43.48 0
## 167 30.49 30.49 0
## 168 32.76 32.76 0
## 169 9.33 9.33 0
## 170 79.25 79.25 0
## 171 -32.15 -32.15 0
## 172 -2.32 -2.32 0
## 173 -19.07 -19.07 0
## 174 11.45 11.45 0
## 175 56.81 56.81 0
## 176 -20.90 -20.90 0
## 177 10.72 10.72 0
## 178 10.72 10.72 0
## 179 99.16 99.16 0
## 180 0.68 0.68 0
## 181 8.07 8.07 0
## 182 43.24 43.24 0
## 183 -53.93 -53.93 0
## 184 -14.41 -14.41 0
## 185 33.06 33.06 0
## 186 -26.80 -26.80 0
## 187 -11.78 -11.78 0
## 188 2.02 2.02 0
## 189 75.55 75.55 0
## 190 -31.29 -31.29 0
## 191 11.46 11.46 0
## 192 -34.64 -34.64 0
## 193 -47.21 -47.21 0
## 194 -20.94 -20.94 0
## 195 -16.29 -16.29 0
## 196 -54.55 -54.55 0
## 197 -31.98 -31.98 0
## 198 8.34 8.34 0
## 199 -9.58 -9.58 0
## 200 49.59 49.59 0Numeral 3 Muestre que los autovalores de x’x son positivos (use el comando eigen)
#Demostracion de la sigma matriz positiva
eigen(x=matriz_xx,symmetric = TRUE)->descomposion
auto_valores<-descomposion$values
print(auto_valores)## [1] 3.114217e+08 7.025253e+04 4.097346e+04 3.714363e+03 1.277350e+01print(auto_valores>0)## [1] TRUE TRUE TRUE TRUE TRUEEjercicio 2 Para una empresa se desea estimar un modelo que relaciona el tiempo (en minutos) en acomodar cajas en una bodega, en función de la distancia (en metros) y del número de cajas nota: las cajas son todas iguales. Los datos se encuentra en “datos_cajas.RData”
Numeral 1 Estime el modelo propuesto, y colóquele el nombre de “modelo_cajas”
options(escipen = 99999999)
load("C:/MEGA DOCS/UES/CICLO I - 2021/ECONOMETTRIA/EJERCICIIOS/GUIA 1/datos_cajas.RData")
modelo_cajas<-lm(formula = Tiempo~Distancia+N_cajas,data = datos_cajas)
summary(modelo_cajas)##
## Call:
## lm(formula = Tiempo ~ Distancia + N_cajas, data = datos_cajas)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.2716 -0.5405 0.5212 1.4051 2.9381
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3112 5.8573 0.395 0.70007
## Distancia 0.4559 0.1468 3.107 0.00908 **
## N_cajas 0.8772 0.1530 5.732 9.43e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.141 on 12 degrees of freedom
## Multiple R-squared: 0.7368, Adjusted R-squared: 0.6929
## F-statistic: 16.8 on 2 and 12 DF, p-value: 0.0003325Numeral 2 Calcule las matrices A, P, M
#Construccion de Matriz x
matriz_x2<-model.matrix(modelo_cajas)
#Construccion de Matriz x-x
matriz_xx2<-t(matriz_x2)%*%matriz_x2
#Construccion de Matriz A
matriz_a2<-solve(matriz_xx2)%*%t(matriz_x2)
print(matriz_a2)## 1 2 3 4 5
## (Intercept) 0.459747079 0.505626389 -0.317731768 0.707001469 0.053149816
## Distancia -0.003015297 -0.009318829 0.018819615 -0.019989342 -0.006641453
## N_cajas -0.017147338 -0.009890695 -0.007919488 -0.004479623 0.011082085
## 6 7 8 9 10
## (Intercept) -0.166576988 0.633594572 -0.125532551 0.1260628274 -0.90735239
## Distancia 0.006550474 -0.009903692 0.009409808 0.0003379213 0.02334256
## N_cajas 0.002768355 -0.016090251 -0.003959744 -0.0038254420 0.01780152
## 11 12 13 14 15
## (Intercept) 0.277217608 0.368482344 0.487274665 -0.3674581822 -0.73350489
## Distancia -0.011931220 -0.007473259 -0.006797416 0.0001559637 0.01645417
## N_cajas 0.006862401 -0.005142468 -0.012793352 0.0238754370 0.01885861#Construccion de Matriz P
matriz_p2<-matriz_x2%*%matriz_a2
#ALternativamente
matriz_p2<-matriz_x2%*%solve(matriz_xx2)%*%t(matriz_x2)
print(matriz_p2)## 1 2 3 4 5 6
## 1 0.19781478 0.127154573 0.16766180 0.062524965 -0.03527291 0.057620774
## 2 0.12715457 0.124295239 0.03396629 0.140073563 0.05334477 0.038710181
## 3 0.16766180 0.033966286 0.35585795 -0.137368460 -0.10168744 0.123125512
## 4 0.06252497 0.140073563 -0.13736846 0.257600846 0.15524536 0.006698639
## 5 -0.03527291 0.053344771 -0.10168744 0.155245361 0.18408997 0.046742309
## 6 0.05762077 0.038710181 0.12312551 0.006698639 0.04674231 0.086318088
## 7 0.17558129 0.144648497 0.07654437 0.133523089 0.01345706 0.036955589
## 8 0.11716423 0.050316476 0.21126231 -0.035350897 -0.01751039 0.094896089
## 9 0.09794605 0.077129229 0.10132526 0.055636570 0.03786105 0.067680430
## 10 -0.02906036 -0.056765574 0.20436525 -0.131155907 0.05122193 0.136694350
## 11 -0.01209498 0.081873124 -0.13140718 0.199703669 0.18629079 0.030873007
## 12 0.09285990 0.104513848 0.01812731 0.131114317 0.07550894 0.044246890
## 13 0.15541865 0.125438973 0.08744449 0.109054124 0.01789770 0.046274418
## 14 -0.12402490 -0.005427535 -0.12246527 0.112857904 0.23285894 0.067134558
## 15 -0.05129385 -0.039271650 0.11324781 -0.060157783 0.09995191 0.116029165
## 7 8 9 10 11 12
## 1 0.17558129 0.11716423 0.09794605 -0.02906036 -0.01209498 0.092859897
## 2 0.14464850 0.05031648 0.07712923 -0.05676557 0.08187312 0.104513848
## 3 0.07654437 0.21126231 0.10132526 0.20436525 -0.13140718 0.018127310
## 4 0.13352309 -0.03535090 0.05563657 -0.13115591 0.19970367 0.131114317
## 5 0.01345706 -0.01751039 0.03786105 0.05122193 0.18629079 0.075508940
## 6 0.03695559 0.09489609 0.06768043 0.13669435 0.03087301 0.044246890
## 7 0.18301556 0.07160552 0.08894348 -0.08682757 0.04935470 0.112467995
## 8 0.07160552 0.13896449 0.08399596 0.13551596 -0.03237026 0.042396988
## 9 0.08894348 0.08399596 0.07465547 0.05440619 0.04101064 0.069478345
## 10 -0.08682757 0.13551596 0.05440619 0.34795579 -0.01326471 -0.021162536
## 11 0.04935470 -0.03237026 0.04101064 -0.01326471 0.20329083 0.095597926
## 12 0.11246799 