Las noticias muestran un aumento constante de accidentes de tránsito
en la ciudad de Lima. Muchos consideran que este problema lo debe
enfrentar la Municipalidad, y que ésta no está haciendo nada por
buscarle alguna solución. Por su parte, la Municipalidad manifiesta que
si bien es cierto, han realizado un sinnúmero de estudios para
enfrentarlos; sin embargo muy pocos han sido planteados por
especialistas conocedores del tema. Por ello, en la actualidad han
decidido que los estudios tengan soporte estadístico. En ese sentido,
con la finalidad de determinar los factores que influyen sobre la tasa
de accidentes de tránsito, la Municipalidad Metropolitana de Lima ha
decidido desarrollar un estudio analítico. Para llevar a cabo dicho
estudio, se seleccionaron al azar 39 segmentos de vías de tránsito
provenientes de calles, avenidas o autopistas, de los cuales se recopiló
datos de las siguientes variables:
TAS: Tasa anual de accidentes de tránsito.
LON: Longitud (en km.) del segmento de la vía de tránsito
seleccionada.
NVD: Número de vehículos (en miles) que pasan por la vía de tránsito al
día.
PVT: Porcentaje de vehículos de transporte urbano que pasan por la
carretera con respecto al total de vehículos.
VLV: Velocidad límite (en km./hora) en la vía de tránsito.
NSV: Número de intersecciones del segmento de la vía seleccionada con
otras vías de tránsito.
NST: Número de señales de tránsito en el segmento de la vía
TCA: Total de carriles en ambas direcciones.
TVT Tipo de vía de tránsito 1: Principal 2: Secundaria
Los datos los puede encontrar en PD5.xlsx
Antes de correr nuestro modelo debemos aplicarle factor a la variables cualitativa, para que así R pueda tomarlo en cuenta al momento de hacer nuestras estimaciones.
Creamos nuestro modelo
##
## Call:
## lm(formula = TAS ~ ., data = PD5)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.33470 -0.04017 -0.00186 0.06374 0.28582
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.3984044 0.9128546 -1.532 0.13602
## LON 0.1874995 0.0671676 2.792 0.00904 **
## NVD 0.0801517 0.0637831 1.257 0.21859
## PVT 0.0788690 0.0167447 4.710 5.28e-05 ***
## VLV -0.0009491 0.0016178 -0.587 0.56183
## NSV 0.0048743 0.0655002 0.074 0.94117
## NST -0.0075934 0.0079035 -0.961 0.34435
## TCA 0.0059667 0.0110360 0.541 0.59274
## TVT2 -0.1000837 0.0391209 -2.558 0.01581 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1176 on 30 degrees of freedom
## Multiple R-squared: 0.9855, Adjusted R-squared: 0.9816
## F-statistic: 254 on 8 and 30 DF, p-value: < 2.2e-16HO: Bj = 0 (Las variables predictoras no son significativas) H1: Bj \(\neq\) 0 (Al menos una variable es significativa) solo se considera significativas a las variables PVT , LON.
modelo2 <- lm(TAS~LON+NVD+PVT+VLV+NSV+NST+TCA, PD5) # modelo sin la variable cualitativa
modelo <- lm(TAS ~ . , PD5) # modelo con las variables predictoras cuantitativasPRueba de hipotesis :
H0 : La inclusión de TVT NO ES significativa H1 : La inclusión de TVT SI es significativa
Usamos la funcion anova para comparar si la inclusion de esa variable es significativa para nuestro modelo.
## Analysis of Variance Table
##
## Model 1: TAS ~ LON + NVD + PVT + VLV + NSV + NST + TCA
## Model 2: TAS ~ LON + NVD + PVT + VLV + NSV + NST + TCA + TVT
## Res.Df RSS Df Sum of Sq Pr(>Chi)
## 1 31 0.50557
## 2 30 0.41503 1 0.090545 0.01052 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1como el pvalor = 0.011 > 0.010 (Se acepta H0) Por lo tanto La inclusión de TVT NO es significativa, porque estamos usando un alfa de 0.01.
Aplicaremos el mejor modelo usando la Raíz del cuadrado medio del error (RMSE)
\[\sqrt{\frac{\sum_{i = 1}^{n}E_{i}^{2}}{n}}\] para ello usaremos la librería “olsrr”
##
## Adjuntando el paquete: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversExplicación del código:
Con el codigo “ols_step_all_possible()” accederemos a diversos métodos
de seleccion de variables a lo que nosotros llamaremos res de
respuestas, luego extramos los resultados y lo guardamos en la variable
“métricas”, como nos piden con el criterio de CP Mallow, por ello
extraemos la columna 6 donde contiene dichos resultados.
Como el criterio de CP mallow dice que el mejor modelo tiene el menor
CP-Mallow, por ello luego extraemos todos los resultados mostrándonos
así todas la variables con el mejor modelo según este criterio.