0.04239699 0.06947834 -0.02116254 0.09559793 0.094228911
## 13 0.15702161 0.07705558 0.08545596 -0.04568349 0.04428588 0.099852268
## 14 -0.07689788 -0.02789930 0.01907176 0.16357209 0.20867158 0.042323339
## 15 -0.07939330 0.08995724 0.04540362 0.29018859 0.04818497 -0.001554438
## 13 14 15
## 1 0.15541865 -0.124024902 -0.051293849
## 2 0.12543897 -0.005427535 -0.039271650
## 3 0.08744449 -0.122465266 0.113247813
## 4 0.10905412 0.112857904 -0.060157783
## 5 0.01789770 0.232858944 0.099951911
## 6 0.04627442 0.067134558 0.116029165
## 7 0.15702161 -0.076897883 -0.079393301
## 8 0.07705558 -0.027899299 0.089957240
## 9 0.08545596 0.019071756 0.045403621
## 10 -0.04568349 0.163572088 0.290188586
## 11 0.04428588 0.208671580 0.048184973
## 12 0.09985227 0.042323339 -0.001554438
## 13 0.13743085 -0.052866482 -0.044080529
## 14 -0.05286648 0.352392093 0.210699107
## 15 -0.04408053 0.210699107 0.262089133#Construccion de Matriz M
n<-nrow(matriz_x2)
matriz_m2<-diag(n)-matriz_p2
print(matriz_m2)## 1 2 3 4 5 6
## 1 0.80218522 -0.127154573 -0.16766180 -0.062524965 0.03527291 -0.057620774
## 2 -0.12715457 0.875704761 -0.03396629 -0.140073563 -0.05334477 -0.038710181
## 3 -0.16766180 -0.033966286 0.64414205 0.137368460 0.10168744 -0.123125512
## 4 -0.06252497 -0.140073563 0.13736846 0.742399154 -0.15524536 -0.006698639
## 5 0.03527291 -0.053344771 0.10168744 -0.155245361 0.81591003 -0.046742309
## 6 -0.05762077 -0.038710181 -0.12312551 -0.006698639 -0.04674231 0.913681912
## 7 -0.17558129 -0.144648497 -0.07654437 -0.133523089 -0.01345706 -0.036955589
## 8 -0.11716423 -0.050316476 -0.21126231 0.035350897 0.01751039 -0.094896089
## 9 -0.09794605 -0.077129229 -0.10132526 -0.055636570 -0.03786105 -0.067680430
## 10 0.02906036 0.056765574 -0.20436525 0.131155907 -0.05122193 -0.136694350
## 11 0.01209498 -0.081873124 0.13140718 -0.199703669 -0.18629079 -0.030873007
## 12 -0.09285990 -0.104513848 -0.01812731 -0.131114317 -0.07550894 -0.044246890
## 13 -0.15541865 -0.125438973 -0.08744449 -0.109054124 -0.01789770 -0.046274418
## 14 0.12402490 0.005427535 0.12246527 -0.112857904 -0.23285894 -0.067134558
## 15 0.05129385 0.039271650 -0.11324781 0.060157783 -0.09995191 -0.116029165
## 7 8 9 10 11 12
## 1 -0.17558129 -0.11716423 -0.09794605 0.02906036 0.01209498 -0.092859897
## 2 -0.14464850 -0.05031648 -0.07712923 0.05676557 -0.08187312 -0.104513848
## 3 -0.07654437 -0.21126231 -0.10132526 -0.20436525 0.13140718 -0.018127310
## 4 -0.13352309 0.03535090 -0.05563657 0.13115591 -0.19970367 -0.131114317
## 5 -0.01345706 0.01751039 -0.03786105 -0.05122193 -0.18629079 -0.075508940
## 6 -0.03695559 -0.09489609 -0.06768043 -0.13669435 -0.03087301 -0.044246890
## 7 0.81698444 -0.07160552 -0.08894348 0.08682757 -0.04935470 -0.112467995
## 8 -0.07160552 0.86103551 -0.08399596 -0.13551596 0.03237026 -0.042396988
## 9 -0.08894348 -0.08399596 0.92534453 -0.05440619 -0.04101064 -0.069478345
## 10 0.08682757 -0.13551596 -0.05440619 0.65204421 0.01326471 0.021162536
## 11 -0.04935470 0.03237026 -0.04101064 0.01326471 0.79670917 -0.095597926
## 12 -0.11246799 -0.04239699 -0.06947834 0.02116254 -0.09559793 0.905771089
## 13 -0.15702161 -0.07705558 -0.08545596 0.04568349 -0.04428588 -0.099852268
## 14 0.07689788 0.02789930 -0.01907176 -0.16357209 -0.20867158 -0.042323339
## 15 0.07939330 -0.08995724 -0.04540362 -0.29018859 -0.04818497 0.001554438
## 13 14 15
## 1 -0.15541865 0.124024902 0.051293849
## 2 -0.12543897 0.005427535 0.039271650
## 3 -0.08744449 0.122465266 -0.113247813
## 4 -0.10905412 -0.112857904 0.060157783
## 5 -0.01789770 -0.232858944 -0.099951911
## 6 -0.04627442 -0.067134558 -0.116029165
## 7 -0.15702161 0.076897883 0.079393301
## 8 -0.07705558 0.027899299 -0.089957240
## 9 -0.08545596 -0.019071756 -0.045403621
## 10 0.04568349 -0.163572088 -0.290188586
## 11 -0.04428588 -0.208671580 -0.048184973
## 12 -0.09985227 -0.042323339 0.001554438
## 13 0.86256915 0.052866482 0.044080529
## 14 0.05286648 0.647607907 -0.210699107
## 15 0.04408053 -0.210699107 0.737910867Numeral 3 Compruebe que los residuos en el objeto “modelo_ventas” son iguales al producto de M*y, donde “y” es la variable endógena en el modelo (“Tiempo”)
#Comprobar residuos
library(magrittr)
residuos_modelo_cajas<-modelo_cajas$residuals
matriz_y<-datos_cajas$Tiempo
residuos_por_matrices<-matriz_m2%*%matriz_y
cbind(residuos_modelo_cajas,
residuos_por_matrices,
residuos_modelo_cajas-residuos_por_matrices)%>%round(digits = 2) %>% as.data.frame()->comparativa
names(comparativa)<-c("Por matrices","En el modelo", "Diferencias")
comparativa## Por matrices En el modelo Diferencias
## 1 -0.76 -0.76 0
## 2 0.13 0.13 0
## 3 -0.32 -0.32 0
## 4 2.94 2.94 0
## 5 -9.27 -9.27 0
## 6 0.77 0.77 0
## 7 1.31 1.31 0
## 8 -2.09 -2.09 0
## 9 1.43 1.43 0
## 10 0.52 0.52 0
## 11 0.52 0.52 0
## 12 1.38 1.38 0
## 13 -1.02 -1.02 0
## 14 2.89 2.89 0
## 15 1.59 1.59 0Numeral 4 Muestre que los autovalores de x’x son positivos (use el comando eigen)
descomposicion2<-eigen(matriz_xx2)
autovalores2<-descomposicion2$values
print(autovalores2)## [1] 1.697678e+04 7.099346e+02 2.872743e-01print(autovalores2>0)## [1] TRUE TRUE TRUEEjercicio 3 Para los EEUU se ha estimado un modelo que relaciona el “número de crímenes” en un estado con el “Nivel de pobreza” y la cantidad de solteros en el mismo.