## Index N Predictors R-Square Adj. R-Square
## 1 1 1 LON 9.703306e-01 0.96952870
## 3 2 1 PVT 9.490535e-01 0.94767654
## 5 3 1 NSV 9.034657e-01 0.90085669
## 2 4 1 NVD 9.009614e-01 0.89828473
## 4 5 1 VLV 1.218754e-02 -0.01451009
## 7 6 1 TCA 4.502429e-03 -0.02240291
## 8 7 1 TVT 1.112482e-03 -0.02588448
## 6 8 1 NST 8.080837e-06 -0.02701873
## 10 9 2 LON PVT 9.801583e-01 0.97905601
## 16 10 2 NVD PVT 9.756569e-01 0.97430449
## 15 11 2 LON TVT 9.730156e-01 0.97151643
## 14 12 2 LON TCA 9.711528e-01 0.96955015
## 13 13 2 LON NST 9.706114e-01 0.96897866
## 23 14 2 PVT NSV 9.705947e-01 0.96896108
## 12 15 2 LON NSV 9.705708e-01 0.96893589
## 11 16 2 LON VLV 9.704136e-01 0.96876991
## 9 17 2 LON NVD 9.703616e-01 0.96871506
## 26 18 2 PVT TVT 9.531701e-01 0.95056847
## 24 19 2 PVT NST 9.501300e-01 0.94735946
## 25 20 2 PVT TCA 9.499448e-01 0.94716401
## 22 21 2 PVT VLV 9.493364e-01 0.94652175
## 18 22 2 NVD NSV 9.142340e-01 0.90946923
## 27 23 2 VLV NSV 9.114468e-01 0.90652715
## 17 24 2 NVD VLV 9.084710e-01 0.90338606
## 31 25 2 NSV NST 9.073740e-01 0.90222810
## 33 26 2 NSV TVT 9.068535e-01 0.90167869
## 32 27 2 NSV TCA 9.044355e-01 0.89912640
## 20 28 2 NVD TCA 9.018921e-01 0.89644164
## 21 29 2 NVD TVT 9.013201e-01 0.89583783
## 19 30 2 NVD NST 9.011069e-01 0.89561282
## 29 31 2 VLV TCA 2.571153e-02 -0.02841561
## 30 32 2 VLV TVT 1.320128e-02 -0.04162087
## 28 33 2 VLV NST 1.227126e-02 -0.04260256
## 36 34 2 TCA TVT 5.073185e-03 -0.05020053
## 34 35 2 NST TCA 4.558539e-03 -0.05074376
## 35 36 2 NST TVT 1.114282e-03 -0.05437937
## 47 37 3 LON PVT TVT 9.835229e-01 0.98211060
## 37 38 3 LON NVD PVT 9.815389e-01 0.97995647
## 45 39 3 LON PVT NST 9.806861e-01 0.97903066
## 44 40 3 LON PVT NSV 9.802315e-01 0.97853706
## 46 41 3 LON PVT TCA 9.802018e-01 0.97850477
## 43 42 3 LON PVT VLV 9.801613e-01 0.97846084
## 62 43 3 NVD PVT TVT 9.782639e-01 0.97640085
## 58 44 3 NVD PVT VLV 9.773103e-01 0.97536545
## 60 45 3 NVD PVT NST 9.763338e-01 0.97430528
## 59 46 3 NVD PVT NSV 9.758775e-01 0.97380990
## 61 47 3 NVD PVT TCA 9.757679e-01 0.97369085
## 79 48 3 PVT NSV TVT 9.749385e-01 0.97279040
## 57 49 3 LON TCA TVT 9.743408e-01 0.97214147
## 56 50 3 LON NST TVT 9.733836e-01 0.97110217
## 54 51 3 LON NSV TVT 9.731820e-01 0.97088329
## 51 52 3 LON VLV TVT 9.730955e-01 0.97078939
## 42 53 3 LON NVD TVT 9.730156e-01 0.97070268
## 77 54 3 PVT NSV NST 9.726679e-01 0.97032514
## 73 55 3 PVT VLV NSV 9.723083e-01 0.96993476
## 53 56 3 LON NSV TCA 9.713932e-01 0.96894117
## 55 57 3 LON NST TCA 9.713092e-01 0.96884999
## 41 58 3 LON NVD TCA 9.711827e-01 0.96871260
## 50 59 3 LON VLV TCA 9.711563e-01 0.96868399
## 39 60 3 LON NVD NSV 9.709410e-01 0.96845018
## 48 61 3 LON VLV NSV 9.708398e-01 0.96834038
## 52 62 3 LON NSV NST 9.707659e-01 0.96826017
## 49 63 3 LON VLV NST 9.707331e-01 0.96822453
## 78 64 3 PVT NSV TCA 9.707064e-01 0.96819549
## 40 65 3 LON NVD NST 9.706398e-01 0.96812325
## 38 66 3 LON NVD VLV 9.704206e-01 0.96788524
## 81 67 3 PVT NST TVT 9.544630e-01 0.95055982
## 82 68 3 PVT TCA TVT 9.536244e-01 0.94964938
## 76 69 3 PVT VLV TVT 9.534622e-01 0.94947322
## 80 70 3 PVT NST TCA 9.513854e-01 0.94721839
## 74 71 3 PVT VLV NST 9.503053e-01 0.94604574
## 75 72 3 PVT VLV TCA 9.499786e-01 0.94569100
## 63 73 3 NVD VLV NSV 9.219389e-01 0.91524790
## 84 74 3 VLV NSV TCA 9.162528e-01 0.90907448
## 69 75 3 NVD NSV TVT 9.159296e-01 0.90872359
## 67 76 3 NVD NSV NST 9.158428e-01 0.90862932
## 68 77 3 NVD NSV TCA 9.151557e-01 0.90788336
## 85 78 3 VLV NSV TVT 9.149575e-01 0.90766816
## 83 79 3 VLV NSV NST 9.142589e-01 0.90690968
## 65 80 3 NVD VLV TCA 9.130391e-01 0.90558532
## 90 81 3 NSV NST TVT 9.111561e-01 0.90354094
## 66 82 3 NVD VLV TVT 9.088715e-01 0.90106048
## 64 83 3 NVD VLV NST 9.084782e-01 0.90063346
## 91 84 3 NSV TCA TVT 9.084379e-01 0.90058970
## 89 85 3 NSV NST TCA 9.078443e-01 0.89994520
## 72 86 3 NVD TCA TVT 9.024462e-01 0.89408449
## 70 87 3 NVD NST TCA 9.019479e-01 0.89354349
## 71 88 3 NVD NST TVT 9.014874e-01 0.89304350
## 86 89 3 VLV NST TCA 2.687989e-02 -0.05653040
## 88 90 3 VLV TCA TVT 2.588696e-02 -0.05760845
## 87 91 3 VLV NST TVT 1.331269e-02 -0.07126051
## 92 92 3 NST TCA TVT 5.138040e-03 -0.08013584
## 97 93 4 LON NVD PVT TVT 9.845562e-01 0.98273933
## 116 94 4 LON PVT NST TVT 9.841955e-01 0.98233611
## 117 95 4 LON PVT TCA TVT 9.837293e-01 0.98181512
## 114 96 4 LON PVT NSV TVT 9.836789e-01 0.98175873
## 111 97 4 LON PVT VLV TVT 9.835245e-01 0.98158623
## 95 98 4 LON NVD PVT NST 9.820749e-01 0.97996601
## 94 99 4 LON NVD PVT NSV 9.818099e-01 0.97966993
## 93 100 4 LON NVD PVT VLV 9.817176e-01 0.97956672
## 96 101 4 LON NVD PVT TCA 9.815529e-01 0.97938265
## 112 102 4 LON PVT NSV NST 9.808804e-01 0.97863098
## 109 103 4 LON PVT VLV NST 9.807037e-01 0.97843359
## 115 104 4 LON PVT NST TCA 9.806933e-01 0.97842193
## 113 105 4 LON PVT NSV TCA 9.802689e-01 0.97794754
## 108 106 4 LON PVT VLV NSV 9.802357e-01 0.97791049
## 110 107 4 LON PVT VLV TCA 9.802024e-01 0.97787324
## 131 108 4 NVD PVT VLV TVT 9.798861e-01 0.97751971
## 136 109 4 NVD PVT NST TVT 9.790883e-01 0.97662807
## 134 110 4 NVD PVT NSV TVT 9.787969e-01 0.97630247
## 137 111 4 NVD PVT TCA TVT 9.782803e-01 0.97572499
## 129 112 4 NVD PVT VLV NST 9.777653e-01 0.97514942
## 128 113 4 NVD PVT VLV NSV 9.776398e-01 0.97500922
## 130 114 4 NVD PVT VLV TCA 9.773542e-01 0.97469004
## 155 115 4 PVT NSV NST TVT 9.773258e-01 0.97465823
## 132 116 4 NVD PVT NSV NST 9.767947e-01 0.97406467
## 150 117 4 PVT VLV NSV TVT 9.766863e-01 0.97394355
## 135 118 4 NVD PVT NST TCA 9.765580e-01 0.97380011
## 133 119 4 NVD PVT NSV TCA 9.759711e-01 0.97314421
## 156 120 4 PVT NSV TCA TVT 9.749405e-01 0.97199237
## 127 121 4 LON NST TCA TVT 9.745350e-01 0.97153911
## 126 122 4 LON NSV TCA TVT 9.745007e-01 0.97150073
## 123 123 4 LON VLV TCA TVT 9.743701e-01 0.97135476
## 107 124 4 LON NVD TCA TVT 9.743410e-01 0.97132231
## 148 125 4 PVT VLV NSV NST 9.740409e-01 0.97098693
## 122 126 4 LON VLV NST TVT 9.735075e-01 0.97039071
## 125 127 4 LON NSV NST TVT 9.734690e-01 0.97034768
## 120 128 4 LON VLV NSV TVT 9.734110e-01 0.97028292
## 106 129 4 LON NVD NST TVT 9.733836e-01 0.97025225
## 104 130 4 LON NVD NSV TVT 9.732962e-01 0.97015458
## 101 131 4 LON NVD VLV TVT 9.731043e-01 0.96994006
## 154 132 4 PVT NSV NST TCA 9.729726e-01 0.96979289
## 149 133 4 PVT VLV NSV TCA 9.723609e-01 0.96910919
## 103 134 4 LON NVD NSV TCA 9.717582e-01 0.96843562
## 124 135 4 LON NSV NST TCA 9.714853e-01 0.96813065
## 119 136 4 LON VLV NSV TCA 9.714190e-01 0.96805651
## 105 137 4 LON NVD NST TCA 9.713372e-01 0.96796513
## 121 138 4 LON VLV NST TCA 9.713094e-01 0.96793402
## 100 139 4 LON NVD VLV TCA 9.711999e-01 0.96781164
## 98 140 4 LON NVD VLV NSV 9.711342e-01 0.96773828
## 102 141 4 LON NVD NSV NST 9.710563e-01 0.96765116
## 118 142 4 LON VLV NSV NST 9.710529e-01 0.96764735
## 99 143 4 LON NVD VLV NST 9.707359e-01 0.96729305
## 157 144 4 PVT NST TCA TVT 9.551962e-01 0.94992518
## 152 145 4 PVT VLV NST TVT 9.546362e-01 0.94929923
## 153 146 4 PVT VLV TCA TVT 9.537160e-01 0.94827082
## 151 147 4 PVT VLV NST TCA 9.513872e-01 0.94566808
## 139 148 4 NVD VLV NSV TCA 9.265464e-01 0.91790485
## 140 149 4 NVD VLV NSV TVT 9.237409e-01 0.91476928
## 138 150 4 NVD VLV NSV NST 9.228819e-01 0.91380914
## 160 151 4 VLV NSV TCA TVT 9.213025e-01 0.91204399
## 159 152 4 VLV NSV NST TVT 9.181035e-01 0.90846857
## 145 153 4 NVD NSV NST TVT 9.178792e-01 0.90821789
## 158 154 4 VLV NSV NST TCA 9.177878e-01 0.90811574
## 146 155 4 NVD NSV TCA TVT 9.172789e-01 0.90754704
## 144 156 4 NVD NSV NST TCA 9.164349e-01 0.90660371
## 143 157 4 NVD VLV TCA TVT 9.140098e-01 0.90389331
## 141 158 4 NVD VLV NST TCA 9.131773e-01 0.90296287
## 162 159 4 NSV NST TCA TVT 9.120751e-01 0.90173098
## 142 160 4 NVD VLV NST TVT 9.088843e-01 0.89816478
## 147 161 4 NVD NST TCA TVT 9.025110e-01 0.89104173
## 161 162 4 VLV NST TCA TVT 2.706497e-02 -0.08739798
## 171 163 5 LON NVD PVT NST TVT 9.852293e-01 0.98299131
## 166 164 5 LON NVD PVT VLV TVT 9.846965e-01 0.98237784
## 172 165 5 LON NVD