Numeral 1 Calcule las matrices A, P, M
options(scipen = 99999999)
load("C:/MEGA DOCS/UES/CICLO I - 2021/ECONOMETTRIA/EJERCICIIOS/GUIA 1/modelo_estimado.RData")
#Construccion de Matriz x
matriz_x3<-model.matrix(modelo_estimado_1)
#Construccion de Matriz x-x
matriz_xx3<-t(matriz_x3)%*%matriz_x3
#Construccion de Matriz A
matriz_a3<-solve(matriz_xx3)%*%t(matriz_x3)
print(matriz_a2)## 1 2 3 4 5
## (Intercept) 0.459747079 0.505626389 -0.317731768 0.707001469 0.053149816
## Distancia -0.003015297 -0.009318829 0.018819615 -0.019989342 -0.006641453
## N_cajas -0.017147338 -0.009890695 -0.007919488 -0.004479623 0.011082085
## 6 7 8 9 10
## (Intercept) -0.166576988 0.633594572 -0.125532551 0.1260628274 -0.90735239
## Distancia 0.006550474 -0.009903692 0.009409808 0.0003379213 0.02334256
## N_cajas 0.002768355 -0.016090251 -0.003959744 -0.0038254420 0.01780152
## 11 12 13 14 15
## (Intercept) 0.277217608 0.368482344 0.487274665 -0.3674581822 -0.73350489
## Distancia -0.011931220 -0.007473259 -0.006797416 0.0001559637 0.01645417
## N_cajas 0.006862401 -0.005142468 -0.012793352 0.0238754370 0.01885861#Construccion de Matriz P
matriz_p3<-matriz_x3%*%matriz_a3
#Construccion de Matriz M
n3<-nrow(matriz_x3)
matriz_m3<-diag(n3)-matriz_p3
print(matriz_m3)## 1 2 3 4 5
## 1 0.838388923 0.0127796253 0.0653080904 -0.027207907 -0.004995312
## 2 0.012779625 0.9685349231 -0.0450195150 -0.021099510 -0.030700881
## 3 0.065308090 -0.0450195150 0.9214410491 -0.019423663 -0.038838489
## 4 -0.027207907 -0.0210995096 -0.0194236628 0.977658788 -0.024424173
## 5 -0.004995312 -0.0307008811 -0.0388384889 -0.024424173 0.965417364
## 6 -0.092237760 0.0008717607 0.0291165550 -0.020671038 -0.005338821
## 7 -0.054323132 -0.0014555968 0.0149893805 -0.014082445 0.001730668
## 8 -0.069626967 -0.0030986911 0.0171998930 -0.018604926 -0.005605850
## 9 0.042019509 -0.0366270037 -0.0604669926 -0.018447422 -0.031093776
## 10 -0.074183205 -0.0099454181 0.0092620561 -0.024537798 -0.018826182
## 11 -0.033001099 -0.0034182300 0.0061606961 -0.010848882 0.004571400
## 12 -0.003083400 -0.0130022202 -0.0154620904 -0.011239145 -0.003299178
## 13 0.016405789 -0.0222075842 -0.0335527599 -0.013630280 -0.013568208
## 14 -0.032150082 -0.0162849295 -0.0114826440 -0.019945572 -0.017514640
## 15 -0.029639461 -0.0134642545 -0.0083959467 -0.017363227 -0.011882559
## 16 0.005512265 -0.0206235772 -0.0282561924 -0.014862970 -0.014010488
## 17 0.072760898 -0.0470134239 -0.0834132808 -0.019236959 -0.040115944
## 18 0.026597072 -0.0539539932 -0.0794281003 -0.034310399 -0.065690838
## 19 -0.050098243 -0.0070760900 0.0061664301 -0.017215896 -0.006788032
## 20 -0.091879085 0.0012747116 0.0295575040 -0.020302131 -0.004534238
## 21 -0.041928113 -0.0082640934 0.0021940108 -0.016291379 -0.006456323
## 22 -0.051718351 -0.0175354918 -0.0075063795 -0.025114767 -0.025419303
## 23 -0.012223150 -0.0146314125 -0.0150179511 -0.014407468 -0.008805392
## 24 0.013749255 -0.0286478850 -0.0414912433 -0.018855703 -0.025526380
## 25 0.011943712 -0.0479548814 -0.0670730541 -0.033177818 -0.059570593
## 26 0.002284283 -0.0242501501 -0.0322247792 -0.018183130 -0.021251731
## 27 -0.011797679 -0.0210647547 -0.0238396001 -0.018955815 -0.019848409
## 28 0.023898157 -0.0189735319 -0.0313498957 -0.009663407 -0.005758814
## 29 -0.013976925 -0.0114182132 -0.0101655228 -0.012471835 -0.003741458
## 30 -0.013259614 -0.0106123038 -0.0092836039 -0.011734023 -0.002132290
## 31 -0.012329555 -0.0130230694 -0.0128125179 -0.013270384 -0.006044635
## 32 -0.049858208 -0.0223570267 -0.0145642200 -0.028187487 -0.033243991
## 33 -0.101590245 0.0024592395 0.0339715188 -0.021565188 -0.005323525
## 34 -0.031724585 -0.0227182754 -0.0203043056 -0.024493916 -0.028557657
## 35 -0.036520858 -0.0142840658 -0.0075114923 -0.019455197 -0.015322030
## 36 0.053232174 -0.0430360250 -0.0723798179 -0.020625989 -0.038933762
## 37 -0.047985819 -0.0098863347 0.0017549634 -0.018782624 -0.011047384
## 38 0.014864749 -0.0222110559 -0.0331111561 -0.013968820 -0.014025783
## 39 -0.041463070 -0.0094694781 0.0004295475 -0.017059559 -0.008412495
## 40 0.006363255 -0.0334902728 -0.0458995198 -0.023959662 -0.036096529
## 41 0.032135147 -0.0269978397 -0.0445849466 -0.013656140 -0.017274706
## 42 0.046961732 -0.0414415952 -0.0684080408 -0.020843060 -0.038003315
## 43 0.004609469 -0.0302770697 -0.0410470830 -0.022024029 -0.031032591
## 44 -0.025587799 -0.0106401078 -0.0057508532 -0.014442341 -0.005792902
## 45 -0.045581566 -0.0054573242 0.0070470730 -0.015063192 -0.002654548
## 46 -0.061098162 -0.0038837436 0.0136684226 -0.017311502 -0.004469558
## 47 -0.055332259 -0.0095007613 0.0044038810 -0.020106415 -0.012530684
## 48 -0.014016459 -0.0166461782 -0.0172227295 -0.016252001 -0.012828306
## 49 0.126724035 -0.0589560548 -0.1151889082 -0.016085484 -0.045035222
## 50 -0.016633486 -0.0178585101 -0.0181039936 -0.017697261 -0.015699630
## 51 -0.169486584 -0.0254418356 0.0159102166 -0.056498849 -0.073651878
## 6 7 8 9 10
## 1 -0.0922377599 -0.054323132 -0.069626967 0.042019509 -0.074183205
## 2 0.0008717607 -0.001455597 -0.003098691 -0.036627004 -0.009945418
## 3 0.0291165550 0.014989380 0.017199893 -0.060466993 0.009262056
## 4 -0.0206710383 -0.014082445 -0.018604926 -0.018447422 -0.024537798
## 5 -0.0053388207 0.001730668 -0.005605850 -0.031093776 -0.018826182
## 6 0.9398166940 -0.046325314 -0.049657601 0.014507419 -0.045082769
## 7 -0.0463253143 0.948474640 -0.043514080 0.002242589 -0.026574141
## 8 -0.0496576009 -0.043514080 0.956952930 0.005481207 -0.035653735
## 9 0.0145074185 0.002242589 0.005481207 0.951682287 0.002230971
## 10 -0.0450827691 -0.026574141 -0.035653735 0.002230971 0.957682639
## 11 -0.0379595101 -0.052952915 -0.039313133 -0.005088182 -0.016572738
## 12 -0.0202404094 -0.039319171 -0.025625073 -0.019901969 -0.006794286
## 13 -0.0061039860 -0.023656425 -0.013328397 -0.031515647 -0.002269591
## 14 -0.0264276188 -0.023732484 -0.024553262 -0.013858209 -0.024140123
## 15 -0.0281148133 -0.030887233 -0.027540841 -0.012698365 -0.021061366
## 16 -0.0108871129 -0.024257870 -0.016137961 -0.027384984 -0.007017238
## 17 0.0331859478 0.017484675 0.020160655 -0.063896367 0.011943140
## 18 0.0248715863 0.046193174 0.023833459 -0.055442446 -0.016681405
## 19 -0.0400866623 -0.039831103 -0.036712140 -0.002678021 -0.027851446
## 20 -0.0604243269 -0.047347419 -0.050084394 0.014673105 -0.044642941
## 21 -0.0364993229 -0.039380020 -0.034604970 -0.005776013 -0.024290717
## 22 -0.0314330794 -0.015435698 -0.024926450 -0.009153426 -0.035220009
## 23 -0.0216631859 -0.033051380 -0.024606872 -0.018397301 -0.012620412
## 24 -0.0012927954 -0.008174465 -0.006224056 -0.035033686 -0.007680018
## 25 0.0150502752 0.036527926 0.015640148 -0.047321742 -0.020657841
## 26 -0.0087178833 -0.015058917 -0.012296802 -0.028876195 -0.010975654
## 27 -0.0158972585 -0.018441171 -0.017226949 -0.022782299 -0.016404119
## 28 -0.0066000667 -0.033140898 -0.016329375 -0.031490581 0.003689098
## 29 -0.0250235363 -0.039920616 -0.028434638 -0.015771307 -0.011541933
## 30 -0.0255055964 -0.041964833 -0.029288235 -0.015439919 -0.010662291
## 31 -0.0231046860 -0.036703939 -0.026451865 -0.017301036 -0.011674500
## 32 -0.0266312472 -0.004913909 -0.019253703 -0.012875670 -0.037244415
## 33 -0.0644890461 -0.047362628 -0.052329362 0.018204586 -0.049017041
## 34 -0.0206616799 -0.009122273 -0.017173332 -0.018243217 -0.027923819
## 35 -0.0295422633 -0.027099528 -0.027238434 -0.011295804 -0.025194476
## 36 0.0236150092 0.013801698 0.013825726 -0.055737139 0.004140852
## 37 -0.0369673443 -0.033983974 -0.033311174 -0.005138319 -0.028490109
## 38 -0.0065813727 -0.023220557 -0.013466200 -0.031082152 -0.003082966
## 39 -0.0352988620 -0.036749573 -0.033186782 -0.006706576 -0.024796816
## 40 0.0006447671 0.004962560 -0.001378097 -0.036155002 -0.014584634
## 41 0.0029942508 -0.017057493 -0.006415471 -0.039139282 0.003026318
## 42 0.0202640241 0.011892640 0.011429560 -0.052906946 0.001833314
## 43 -0.0027155901 -0.001906681 -0.005205868 -0.033529002 -0.013506159
## 44 -0.0293246212 -0.038477851 -0.030390617 -0.011972017 -0.017169236
## 45 -0.0400960207 -0.044791276 -0.038143735 -0.002882226 -0.024465426
## 46 -0.0463112824 -0.044085102 -0.041366692 0.002548901 -0.031653178
## 47 -0.0395952552 -0.032826716 -0.034426956 -0.002805195 -0.032117120
## 48 -0.0204580515 -0.027940847 -0.022472891 -0.019225757 -0.014819527
## 49 0.0604666469 0.029841231 0.038752062 -0.087073601 0.032909916
## 50 -0.0202123570 -0.024438657 -0.021330304 -0.019289336 -0.016952371
## 51 -0.0612247882 0.035367152 -0.026738755 0.018909558 -0.102139135
## 11 12 13 14 15
## 1 -0.033001099 -0.003083400 0.0164057895 -0.032150082 -0.0296394607
## 2 -0.003418230 -0.013002220 -0.0222075842 -0.016284930 -0.0134642545
## 3 0.006160696 -0.015462090 -0.0335527599 -0.011482644 -0.0083959467
## 4 -0.010848882 -0.011239145 -0.0136302797 -0.019945572 -0.0173632265
## 5 0.004571400 -0.003299178 -0.0135682081 -0.017514640 -0.0118825586
## 6 -0.037959510 -0.020240409 -0.0061039860 -0.026427619 -0.0281148133
## 7 -0.052952915 -0.039319171 -0.0236564253 -0.023732484 -0.0308872331
## 8 -0.039313133 -0.025625073 -0.0133283967 -0.024553262 -0.0275408413
## 9 -0.005088182 -0.019901969 -0.0315156470 -0.013858209 -0.0126983655
## 10 -0.016572738 -0.006794286 -0.0022695914 -0.024140123 -0.0210613665
## 11 0.940536222 -0.048531233 -0.0327063281 -0.022149205 -0.0318824765
## 12 -0.048531233 0.954393553 -0.0368271023 -0.019221275 -0.0273881407
## 13 -0.032706328 -0.036827102 0.9642083854 -0.017007601 -0.0219056920
## 14 -0.022149205 -0.019221275 -0.0170076006 0.979236566 -0.0208926221
## 15 -0.031882477 -0.027388141 -0.0219056920 -0.020892622 0.9763581307
## 16 -0.031087826 -0.033469599 -0.0318979738 -0.017876622 -0.0218985614
## 17 0.007727752 -0.015646825 -0.0350735318 -0.010793969 -0.0076157965
## 18 0.054701898 0.030265921 -0.0014273628 -0.013064630 0.0041898611
## 19 -0.038871660 -0.029003659 -0.0188796609 -0.022877707 -0.0265723376
## 20 -0.039349978 -0.021407108 -0.0068037177 -0.026446073 -0.0285075624
## 21 -0.040085535 -0.031521783 -0.0217998869 -0.022225942 -0.0265776855
## 22 -0.007207250 -0.003684759 -0.0048695833 -0.021900870 -0.0173471827
## 23 -0.038481633 -0.035924490 -0.0298453483 -0.019644453 -0.0248308123
## 24 -0.012253950 -0.020166053 -0.0262691136 -0.016513515 -0.0160162331
## 25 0.045513004 0.025804963 -0.0010478759 -0.014633660 0.0008630804
## 26 -0.018573624 -0.022969338 -0.0256004177 -0.017710526 -0.0183638179
## 27 -0.019824348 -0.021269504 -0.0219959740 -0.018951570 -0.0193358870
## 28 -0.046522708 -0.049169776 -0.0438991476 -0.016857042 -0.0256394868
## 29 -0.046912731 -0.042248944 -0.0329334615 -0.020090296 -0.0273810101
## 30 -0.049693667 -0.044582334 -0.0343329143 -0.020127207 -0.0281665101
## 31 -0.043145955 -0.039588230 -0.0318076813 -0.019817677 -0.0262045455
## 32 0.005888169 0.006303442 0.0001808736 -0.021281807 -0.0134232536
## 33 -0.037238553 -0.017885945 -0.0030469192 -0.027197238 -0.0283049477
## 34 -0.003491924 -0.004566297 -0.0091582355 -0.020070549 -0.0153976967
## 35 -0.025511358 -0.021042611 -0.0171599647 -0.021253310 -0.0220673058
## 36 0.007286280 -0.012268239 -0.0295222676 -0.012469523 -0.0085843002
## 37 -0.031831027 -0.023845895 -0.0164912701 -0.022450321 -0.0244148889
## 38 -0.031808783 -0.035824064 -0.0349550407 -0.017107002 -0.0217084271
## 39 -0.036811682 -0.029024734 -0.0205372750 -0.022071176 -0.0255967032
## 40 0.006226751 -0.004159633 -0.0161992371 -0.016490852 -0.0109087069
## 41 -0.027688833 -0.035866230 -0.0382702874 -0.015493935 -0.0197571584
## 42 0.006212146 -0.011919844 -0.0281383380 -0.013040343 -0.0091689663
## 43 -0.002204351 -0.010484089 -0.0192873490 -0.016936696 -0.0134589066
## 44 -0.042513293 -0.036558045 -0.0276403573 -0.020922409 -0.0265883814
## 45 -0.046228619 -0.035676507 -0.0233517051 -0.022752730 -0.0285378674
## 46 -0.041917475 -0.029309895 -0.0169483544 -0.023919951 -0.0279389383
## 47 -0.028733762 -0.019997413 -0.0130081546 -0.022965776 -0.0238213077
## 48 -0.031529298 -0.030091013 -0.0263467097 -0.019552176 -0.0228670652
## 49 0.011744812 -0.022773480 -0.0492176249 -0.006065502 -0.0041184849
## 50 -0.026460349 -0.025587887 -0.0234109512 -0.019596212 -0.0214915512
## 51 0.083834974 0.090701039 0.0686582458 -0.028707029 0.0043182118
## 16 17 18 19 20
## 1 0.005512265 0.072760898 0.026597072 -0.050098243 -0.091879085
## 2 -0.020623577 -0.047013424 -0.053953993 -0.007076090 0.001274712
## 3 -0.028256192 -0.083413281 -0.079428100 0.006166430 0.029557504
## 4 -0.014862970 -0.019236959 -0.034310399 -0.017215896 -0.020302131
## 5 -0.014010488 -0.040115944 -0.065690838 -0.006788032 -0.004534238
## 6 -0.010887113 0.033185948 0.024871586 -0.040086662 -0.060424327
## 7 -0.024257870 0.017484675 0.046193174 -0.039831103 -0.047347419
## 8 -0.016137961 0.020160655 0.023833459 -0.036712140 -0.050084394
## 9 -0.027384984 -0.063896367 -0.055442446 -0.002678021 