PVT TCA TVT 9.846892e-01 0.98236942
## 169 166 5 LON NVD PVT NSV TVT 9.846270e-01 0.98229775
## 190 167 5 LON PVT NSV NST TVT 9.845475e-01 0.98220623
## 192 168 5 LON PVT NST TCA TVT 9.842990e-01 0.98192009
## 187 169 5 LON PVT VLV NST TVT 9.842118e-01 0.98181965
## 191 170 5 LON PVT NSV TCA TVT 9.838686e-01 0.98142441
## 188 171 5 LON PVT VLV TCA TVT 9.837493e-01 0.98128713
## 185 172 5 LON PVT VLV NSV TVT 9.836982e-01 0.98122818
## 164 173 5 LON NVD PVT VLV NST 9.821919e-01 0.97949369
## 167 174 5 LON NVD PVT NSV NST 9.821883e-01 0.97948953
## 170 175 5 LON NVD PVT NST TCA 9.820749e-01 0.97935900
## 163 176 5 LON NVD PVT VLV NSV 9.818981e-01 0.97915542
## 168 177 5 LON NVD PVT NSV TCA 9.818259e-01 0.97907222
## 165 178 5 LON NVD PVT VLV TCA 9.818058e-01 0.97904911
## 183 179 5 LON PVT VLV NSV NST 9.808830e-01 0.97798649
## 189 180 5 LON PVT NSV NST TCA 9.808821e-01 0.97798541
## 186 181 5 LON PVT VLV NST TCA 9.807049e-01 0.97778144
## 200 182 5 NVD PVT VLV NSV TVT 9.805816e-01 0.97763937
## 202 183 5 NVD PVT VLV NST TVT 9.804653e-01 0.97750554
## 184 184 5 LON PVT VLV NSV TCA 9.802915e-01 0.97730538
## 203 185 5 NVD PVT VLV TCA TVT 9.800736e-01 0.97705447
## 205 186 5 NVD PVT NSV NST TVT 9.800491e-01 0.97702627
## 207 187 5 NVD PVT NST TCA TVT 9.791636e-01 0.97600652
## 206 188 5 NVD PVT NSV TCA TVT 9.788017e-01 0.97558986
## 214 189 5 PVT VLV NSV NST TVT 9.787054e-01 0.97547898
## 198 190 5 NVD PVT VLV NSV NST 9.783196e-01 0.97503472
## 201 191 5 NVD PVT VLV NST TCA 9.777682e-01 0.97439971
## 199 192 5 NVD PVT VLV NSV TCA 9.777121e-01 0.97433516
## 217 193 5 PVT NSV NST TCA TVT 9.773969e-01 0.97397214
## 204 194 5 NVD PVT NSV NST TCA 9.770049e-01 0.97352079
## 215 195 5 PVT VLV NSV TCA TVT 9.770017e-01 0.97351714
## 197 196 5 LON NSV NST TCA TVT 9.746358e-01 0.97079268
## 181 197 5 LON NVD NSV TCA TVT 9.745931e-01 0.97074360
## 196 198 5 LON VLV NST TCA TVT 9.745434e-01 0.97068634
## 182 199 5 LON NVD NST TCA TVT 9.745354e-01 0.97067715
## 195 200 5 LON VLV NSV TCA TVT 9.745007e-01 0.97063712
## 178 201 5 LON NVD VLV TCA TVT 9.743727e-01 0.97048978
## 213 202 5 PVT VLV NSV NST TCA 9.740430e-01 0.97011014
## 194 203 5 LON VLV NSV NST TVT 9.737174e-01 0.96973517
## 180 204 5 LON NVD NSV NST TVT 9.735270e-01 0.96951592
## 177 205 5 LON NVD VLV NST TVT 9.735251e-01 0.96951377
## 175 206 5 LON NVD VLV NSV TVT 9.734873e-01 0.96947023
## 179 207 5 LON NVD NSV NST TCA 9.717979e-01 0.96752480
## 174 208 5 LON NVD VLV NSV TCA 9.717634e-01 0.96748512
## 193 209 5 LON VLV NSV NST TCA 9.715238e-01 0.96720925
## 176 210 5 LON NVD VLV NST TCA 9.713400e-01 0.96699754
## 173 211 5 LON NVD VLV NSV NST 9.712699e-01 0.96691680
## 216 212 5 PVT VLV NST TCA TVT 9.552010e-01 0.94841329
## 210 213 5 NVD VLV NSV TCA TVT 9.294830e-01 0.91879855
## 208 214 5 NVD VLV NSV NST TCA 9.268185e-01 0.91573038
## 209 215 5 NVD VLV NSV NST TVT 9.249509e-01 0.91357979
## 218 216 5 VLV NSV NST TCA TVT 9.229371e-01 0.91126088
## 212 217 5 NVD NSV NST TCA TVT 9.188153e-01 0.90651457
## 211 218 5 NVD VLV NST TCA TVT 9.141396e-01 0.90113048
## 223 219 6 LON NVD PVT VLV NST TVT 9.853090e-01 0.98255440
## 228 220 6 LON NVD PVT NST TCA TVT 9.852823e-01 0.98252277
## 226 221 6 LON NVD PVT NSV NST TVT 9.852308e-01 0.98246157
## 224 222 6 LON NVD PVT VLV TCA TVT 9.849912e-01 0.98217704
## 227 223 6 LON NVD PVT NSV TCA TVT 9.847588e-01 0.98190110
## 221 224 6 LON NVD PVT VLV NSV TVT 9.847270e-01 0.98186330
## 238 225 6 LON PVT NSV NST TCA TVT 9.846202e-01 0.98173654
## 235 226 6 LON PVT VLV NSV NST TVT 9.845634e-01 0.98166903
## 237 227 6 LON PVT VLV NST TCA TVT 9.842990e-01 0.98135509
## 236 228 6 LON PVT VLV NSV TCA TVT 9.839822e-01 0.98097886
## 219 229 6 LON NVD PVT VLV NSV NST 9.822605e-01 0.97893433
## 222 230 6 LON NVD PVT VLV NST TCA 9.822116e-01 0.97887624
## 225 231 6 LON NVD PVT NSV NST TCA 9.821885e-01 0.97884879
## 220 232 6 LON NVD PVT VLV NSV TCA 9.819652e-01 0.97858370
## 241 233 6 NVD PVT VLV NSV NST TVT 9.815534e-01 0.97809470
## 234 234 6 LON PVT VLV NSV NST TCA 9.808875e-01 0.97730391
## 242 235 6 NVD PVT VLV NSV TCA TVT 9.808745e-01 0.97728850
## 243 236 6 NVD PVT VLV NST TCA TVT 9.805363e-01 0.97688680
## 244 237 6 NVD PVT NSV NST TCA TVT 9.801026e-01 0.97637186
## 246 238 6 PVT VLV NSV NST TCA TVT 9.787832e-01 0.97480508
## 240 239 6 NVD PVT VLV NSV NST TCA 9.783281e-01 0.97426459
## 233 240 6 LON NVD NSV NST TCA TVT 9.746931e-01 0.96994808
## 239 241 6 LON VLV NSV NST TCA TVT 9.746373e-01 0.96988175
## 231 242 6 LON NVD VLV NSV TCA TVT 9.745950e-01 0.96983155
## 232 243 6 LON NVD VLV NST TCA TVT 9.745436e-01 0.96977053
## 230 244 6 LON NVD VLV NSV NST TVT 9.737466e-01 0.96882406
## 229 245 6 LON NVD VLV NSV NST TCA 9.718082e-01 0.96652224
## 245 246 6 NVD VLV NSV NST TCA TVT 9.298737e-01 0.91672498
## 250 247 7 LON NVD PVT VLV NST TCA TVT 9.854489e-01 0.98216319
## 248 248 7 LON NVD PVT VLV NSV NST TVT 9.853099e-01 0.98199272
## 251 249 7 LON NVD PVT NSV NST TCA TVT 9.852847e-01 0.98196190
## 249 250 7 LON NVD PVT VLV NSV TCA TVT 9.850040e-01 0.98161776
## 253 251 7 LON PVT VLV NSV NST TCA TVT 9.846858e-01 0.98122778
## 247 252 7 LON NVD PVT VLV NSV NST TCA 9.822776e-01 0.97827581
## 254 253 7 NVD PVT VLV NSV NST TCA TVT 9.816726e-01 0.97753418
## 252 254 7 LON NVD VLV NSV NST TCA TVT 9.746931e-01 0.96897866
## 255 255 8 LON NVD PVT VLV NSV NST TCA TVT 9.854516e-01 0.98157203
## Mallow's Cp
## 1 0.96417670
## 3 0.92818011
## 5 0.88618651
## 2 0.88452145
## 4 -0.08722857
## 7 -0.11591732
## 8 -0.10818048
## 6 -0.11155478
## 10 0.97463492
## 16 0.96314702
## 15 0.96562261
## 14 0.96326670
## 13 0.96246184
## 23 0.95461179
## 12 0.96240126
## 11 0.96277536
## 9 0.96257707
## 26 0.93152666
## 24 0.92562311
## 25 0.92625550
## 22 0.92621971
## 18 0.89567894
## 27 0.89041503
## 17 0.88766607
## 31 0.88421157
## 33 0.88376243
## 32 0.88250430
## 20 0.87972469
## 21 0.87845746
## 19 0.87793976
## 29 -0.13323964
## 30 -0.14580440
## 28 -0.16032912
## 36 -0.17528187
## 34 -0.17469408
## 35 -0.17086788
## 47 0.97872504
## 37 0.97470126
## 45 0.97274716
## 44 0.97368446
## 46 0.97299922
## 43 0.97359592
## 62 0.96586531
## 58 0.96506639
## 60 0.96063548
## 59 0.95924670
## 61 0.96105662
## 79 0.96098502
## 57 0.96551904
## 56 0.96421375
## 54 0.96354663
## 51 0.96432782
## 42 0.96404349
## 77 0.95403307
## 73 0.95682413
## 53 0.96112293
## 55 0.96152808
## 41 0.96146111
## 50 0.96209396
## 39 0.96138488
## 48 0.96093276
## 52 0.96000940
## 49 0.96047945
## 78 0.95187664
## 40 0.96072694
## 38 0.96094522
## 81 0.92924829
## 82 0.92877002
## 76 0.92945122
## 80 0.92433162
## 74 0.92305184
## 75 0.92496437
## 63 0.90039077
## 84 0.89242541
## 69 0.89152983
## 67 0.89148421
## 68 0.89185803
## 85 0.88885221
## 83 0.88688369
## 65 0.88627988
## 90 0.88291970
## 66 0.88181289
## 64 0.87982445
## 91 0.88106369
## 89 0.88041621
## 72 0.87410413
## 70 0.87360897
## 71 0.87167296
## 86 -0.20629244
## 88 -0.19710901
## 87 -0.22446163
## 92 -0.23929635
## 97 0.97873085
## 116 0.97748982
## 117 0.97746491
## 114 0.97791412
## 111 0.97778942
## 95 0.97252020
## 94 0.97264439
## 93 0.97370093
## 96 0.97286349
## 112 0.97163443
## 109 0.97128970
## 115 0.97104420
## 113 0.97198976
## 108 0.97269623
## 110 0.97229609
## 131 0.96790514
## 136 0.96372103
## 134 0.96320038
## 137 0.96374752
## 129 0.96173940
## 128 0.96199277
## 130 0.96318998
## 155 0.96133457
## 132 0.95747103
## 150 0.96343110
## 135 0.95880007
## 133 0.95682768
## 156 0.95816987
## 127 0.96395085
## 126 0.96323518
## 123 0.96458606
## 107 0.96374723
## 148 0.95549012
## 122 0.96250248
## 125 0.96158070
## 120 0.96205761
## 106 0.96248836
## 104 0.96216690
## 101 0.96249145
## 154 0.95175607
## 149 0.95477498
## 103 0.95994220
## 124 0.95868572
## 119 0.95974404
## 105 0.95959476
## 121 0.95979119
## 100 0.96015725
## 98 0.95971095
## 102 0.95865729
## 118 0.95813045
## 99 0.95845138
## 157 0.92691184
## 152 0.92656564
## 153 0.92740702
## 151 0.92245723
## 139 0.90092391
## 140 0.89681467
## 138 0.89451211
## 160 0.89348403
## 159 0.88615915
## 145 