0.014673105
## 10 -0.007017238 0.011943140 -0.016681405 -0.027851446 -0.044642941
## 11 -0.031087826 0.007727752 0.054701898 -0.038871660 -0.039349978
## 12 -0.033469599 -0.015646825 0.030265921 -0.029003659 -0.021407108
## 13 -0.031897974 -0.035073532 -0.001427363 -0.018879661 -0.006803718
## 14 -0.017876622 -0.010793969 -0.013064630 -0.022877707 -0.026446073
## 15 -0.021898561 -0.007615796 0.004189861 -0.026572338 -0.028507562
## 16 0.970978582 -0.029264481 -0.002678779 -0.020095101 -0.011461679
## 17 -0.029264481 0.911321892 -0.083419388 0.008133616 0.033639964
## 18 -0.002678779 -0.083419388 0.838565713 0.020017550 0.027336512
## 19 -0.020095101 0.008133616 0.020017550 0.966886322 -0.040614464
## 20 -0.011461679 0.033639964 0.027336512 -0.040614464 0.939281181
## 21 -0.022252515 0.003776834 0.020956111 -0.032202099 -0.037120999
## 22 -0.008390716 -0.006166587 -0.037126086 -0.019950638 -0.030782549
## 23 -0.027937093 -0.014967325 0.013461762 -0.026332583 -0.022404096
## 24 -0.023998670 -0.043336153 -0.038088405 -0.010658741 -0.001221758
## 25 -0.002888156 -0.070120480 -0.142515978 0.013556129 0.017264095
## 26 -0.023850346 -0.033350676 -0.024863111 -0.015344871 -0.008811213
## 27 -0.021331484 -0.024228162 -0.020421494 -0.018335613 -0.015952162
## 28 -0.038435035 -0.032938706 0.022458728 -0.023438008 -0.007854707
## 29 -0.030593043 -0.009837774 0.029014505 -0.030219100 -0.026065069
## 30 -0.031742168 -0.008929719 0.033944364 -0.031274710 -0.026654070
## 31 -0.029588488 -0.012652092 0.021932584 -0.028331832 -0.024017098
## 32 -0.004083363 -0.013611347 -0.061149643 -0.014064879 -0.025508592
## 33 -0.008657411 0.038495867 0.025009056 -0.041414071 -0.064647282
## 34 -0.011271019 -0.020054820 -0.046947884 -0.014880735 -0.019994128
## 35 -0.018162034 -0.006527372 -0.006295554 -0.025068840 -0.029658547
## 36 -0.025307341 -0.076651069 -0.079603479 0.004535153 0.024170035
## 37 -0.018013710 0.003458095 0.006929730 -0.029754966 -0.037247994
## 38 -0.031251119 -0.034574400 -0.002816248 -0.018767693 -0.007238723
## 39 -0.021175678 0.001915641 0.014950222 -0.030730659 -0.035802507
## 40 -0.015810207 -0.047786188 -0.070445310 -0.004101151 0.001442215
## 41 -0.033412287 -0.047010377 -0.012950898 -0.014001648 0.002385213
## 42 -0.024371341 -0.072339389 -0.076688232 0.002983801 0.020817072
## 43 -0.018466157 -0.042656629 -0.054892557 -0.007987672 -0.002218765
## 44 -0.026567356 -0.004936756 0.022833238 -0.030378936 -0.030134046
## 45 -0.023687052 0.008951477 0.032655035 -0.035448839 -0.040922467
## 46 -0.018869941 0.016257890 0.027236945 -0.036328364 -0.046885420
## 47 -0.015354019 0.006407713 0.002450203 -0.029722909 -0.039717471
## 48 -0.025064278 -0.017237442 0.001137130 -0.023693564 -0.020931608
## 49 -0.039195353 -0.123261887 -0.099033795 0.019264925 0.060744778
## 50 -0.022693733 -0.018100381 -0.007646540 -0.021998183 -0.020483120
## 51 0.049099283 0.021143638 -0.183959802 -0.001860398 -0.056506876
## 21 22 23 24 25
## 1 -0.0419281127 -0.051718351 -0.012223150 0.013749255 0.0119437117
## 2 -0.0082640934 -0.017535492 -0.014631413 -0.028647885 -0.0479548814
## 3 0.0021940108 -0.007506379 -0.015017951 -0.041491243 -0.0670730541
## 4 -0.0162913794 -0.025114767 -0.014407468 -0.018855703 -0.0331778182
## 5 -0.0064563227 -0.025419303 -0.008805392 -0.025526380 -0.0595705928
## 6 -0.0364993229 -0.031433079 -0.021663186 -0.001292795 0.0150502752
## 7 -0.0393800202 -0.015435698 -0.033051380 -0.008174465 0.0365279257
## 8 -0.0346049704 -0.024926450 -0.024606872 -0.006224056 0.0156401479
## 9 -0.0057760130 -0.009153426 -0.018397301 -0.035033686 -0.0473217421
## 10 -0.0242907171 -0.035220009 -0.012620412 -0.007680018 -0.0206578411
## 11 -0.0400855353 -0.007207250 -0.038481633 -0.012253950 0.0455130038
## 12 -0.0315217825 -0.003684759 -0.035924490 -0.020166053 0.0258049627
## 13 -0.0217998869 -0.004869583 -0.029845348 -0.026269114 -0.0010478759
## 14 -0.0222259425 -0.021900870 -0.019644453 -0.016513515 -0.0146336599
## 15 -0.0265776855 -0.017347183 -0.024830812 -0.016016233 0.0008630804
## 16 -0.0222525147 -0.008390716 -0.027937093 -0.023998670 -0.0028881565
## 17 0.0037768344 -0.006166587 -0.014967325 -0.043336153 -0.0701204805
## 18 0.0209561105 -0.037126086 0.013461762 -0.038088405 -0.1425159781
## 19 -0.0322020992 -0.019950638 -0.026332583 -0.010658741 0.0135561288
## 20 -0.0371209990 -0.030782549 -0.022404096 -0.001221758 0.0172640947
## 21 0.9681373711 -0.017309793 -0.027763772 -0.012361571 0.0149363370
## 22 -0.0173097926 0.966962681 -0.010113892 -0.013747203 -0.0373184518
## 23 -0.0277637720 -0.010113892 0.970084075 -0.019208787 0.0102649599
## 24 -0.0123615708 -0.013747203 -0.019208787 0.972097675 -0.0337950952
## 25 0.0149363370 -0.037318452 0.010264960 -0.033795095 0.8733110174
## 26 -0.0166574230 -0.014245466 -0.021268915 -0.024638023 -0.0228125274
## 27 -0.0188339802 -0.017460712 -0.020497332 -0.021338560 -0.0198083680
## 28 -0.0275360867 0.002630853 -0.037599578 -0.026445652 0.0206735215
## 29 -0.0319744104 -0.007205892 -0.034016235 -0.017895610 0.0239646821
## 30 -0.0332177672 -0.005904840 -0.035498051 -0.017753527 0.0283923251
## 31 -0.0299962246 -0.008277196 -0.032270570 -0.018676335 0.0177832958
## 32 -0.0108667063 -0.037782025 -0.003658934 -0.015592823 -0.0585365059
## 33 -0.0372062083 -0.034188802 -0.020363918 0.000729358 0.0145469363
## 34 -0.0132961496 -0.029247682 -0.010225864 -0.018643294 -0.0447069834
## 35 -0.0243172893 -0.021709854 -0.020913052 -0.015165174 -0.0089123377
## 36 0.0013739633 -0.011142399 -0.013241614 -0.038901468 -0.0680364614
## 37 -0.0286131381 -0.022208116 -0.022973179 -0.011900875 0.0020702217
## 38 -0.0215456293 -0.005634993 -0.029236361 -0.026020824 -0.0023848176
## 39 -0.0302518570 -0.018495967 -0.026150034 -0.012822977 0.0096318246
## 40 -0.0043929230 -0.023084345 -0.009099908 -0.028258230 -0.0630348246
## 41 -0.0176451427 -0.002725634 -0.028871272 -0.030349307 -0.0102334172
## 42 0.0001585582 -0.012367312 -0.013160318 -0.037375885 -0.0658659127
## 43 -0.0086035648 -0.020176345 -0.013200219 -0.026945050 -0.0493350940
## 44 -0.0311836860 -0.012028085 -0.030626159 -0.015767241 0.0176967624
## 45 -0.0351973290 -0.015817723 -0.030514187 -0.010871150 0.0250852940
## 46 -0.0348871761 -0.021635074 -0.026778972 -0.007855849 0.0192341757
## 47 -0.0279635137 -0.025384613 -0.020669157 -0.010588409 -0.0024006838
## 48 -0.0246553858 -0.013366528 -0.026211383 -0.019563986 -0.0008041373
## 49 0.0117482331 0.006464639 -0.018317499 -0.055895357 -0.0803833795
## 50 -0.0225360954 -0.016083520 -0.023379668 -0.019528816 -0.0087825417
## 51 0.0128088006 -0.100506538 0.047810391 0.002779615 -0.1756410645
## 26 27 28 29 30
## 1 0.002284283 -0.011797679 0.023898157 -0.013976925 -0.013259614
## 2 -0.024250150 -0.021064755 -0.018973532 -0.011418213 -0.010612304
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## 31 32 33 34 35