0.88828988
## 158 0.88840812
## 146 0.88852408
## 144 0.88796834
## 143 0.88187827
## 141 0.87945288
## 162 0.87982934
## 142 0.87351850
## 147 0.86777848
## 161 -0.27713966
## 171 0.97721662
## 166 0.97775066
## 172 0.97729128
## 169 0.97685656
## 190 0.97681006
## 192 0.97621096
## 187 0.97626971
## 191 0.97658984
## 188 0.97694910
## 185 0.97700215
## 164 0.97103182
## 167 0.97004422
## 170 0.97058939
## 163 0.97179683
## 168 0.97066098
## 165 0.97244423
## 183 0.97047833
## 189 0.96997583
## 186 0.96988565
## 200 0.96622848
## 202 0.96481783
## 184 0.97135107
## 203 0.96656744
## 205 0.96236251
## 207 0.96180532
## 206 0.96058375
## 214 0.96297466
## 198 0.95924027
## 201 0.95997622
## 199 0.95987900
## 217 0.95876631
## 204 0.95537639
## 215 0.96232299
## 197 0.96112098
## 181 0.96154950
## 196 0.96259619
## 182 0.96201967
## 195 0.96178345
## 178 0.96267524
## 213 0.95315202
## 194 0.95984705
## 180 0.95981964
## 177 0.96050222
## 175 0.96047229
## 179 0.95728194
## 174 0.95841985
## 193 0.95695916
## 176 0.95767380
## 173 0.95646768
## 216 0.92484107
## 210 0.89979397
## 208 0.89533549
## 209 0.89152233
## 218 0.88977124
## 212 0.88551150
## 211 0.87472709
## 223 0.97580352
## 228 0.97578094
## 226 0.97505460
## 224 0.97711567
## 227 0.97529000
## 221 0.97595501
## 238 0.97555378
## 235 0.97586320
## 237 0.97537485
## 236 0.97619740
## 219 0.96891235
## 222 0.96979078
## 225 0.96804980
## 220 0.97029462
## 241 0.96426412
## 234 0.96908514
## 242 0.96492513
## 243 0.96356072
## 244 0.96000913
## 246 0.96128600
## 240 0.95720296
## 233 0.95916563
## 239 0.95946231
## 231 0.96004708
## 232 0.96051394
## 230 0.95780484
## 229 0.95531628
## 245 0.89459341
## 250 0.97524102
## 248 0.97394625
## 251 0.97354290
## 249 0.97517985
## 253 0.97503172
## 247 0.96742875
## 254 0.96291220
## 252 0.95741087
## 255 0.97323179## [1] 255## mindex n predictors rsquare adjr rmse
## 255 255 8 LON NVD PVT VLV NSV NST TCA TVT 0.9854516 0.981572 0.103159Con el método de CP-Mallow se considera a las variables LON, NVD, PVT, VLV, NSV, NST, TCA, TVT como mejor modelo.
CP-Mallow
\[C_{p}=(\frac{SCRES_{c}}{\sigma
\hat{^{2}}})+2p_{c}-n\] Dónde:
p: Número de variables predictoras en el modelo
pc=p+1: Número de coeficientes estimados incluyendo el intercepto
## [1] 93## mindex n predictors rsquare adjr rmse
## 97 93 4 LON NVD PVT TVT 0.9845562 0.9827393 0.106286## [1] 2.846303con el criterio de CP - mallow se esta considerando a las variables (LON, NVD, PVT, TVT), para nuestro modelo.
SP de Hockings
\[hsp=\frac{CME}{n-pc-1}\]
## [1] 93## mindex n predictors rsquare adjr rmse
## 97 93 4 LON NVD PVT TVT 0.9845562 0.9827393 0.106286## [1] 0.0003926663Ya que con los criterios CP - Mallow y SP de Hockings coinciden en selección de variables creamos el modelo3
Ya que hemos determinado al modelo3 como el mejor modelo según los métodos antes mencionado, ahora debemos comprobar los supuestos para dar como válida dicho análisis.
Evaluación de supuestos.
##
## Shapiro-Wilk normality test
##
## data: modelo3$residuals
## W = 0.93018, p-value = 0.01821## Cargando paquete requerido: zoo##
## Adjuntando el paquete: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## studentized Breusch-Pagan test
##
## data: modelo3
## BP = 9.4944, df = 4, p-value = 0.04986##
## Durbin-Watson test
##
## data: modelo3
## DW = 2.2863, p-value = 0.8357
## alternative hypothesis: true autocorrelation is greater than 0Con el criterio de RMSE
##
## Shapiro-Wilk normality test
##
## data: modelo$residuals
## W = 0.9522, p-value = 0.09744##
## studentized Breusch-Pagan test
##
## data: modelo
## BP = 16.31, df = 8, p-value = 0.03815##
## Durbin-Watson test
##
## data: modelo
## DW = 2.2779, p-value = 0.8053
## alternative hypothesis: true autocorrelation is greater than 0se consideraría como mejor modelo al modelo con 4 variables, ya que por parcimonia tiene más variables significativas.
Determine el mejor modelo de regresión lineal y evalúe los supuestos de normalidad y homogeneidad de varianzas.
## Start: AIC=-159.18
## TAS ~ LON + NVD + PVT + VLV + NSV + NST + TCA + TVT
##
## Df Sum of Sq RSS AIC
## - NSV 1 0.000077 0.41511 -161.17
## - TCA 1 0.004044 0.41907 -160.80
## - VLV 1 0.004761 0.41979 -160.73
## - NST 1 0.012770 0.42780 -159.99
## <none> 0.41503 -159.18
## - NVD 1 0.021846 0.43688 -159.18
## - TVT 1 0.090545 0.50557 -153.48
## - LON 1 0.107805 0.52283 -152.17
## - PVT 1 0.306913 0.72194 -139.59
##
## Step: AIC=-161.17
## TAS ~ LON + NVD + PVT + VLV + NST + TCA + TVT
##
## Df Sum of Sq RSS AIC
## - TCA 1 0.003992 0.41910 -162.79
## - VLV 1 0.004752 0.41986 -162.72
## - NST 1 0.013058 0.42816 -161.96
## <none> 0.41511 -161.17
## - NVD 1 0.032804 0.44791 -160.20
## - TVT 1 0.092353 0.50746 -155.33
## - LON 1 0.140146 0.55525 -151.82
## - PVT 1 0.311101 0.72621 -141.36
##
## Step: AIC=-162.8
## TAS ~ LON + NVD + PVT + VLV + NST + TVT
##
## Df Sum of Sq RSS AIC
## - VLV 1 0.00227 0.42137 -164.58
## - NST 1 0.01747 0.43657 -163.20
## <none> 0.41910 -162.79
## - NVD 1 0.03130 0.45040 -161.99
## - TVT 1 0.08892 0.50802 -157.29
## - LON 1 0.13818 0.55727 -153.68
## - PVT 1 0.33616 0.75526 -141.83
##
## Step: AIC=-164.58
## TAS ~ LON + NVD + PVT + NST + TVT
##
## Df Sum of Sq RSS AIC
## - NST 1 0.01920 0.44057 -164.85
## <none> 0.42137 -164.58
## - NVD 1 0.02949 0.45086 -163.95
## - TVT 1 0.08999 0.51136 -159.04
## - LON 1 0.17519 0.59656 -153.03
## - PVT 1 0.33793 0.75930 -143.62
##
## Step: AIC=-164.85
## TAS ~ LON + NVD + PVT + TVT
##
## Df Sum of Sq RSS AIC
## <none> 0.44057 -164.85
## - NVD 1 0.02948 0.47005 -164.32
## - TVT 1 0.08608 0.52665 -159.89
## - LON 1 0.17950 0.62008 -153.52
## - PVT 1 0.32922 0.76980 -145.08##
## Call:
## lm(formula = TAS ~ LON + NVD + PVT + TVT, data = PD5)
##
## Coefficients:
## (Intercept) LON NVD PVT TVT2
## -1.40595 0.19940 0.07225 0.07794 -0.09514Usando otras funciones.
##
## Adjuntando el paquete: 'MASS'## The following object is masked from 'package:olsrr':
##
## cement## Start: AIC=-159.18
## TAS ~ LON + NVD + PVT + VLV + NSV + NST + TCA + TVT
##
## Df Sum of Sq RSS AIC
## - NSV 1 0.000077 0.41511 -161.17
## - TCA 1 0.004044 0.41907 -160.80
## - VLV 1 0.004761 0.41979 -160.73
## - NST 1 0.012770 0.42780 -159.99
## <none> 0.41503 -159.18
## - NVD 1 0.021846 0.43688 -159.18
## - TVT 1 0.090545 0.50557 -153.48
## - LON 1 0.107805 0.52283 -152.17
## - PVT 1 0.306913 0.72194 -139.59
##
## Step: AIC=-161.17
## TAS ~ LON + NVD + PVT + VLV + NST + TCA + TVT
##
## Df Sum of Sq RSS AIC
## - TCA 1 0.003992 0.41910 -162.79
## - VLV 1 0.004752 0.41986 -162.72
## - NST 1 0.013058 0.42816 -161.96
## <none> 0.41511 -161.17
## - NVD 1 0.032804 0.44791 -160.20
## - TVT 1 0.092353 0.50746 -155.33
## - LON 1 0.140146 0.55525 -151.82
## - PVT 1 0.311101 0.72621 -141.36
##
## Step: AIC=-162.8
## TAS ~ LON + NVD + PVT + VLV + NST + TVT
##
## Df Sum of Sq RSS AIC
## - VLV 1 0.00227 0.42137 -164.58
## - NST 1 0.01747 0.43657 -163.20
## <none> 0.41910 -162.79
## - NVD 1 0.03130 0.45040 -161.99
## - TVT 1 0.08892 0.50802 -157.29
## - LON 1 0.13818 0.55727 -153.68
## - PVT 1 0.33616 0.75526 -141.83
##
## Step: AIC=-164.58
## TAS ~ LON + NVD + PVT + NST + TVT
##
## Df Sum of Sq RSS AIC
## - NST 1 0.01920 0.44057 -164.85
## <none> 0.42137 -164.58
## - NVD 1 0.02949 0.45086 -163.95
## - TVT 1 0.08999 0.51136 -159.04
## - LON 1 0.17519 0.59656 -153.03
## - PVT 1 0.33793 0.75930 -143.62
##
## Step: AIC=-164.85
## TAS ~ LON + NVD + PVT + TVT
##
## Df Sum of Sq RSS AIC
## <none> 0.44057 -164.85
## - NVD 1 0.02948 0.47005 -164.32
## - TVT 1 0.08608 0.52665 -159.89
## - LON 1 0.17950 0.62008 -153.52
## - PVT 1 0.32922 0.76980 -145.08##
## Call:
## lm(formula = TAS ~ LON + NVD + PVT + TVT, data = PD5)
##
## Coefficients:
## (Intercept) LON NVD PVT TVT2
## -1.40595 0.19940 0.07225 0.07794 -0.09514##
##
## Stepwise Summary
## --------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## --------------------------------------------------------------------------
## 0 Full Model -46.499 -29.863 -151.956 0.98545 0.98157
## 1 NSV -48.491 -33.519 -155.173 0.98545 0.98216
## 2 TCA -50.118 -36.810 -157.828 0.98531 0.98255
## 3 VLV -51.907 -40.262 -160.469 0.98523 0.98299
## 4 NST -52.169 -42.188 -161.419 0.98456 0.98274
## --------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## ---------------------------------------------------------------
## R 0.992 RMSE 0.106
## R-Squared 0.985 MSE 0.013
## Adj. R-Squared 0.983 Coef. Var 2.380
## Pred R-Squared 0.979 AIC -52.169
## MAE 0.074 SBC -42.188
## ---------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## --------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------
## Regression 28.087 4 7.022 541.884 0.0000
## Residual 0.441 34 0.013
## Total 28.527 38
## --------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------
## (Intercept) -1.406 0.858 -1.638 0.111 -3.151 0.339
## LON 0.199 0.054 0.478 3.722 0.001 0.091 0.308
## NVD 