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## 36 37 38 39 40
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## 46 47 48 49 50
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## 8 -0.0413666923 -0.03442695554 -0.0224728906 0.0387520617 -0.021330304
## 9 0.0025489007 -0.00280519452 -0.0192257569 -0.0870736011 -0.019289336
## 10 -0.0316531775 -0.03211711988 -0.0148195267 0.0329099159 -0.016952371
## 11 -0.0419174754 -0.02873376166 -0.0315292980 0.0117448120 -0.026460349
## 12 -0.0293098947 -0.01999741335 -0.0300910133 -0.0227734801 -0.025587887
## 13 -0.0169483544 -0.01300815463 -0.0263467097 -0.0492176249 -0.023410951
## 14 -0.0239199513 -0.02296577564 -0.0195521764 -0.0060655020 -0.019596212
## 15 -0.0279389383 -0.02382130771 -0.0228670652 -0.0041184849 -0.021491551
## 16 -0.0188699407 -0.01535401915 -0.0250642779 -0.0391953530 -0.022693733
## 17 0.0162578898 0.00640771321 -0.0172374416 -0.1232618867 -0.018100381
## 18 0.0272369450 0.00245020324 0.0011371298 -0.0990337955 -0.007646540
## 19 -0.0363283635 -0.02972290933 -0.0236935635 0.0192649252 -0.021998183
## 20 -0.0468854200 -0.03971747067 -0.0209316081 0.0607447782 -0.020483120
## 21 -0.0348871761 -0.02796351374 -0.0246553858 0.0117482331 -0.022536095
## 22 -0.0216350737 -0.02538461273 -0.0133665276 0.0064646395 -0.016083520
## 23 -0.0267789716 -0.02066915744 -0.0262113827 -0.0183174990 -0.023379668
## 24 -0.0078558491 -0.01058840945 -0.0195639858 -0.0558953572 -0.019528816
## 25 0.0192341757 -0.00240068385 -0.0008041373 -0.0803833795 -0.008782542
## 26 -0.0137026836 -0.01425405946 -0.0208022767 -0.0416986194 -0.020256868
## 27 -0.0177802192 -0.01778517341 -0.0202228196 -0.0272226188 -0.019947599
## 28 -0.0216820941 -0.01328952935 -0.0313264015 -0.0503336190 -0.026252155
## 29 -0.0312314810 -0.02234327786 -0.0288085816 -0.0127512081 -0.024870669
## 30 -0.0323797658 -0.02258771784 -0.0297556925 -0.0121949084 -0.025412194
## 31 -0.0290286694 -0.02139016243 -0.0277085212 -0.0160911819 -0.024237684
## 32 -0.0149328762 -0.02298949630 -0.0092721879 -0.0013279314 -0.013734502
## 33 -0.0482797356 -0.04170899129 -0.0195727024 0.0693751879 -0.019720173
## 34 -0.0149211944 -0.02008178601 -0.0135636164 -0.0149706458 -0.016164144
## 35 -0.0266031669 -0.02450536339 -0.0203316281 -0.0002199351 -0.020049892
## 36 0.0112195610 0.00170366700 -0.0160167687 -0.1037747501 -0.017432503
## 37 -0.0324499964 -0.02817101001 -0.0215699182 0.0139767894 -0.020777944
## 38 -0.0169014875 -0.01324028304 -0.0259496270 -0.0481038940 -0.023185917
## 39 -0.0332116256 -0.02736473324 -0.0236318017 0.0098000845 -0.021948841
## 40 -0.0008724212 -0.00958603873 -0.0130871533 -0.0570056431 -0.015829594
## 41 -0.0106680025 -0.00852391966 -0.0258261094 -0.0670336232 -0.023087238
## 42 0.0091573645 0.00005417871 -0.0159255826 -0.0970936339 -0.017390386
## 43 -0.0053249356 -0.01126016252 -0.0156843529 -0.0514393389 -0.017320596
## 44 -0.0320047921 -0.02444471137 -0.0265790365 -0.0032851987 -0.023611924
## 45 -0.0387186714 -0.02974753809 -0.0263819477 0.0181500866 -0.023531300
## 46 0.9595003575 -0.03278977545 -0.0239082695 0.0315135010 -0.022138980
## 47 -0.0327897755 0.97054615381 -0.0200580654 0.0198234879 -0.019923538
## 48 -0.0239082695 -0.02005806536 0.9761563951 -0.0197082164 -0.022025855
## 49 0.0315135010 0.01982348795 -0.0197082164 0.8216178089 -0.019428916
## 50 -0.0221389802 -0.01992353828 -0.0220258547 -0.0194289164 0.979011468
## 51 -0.0073516449 -0.03977540282 0.0242209261 0.0813672909 0.005263400
## 51
## 1 -0.169486584
## 2 -0.025441836
## 3 0.015910217
## 4 -0.056498849
## 5 -0.073651878
## 6 -0.061224788
## 7 0.035367152
## 8 -0.026738755
## 9 0.018909558
## 10 -0.102139135
## 11 0.083834974
## 12 0.090701039
## 13 0.068658246
## 14 -0.028707029
## 15 0.004318212
## 16 0.049099283
## 17 0.021143638
## 18 -0.183959802
## 19 -0.001860398
## 20 -0.056506876
## 21 0.012808801
## 22 -0.100506538
## 23 0.047810391
## 24 0.002779615
## 25 -0.175641065
## 26 0.006638218
## 27 -0.008460658
## 28 0.120812865
## 29 0.071142077
## 30 0.080577853
## 31 0.061878106
## 32 -0.137905986
## 33 -0.075979912
## 34 -0.084978031
## 35 -0.024332822
## 36 -0.003734719
## 37 -0.020474219
## 38 0.063854408
## 39 0.003458950
## 40 -0.063442766
## 41 0.074493197
## 42 -0.008882214
## 43 -0.040111081
## 44 0.042147291
## 45 0.026618784
## 46 -0.007351645
## 47 -0.039775403
## 48 0.024220926
## 49 0.081367291
## 50 0.005263400
## 51 0.463978500Numeral 2 Compruebe que los residuos en el objeto “modelo_estimado” son iguales al producto de M*y, donde “y” es la variable endógena en el modelo (“crime”)
#Comprobacion de los residuos
residuos_estimados<-matriz_m3%*%modelo_estimado_1$model$crime
comparativo<-as.data.frame(cbind(residuos_estimados,modelo_estimado_1$residuals,residuos_estimados-modelo_estimado_1$residuals))
names(comparativo)<-c("Residuos_estimados","Reciduos_modelo","Diferencia")
comparativo## Residuos_estimados Reciduos_modelo Diferencia
## 1 -311.70552 -311.70552 -0.00000000000676436684
## 2 116.80291 116.80291 0.00000000000024158453
## 3 45.25394 45.25394 0.00000000000013500312
## 4 -34.44604 -34.44604 -0.00000000000049737992
## 5 243.00035 243.00035 0.00000000000073896445
## 6 -145.11556 -145.11556 -0.00000000000153477231
## 7 86.13208 86.13208 -0.00000000000197530881
## 8 88.30923 88.30923 -0.00000000000142108547
## 9 689.82331 689.82331 0.00000000000011368684
## 10 -163.28540 -163.28540 -0.00000000000034106051
## 11 60.89843 60.89843 -0.00000000000240163445
## 12 126.92483 126.92483 -0.00000000000203215222
## 13 -19.26611 -19.26611 -0.00000000000094146912
## 14 322.59487 322.59487 -0.00000000000090949470
## 15 -22.44199 -22.44199 -0.00000000000097344355
## 16 128.18489 128.18489 -0.00000000000090949470
## 17 -70.82382 -70.82382 0.00000000000063948846
## 18 -227.95033 -227.95033 0.00000000000306954462
## 19 287.10188 287.10188 -0.00000000000125055521
## 20 303.87924 303.87924 -0.00000000000130739863
## 21 -341.98644 -341.98644 -0.00000000000170530257
## 22 -107.18138 -107.18138 -0.00000000000002842171
## 23 -30.63408 -30.63408 -0.00000000000126476607
## 24 189.45014 189.45014 0.00000000000002842171
## 25 -811.13733 -811.13733 0.00000000000204636308
## 26 -351.76785 -351.76785 -0.00000000000022737368
## 27 102.71399 102.71399 -0.00000000000044053650
## 28 -23.36012 -23.36012 -0.00000000000157029945
## 29 73.37583 73.37583 -0.00000000000201794137
## 30 -91.63472 -91.63472 -0.00000000000181898940
## 31 324.02875 324.02875 -0.00000000000136424205
## 32 -115.85426 -115.85426 0.00000000000062527761
## 33 113.65150 113.65150 -0.00000000000140687462
## 34 217.94310 217.94310 0.00000000000008526513
## 35 -112.69538 -112.69538 -0.00000000000100897068
## 36 21.38352 21.38352 0.00000000000076028073
## 37 -88.91338 -88.91338 -0.00000000000109423581
## 38 99.41783 99.41783 -0.00000000000083844043
## 39 -102.65463 -102.65463 -0.00000000000110844667
## 40 217.88117 217.88117 0.00000000000054001248
## 41 -84.09487 -84.09487 -0.00000000000100897068
## 42 137.78255 137.78255 0.00000000000073896445
## 43 48.89108 48.89108 0.00000000000021316282
## 44 -67.16278 -67.16278 -0.00000000000156319402
## 45 -39.28725 -39.28725 -0.00000000000162714286
## 46 -415.78430 -415.78430 -0.00000000000119371180
## 47 -145.49859 -145.49859 -0.00000000000090949470
## 48 -183.60777 -183.60777 -0.00000000000110844667
## 49 -138.39375 -138.39375 0.00000000000093791641
## 50 -232.90808 -232.90808 -0.00000000000065369932
## 51 434.16632 434.16632 0.00000000000494537744Numeral 3 Muestre que los autovalores de x’x son positivos (use el comando eigen)
#Autovalores positivos
descomposicion3<-eigen(matriz_xx3)
autovalores3<-descomposicion3$values
print(autovalores3)## [1] 17956.580914 279.157317 1.681762print(autovalores3>0)## [1] TRUE TRUE TRUEEjercicio 4 Dentro del archivo “Investiment_Equation.xlsx” se encuentran datos para estimar una función de inversión, para un país, y contiene las siguientes variables: InvReal=Inversión Real en millones de US, Trend=tendencia, Inflation=inflación, PNBr=Producto Nacional Bruto Real en US, Interest=Tasa de interés
Numeral 1 Estima la ecuación de inversión, presenta sus resultados en formato APA.
options(scipen = 99999999)
library(stargazer)##
## Please cite as:## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.2. https://CRAN.R-project.org/package=stargazerlibrary(readxl)
Investiment_Equation <- read_excel("C:/MEGA DOCS/UES/CICLO I - 2021/ECONOMETTRIA/EJERCICIIOS/GUIA 1/Investiment_Equation.xlsx")
funcion_inversion<-lm(formula=InvReal~Trend+Inflation+PNBr+Interest,data = Investiment_Equation)
stargazer(funcion_inversion,title = "Ecuacion de Inversion",type = "text")##
## Ecuacion de Inversion
## ===============================================
## Dependent variable:
## ---------------------------
## InvReal
## -----------------------------------------------
## Trend -0.016***
## (0.002)
##
## Inflation 0.00002
## (0.001)
##
## PNBr 0.665***
## (0.054)
##
## Interest -0.240*
## (0.120)
##
## Constant -0.503***
## (0.054)
##
## -----------------------------------------------
## Observations 15
## R2 0.973
## Adjusted R2 0.962
## Residual Std. Error 0.007 (df = 10)
## F Statistic 90.089*** (df = 4; 10)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Numeral 2 Calcule los residuos a través de la matriz M
#Construccion de Matriz x
matriz_x4<-model.matrix(funcion_inversion)
#Construccion de Matriz x-x
matriz_xx4<-t(matriz_x4)%*%matriz_x4
#Construccion de Matriz A
matriz_a4<-solve(matriz_xx4)%*%t(matriz_x4)
#Construccion de Matriz P
matriz_p4<-matriz_x4%*%matriz_a4
#Construccion de Matriz M
n4<-nrow(matriz_x4)
matriz_m4<-diag(n4)-matriz_p4
#Residuos usando matriz M
matriz_m4%*%funcion_inversion$model$InvReal## [,1]
## 1 -0.0100602233
## 2 -0.0009290882
## 3 0.0029656679
## 4 0.0078576839
## 5 0.0028109133
## 6 0.0006259732
## 7 0.0075909286
## 8 -0.0055352778
## 9 -0.0037254127
## 10 0.0006953129
## 11 0.0019904770
## 12 -0.0001288433
## 13 -0.0101976729
## 14 0.0068712384
## 15 -0.0008316770Numeral 3 Calcule un intervalo de confianza del 93% para el impacto del PNBr en la Inversión, e interprételo.
confint(funcion_inversion,parm = "PNBr",level = 0.93)## 3.5 % 96.5 %
## PNBr 0.554777 0.774317Interpretación: En el 93% de las veces, que se estime la función de inversión, por cadan $1 que aumente el PNBr la inversión aumentará entre 0.55 y 0.77 US.
Ejercicio 5 Dentro del archivo “consumption_equation.RData” se encuentran objetos relacionados a una función de consumo, que se construyó usando las variables: C=Consumo en millones de US$, Yd=Ingreso disponible, W=Riqueza, I=Tasa de interés
Numeral 1 Calcule los residuos del modelo.
options(scipen = 99999999)
load("C:/MEGA DOCS/UES/CICLO I - 2021/ECONOMETTRIA/EJERCICIIOS/GUIA 1/consumption_equation.RData")
n5<-nrow(P)
#Opteniendo matriz M
matriz_m5<-diag(n5)-P
#Opteniendo los residuos
residuos_m5<-matriz_m5%*%C
print(residuos_m5)## [,1]
## 1 -5.859103
## 2 2.605057
## 3 45.765735
## 4 31.102448
## 5 -21.037889
## 6 7.008120
## 7 17.859663
## 8 10.705631
## 9 22.002328
## 10 -2.689665
## 11 7.784083
## 12 -13.127696
## 13 17.521565
## 14 17.304695
## 15 -16.308260
## 16 -5.255508
## 17 2.788211
## 18 -16.379339
## 19 -14.327554
## 20 11.749135
## 21 -31.424669
## 22 -23.329596
## 23 22.171806
## 24 -5.040038
## 25 -36.191398
## 26 -25.211753
## 27 -21.411271
## 28 1.410519
## 29 -24.229564
## 30 20.971808
## 31 43.342653
## 32 36.808458
## 33 17.882297
## 34 -33.100273
## 35 -37.819995
## 36 -49.370820
## 37 23.456143
## 38 -25.510341
## 39 -11.960629
## 40 -9.234201
## 41 21.949616
## 42 3.211123
## 43 -14.511436
## 44 3.197576
## 45 -62.396763
## 46 -66.854500
## 47 8.330745
## 48 91.963380
## 49 61.620735
## 50 48.148861
## 51 -10.717721
## 52 -84.069717
## 53 -56.426627
## 54 125.113605Numeral 2 Calcule la varianza del error del modelo.
#Sigma cuadrado
k<-4
#Varianza del error
Var_error<-t(residuos_m5)%*%residuos_m5/(n5-k)
print(Var_error)## [,1]
## [1,] 1428.746Numeral 3 Obtenga la matriz de Var-Cov del modelo.
var_error<-as.vector(Var_error)
#Opteniendo matriz de var-covar
var_cov<-var_error*solve(XX)
print(var_cov)## (Intercept) Yd W I
## (Intercept) 164.522304918 -0.09333539523 0.009670913575 10.5186890800
## Yd -0.093335395 0.00018911268 -0.000032769561 -0.0072901023
## W 0.009670914 -0.00003276956 0.000006165749 0.0004193421
## I 10.518689080 -0.00729010228 0.000419342092 5.3203789879Numeral 4 Obtenga las estimaciones del Consumo, del modelo propuesto.
C_estimado<-P%*%C
print(C_estimado)## [,1]
## 1 982.2591
## 2 995.4949
## 3 979.5343
## 4 1059.7976
## 5 1128.1379
## 6 1135.3919
## 7 1179.3403
## 8 1211.1944
## 9 1288.3977
## 10 1351.4897
## 11 1374.0159
## 12 1406.1277
## 13 1453.1784
## 14 1493.4953
## 15 1557.5083
## 16 1622.5555
## 17 1681.2118
## 18 1801.1793
## 19 1911.9276
## 20 1994.3509
## 21 2097.6247
## 22 2207.5296
## 23 2242.6282
## 24 2322.5400
## 25 2441.3914
## 26 2575.7118
## 27 2697.3113
## 28 2652.2895
## 29 2735.1296
## 30 2847.9282
## 31 2948.7573
## 32 3087.8915
## 33 3185.3177
## 34 3226.1003
## 35 3273.8200
## 36 3324.8708
## 37 3430.8439
## 38 3666.1103
## 39 3832.8606
## 40 3990.4342
## 41 4091.4504
## 42 4276.2889
## 43 4408.2114
## 44 4471.3024
## 45 4528.9968
## 46 4661.3545
## 47 4740.5693
## 48 4836.1366
## 49 5013.9793
## 50 5189.3511
## 51 5434.6177
## 52 5767.7697
## 53 6024.8266
## 54 6132.6864plot(C_estimado)
as.data.frame(cbind(C,C_estimado,residuos_m5))->cuadro
names(cuadro)<-c("C","C_estimado","Residuos")
print(cuadro)## C C_estimado Residuos
## 1 976.4 982.2591 -5.859103
## 2 998.1 995.4949 2.605057
## 3 1025.3 979.5343 45.765735
## 4 1090.9 1059.7976 31.102448
## 5 1107.1 1128.1379 -21.037889
## 6 1142.4 1135.3919 7.008120
## 7 1197.2 1179.3403 17.859663
## 8 1221.9 1211.1944 10.705631
## 9 1310.4 1288.3977 22.002328
## 10 1348.8 1351.4897 -2.689665
## 11 1381.8 1374.0159 7.784083
## 12 1393.0 1406.1277 -13.127696
## 13 1470.7 1453.1784 17.521565
## 14 1510.8 1493.4953 17.304695
## 15 1541.2 1557.5083 -16.308260
## 16 1617.3 1622.5555 -5.255508
## 17 1684.0 1681.2118 2.788211
## 18 1784.8 1801.1793 -16.379339
## 19 1897.6 1911.9276 -14.327554
## 20 2006.1 1994.3509 11.749135
## 21 2066.2 2097.6247 -31.424669
## 22 2184.2 2207.5296 -23.329596
## 23 2264.8 2242.6282 22.171806
## 24 2317.5 2322.5400 -5.040038
## 25 2405.2 2441.3914 -36.191398
## 26 2550.5 2575.7118 -25.211753
## 27 2675.9 2697.3113 -21.411271
## 28 2653.7 2652.2895 1.410519
## 29 2710.9 2735.1296 -24.229564
## 30 2868.9 2847.9282 20.971808
## 31 2992.1 2948.7573 43.342653
## 32 3124.7 3087.8915 36.808458
## 33 3203.2 3185.3177 17.882297
## 34 3193.0 3226.1003 -33.100273
## 35 3236.0 3273.8200 -37.819995
## 36 3275.5 3324.8708 -49.370820
## 37 3454.3 3430.8439 23.456143
## 38 3640.6 3666.1103 -25.510341
## 39 3820.9 3832.8606 -11.960629
## 40 3981.2 3990.4342 -9.234201
## 41 4113.4 4091.4504 21.949616
## 42 4279.5 4276.2889 3.211123
## 43 4393.7 4408.2114 -14.511436
## 44 4474.5 4471.3024 3.197576
## 45 4466.6 4528.9968 -62.396763
## 46 4594.5 4661.3545 -66.854500
## 47 4748.9 4740.5693 8.330745
## 48 4928.1 4836.1366 91.963380
## 49 5075.6 5013.9793 61.620735
## 50 5237.5 5189.3511 48.148861
## 51 5423.9 5434.6177 -10.717721
## 52 5683.7 5767.7697 -84.069717
## 53 5968.4 6024.8266 -56.426627
## 54 6257.8 6132.6864 125.113605Ejercicio 6 Dentro del archivo “datos_ventas.RData” se encuentran los datos para estimar una función de ventas, para una empresa, y contiene las siguientes variables: ventas=Ventas en milones de US, tv=gasto en publicidad en TV en millones de US, radio=gasto en publicidad en radio en millones de US$. periodico=gasto en publicidad en periodico en millones de US
Numeral 1 Estima la ecuación de ventas, presenta sus resultados en formato APA.
options(scipen = 99999999)
load("C:/MEGA DOCS/UES/CICLO I - 2021/ECONOMETTRIA/EJERCICIIOS/GUIA 1/datos_ventas.RData")
library(stargazer)
modelo_de_ventas<-lm(formula = ventas~tv+radio+periodico,data = datos_ventas)
stargazer(modelo_de_ventas,title = "Ecuacion de Ventas",type = "text")##
## Ecuacion de Ventas
## ===============================================
## Dependent variable:
## ---------------------------
## ventas
## -----------------------------------------------
## tv 0.045
## (0.118)
##
## radio -3.450***
## (0.206)
##
## periodico 18.485***
## (0.563)
##
## Constant -33.289***
## (7.172)
##
## -----------------------------------------------
## Observations 200
## R2 0.847
## Adjusted R2 0.844
## Residual Std. Error 33.875 (df = 196)
## F Statistic 360.758*** (df = 3; 196)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Numeral 2 Calcule los residuos a través de la matriz M
#Construccion de Matriz x
matriz_x6<-model.matrix(modelo_de_ventas)
#Construccion de Matriz x-x
matriz_xx6<-t(matriz_x6)%*%matriz_x6
#Construccion de Matriz A
matriz_a6<-solve(matriz_xx6)%*%t(matriz_x6)
#Construccion de Matriz P
matriz_p6<-matriz_x6%*%matriz_a6
#Construccion de Matriz M
n6<-nrow(matriz_x6)
matriz_m6<-diag(n6)-matriz_p6
#Residuos usando matriz M
matriz_m6%*%modelo_de_ventas$model$ventas## [,1]
## 1 -17.8524638
## 2 19.0821552
## 3 33.7931916
## 4 -17.3508987
## 5 10.2572135
## 6 74.2038531
## 7 -15.2465204
## 8 -23.4242974
## 9 -39.6405207
## 10 45.1613878
## 11 -40.6649446
## 12 8.9590198
## 13 5.1392043
## 14 -22.6236420
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## 138 19.5045244
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## 148 -25.9962973
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## 150 -20.6385139
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## 152 -33.3544363
## 153 3.7729886
## 154 -11.3760631
## 155 5.0805779
## 156 17.9950120
## 157 -7.8494101
## 158 -0.2201702
## 159 35.3022384
## 160 -11.5540752
## 161 0.6591253
## 162 -5.5871655
## 163 7.5462798
## 164 -9.3303245
## 165 -19.0175482
## 166 55.7263685
## 167 32.0402256
## 168 31.6353338
## 169 11.4108832
## 170 76.5904762
## 171 -32.7991015
## 172 -0.2825814
## 173 -19.0264844
## 174 9.3293014
## 175 54.2493038
## 176 -22.1047290
## 177 11.5543472
## 178 12.5352601
## 179 98.7318828
## 180 -0.3195726
## 181 4.3908269
## 182 43.6649823
## 183 -53.0060931
## 184 -18.3203130
## 185 33.8772333
## 186 -24.7792769
## 187 -11.5610805
## 188 2.7811315
## 189 73.1591927
## 190 -31.1749134
## 191 14.6672356
## 192 -37.2279106
## 193 -45.8529068
## 194 -17.4973688
## 195 -14.2672641
## 196 -56.8557034
## 197 -35.2780738
## 198 5.4730833
## 199 -12.5781921
## 200 46.9637691Numeral 3 Calcule un intervalo de confianza del 96.8% para el impacto del gasto de publicidad en TV, en las ventas, e interprételo.
confint(modelo_de_ventas,parm = "tv",level = 0.968)## 1.6 % 98.4 %
## tv -0.2097376 0.2998052Indica que el gasto en TV no es estadisticamente significativo, de forma individual, ya que incluye el “0” dentro del intervalo.