0.072 0.048 0.124 1.508 0.141 -0.025 0.170
## PVT 0.078 0.015 0.409 5.041 0.000 0.047 0.109
## TVT2 -0.095 0.037 -0.055 -2.577 0.014 -0.170 -0.020
## ----------------------------------------------------------------------------------------## Start: AIC=-159.18
## TAS ~ LON + NVD + PVT + VLV + NSV + NST + TCA + TVT
##
## Df Sum of Sq RSS AIC
## - NSV 1 0.000077 0.41511 -161.17
## - TCA 1 0.004044 0.41907 -160.80
## - VLV 1 0.004761 0.41979 -160.73
## - NST 1 0.012770 0.42780 -159.99
## <none> 0.41503 -159.18
## - NVD 1 0.021846 0.43688 -159.18
## - TVT 1 0.090545 0.50557 -153.48
## - LON 1 0.107805 0.52283 -152.17
## - PVT 1 0.306913 0.72194 -139.59
##
## Step: AIC=-161.17
## TAS ~ LON + NVD + PVT + VLV + NST + TCA + TVT
##
## Df Sum of Sq RSS AIC
## - TCA 1 0.003992 0.41910 -162.79
## - VLV 1 0.004752 0.41986 -162.72
## - NST 1 0.013058 0.42816 -161.96
## <none> 0.41511 -161.17
## - NVD 1 0.032804 0.44791 -160.20
## + NSV 1 0.000077 0.41503 -159.18
## - TVT 1 0.092353 0.50746 -155.33
## - LON 1 0.140146 0.55525 -151.82
## - PVT 1 0.311101 0.72621 -141.36
##
## Step: AIC=-162.8
## TAS ~ LON + NVD + PVT + VLV + NST + TVT
##
## Df Sum of Sq RSS AIC
## - VLV 1 0.00227 0.42137 -164.58
## - NST 1 0.01747 0.43657 -163.20
## <none> 0.41910 -162.79
## - NVD 1 0.03130 0.45040 -161.99
## + TCA 1 0.00399 0.41511 -161.17
## + NSV 1 0.00003 0.41907 -160.80
## - TVT 1 0.08892 0.50802 -157.29
## - LON 1 0.13818 0.55727 -153.68
## - PVT 1 0.33616 0.75526 -141.83
##
## Step: AIC=-164.58
## TAS ~ LON + NVD + PVT + NST + TVT
##
## Df Sum of Sq RSS AIC
## - NST 1 0.01920 0.44057 -164.85
## <none> 0.42137 -164.58
## - NVD 1 0.02949 0.45086 -163.95
## + VLV 1 0.00227 0.41910 -162.79
## + TCA 1 0.00151 0.41986 -162.72
## + NSV 1 0.00004 0.42133 -162.59
## - TVT 1 0.08999 0.51136 -159.04
## - LON 1 0.17519 0.59656 -153.03
## - PVT 1 0.33793 0.75930 -143.62
##
## Step: AIC=-164.85
## TAS ~ LON + NVD + PVT + TVT
##
## Df Sum of Sq RSS AIC
## <none> 0.44057 -164.85
## + NST 1 0.01920 0.42137 -164.58
## - NVD 1 0.02948 0.47005 -164.32
## + VLV 1 0.00400 0.43657 -163.20
## + TCA 1 0.00379 0.43678 -163.18
## + NSV 1 0.00202 0.43855 -163.03
## - TVT 1 0.08608 0.52665 -159.89
## - LON 1 0.17950 0.62008 -153.52
## - PVT 1 0.32922 0.76980 -145.08##
## Call:
## lm(formula = TAS ~ LON + NVD + PVT + TVT, data = PD5)
##
## Coefficients:
## (Intercept) LON NVD PVT TVT2
## -1.40595 0.19940 0.07225 0.07794 -0.09514con el metodo de stepwise se considera el mejor modelo con las variables predictoras : LON, NVD, PVT Y TVT.
Quedando el modelo final con el metodo de stepwise
TAS = -1.40595 + 0.19940LON + 0.07225NVD + 0.07794PVT - 0.09514TVT2
Haciéndolo de manera tradicional.
\[\frac{\sum_{i = 1}^{n}E_{i}^{2}}{n}\]
modelo1 <- lm(TAS ~ PVT + LON, PD5)
n <- nrow(PD5) #numero de observaciones
MSE <- sum(modelo1$residuals**2) / n
MSE ## [1] 0.01451367Intentaremos hacerlo con la funcion ols_step_all_possible()
Creamos una columna con nombre MSE, sabiendo que es el RMSE^2.
modelo1 |> ols_step_all_possible()-> res_1
res_1$result -> metricas_1
RMSE_1 <- metricas_1[,6]
library(dplyr)##
## Adjuntando el paquete: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## [1] 3## [1] 0.01451367Llegamos a la misma respuesta haciendolo de manera tradicional y creando una nueva columna con la función ols_step_all_posible()
tme <- round(0.8*n) #tamaño de muestra de entrenamiento
tmp <- n - tme # tamaño de muestra de pruebasiempre que se hace una seleccion aleatoria se plantea una semilla set.seed(40)
## [1] 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 19 20 21 22 23 25 26 27 28 30
## [26] 32 34 35 37 38 39construimos nuestro modelo con nuestra “me”
##
## Call:
## lm(formula = TAS ~ LON + PVT, data = me)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.41567 -0.06980 0.01339 0.07239 0.33932
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.73959 0.90035 -0.821 0.418334
## LON 0.26088 0.03974 6.565 4.06e-07 ***
## PVT 0.07034 0.01810 3.887 0.000569 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1372 on 28 degrees of freedom
## Multiple R-squared: 0.9803, Adjusted R-squared: 0.9789
## F-statistic: 697.7 on 2 and 28 DF, p-value: < 2.2e-16y_estima<- predict(modelo_entre, data.frame(mp[,c(2,4)]))
ei<- mp$TAS-y_estima
MSE_prueba <- sum(ei**2)/tmp
MSE_prueba## [1] 0.00511619Crear iteracciones de manera automática
MSE <- c()
for(i in 1:1000){
ime <- sort(sample(n,tme))
me <- PD5[ime,]
mp <- PD5[-ime,]
modelo_entre<- lm(TAS~LON+PVT, data = me)
y_estima<- predict(modelo_entre, data.frame(mp[,c(2,4)]))
ei<- mp$TAS-y_estima
MSE[i]<- sum(ei**2)/tmp
}
mean(MSE)## [1] 0.01880616Cuando la muestra es más grande la media de los MSE no varía mucho,
por ello al crear las iteracciones, ello hará que no varíe mucho.
Se ajusta un modelo de regresión lineal en el conjunto de entrenamiento,
y se predicen los valores de la variable dependiente en el conjunto de
prueba.