library(wooldridge)
## Warning: package 'wooldridge' was built under R version 4.3.3
data(hpricel)
## Warning in data(hpricel): data set 'hpricel' not found
head(force(hprice1),n=5)

1. estimar el modelo

library(stargazer)
modelo_estimado<-lm("price~.",data = hprice1)
stargazer(modelo_estimado,title = "Modelo estimado", type = "text")
## 
## Modelo estimado
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                 NA             
## -----------------------------------------------
## assess                       1.233***          
##                               (0.097)          
##                                                
## bdrms                          2.652           
##                               (2.118)          
##                                                
## lotsize                       0.00003          
##                              (0.0003)          
##                                                
## sqrft                          0.008           
##                               (0.019)          
##                                                
## colonial                      -0.410           
##                               (3.390)          
##                                                
## lprice                      276.094***         
##                              (10.186)          
##                                                
## lassess                     -396.819***        
##                              (38.182)          
##                                                
## llotsize                       1.755           
##                               (5.791)          
##                                                
## lsqrft                        -3.954           
##                              (41.502)          
##                                                
## Constant                     606.372**         
##                              (246.442)         
##                                                
## -----------------------------------------------
## Observations                    88             
## R2                             0.986           
## Adjusted R2                    0.984           
## Residual Std. Error      12.921 (df = 78)      
## F Statistic           602.196*** (df = 9; 78)  
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

2.Verifique el supuesto de normalidad, a través de:

a) La prueba JB

library(tseries)
## Warning: package 'tseries' was built under R version 4.3.3
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
salida_JB<-jarque.bera.test(modelo_estimado$residuals)
salida_JB
## 
##  Jarque Bera Test
## 
## data:  modelo_estimado$residuals
## X-squared = 86.125, df = 2, p-value < 2.2e-16
library(fastGraph)
## Warning: package 'fastGraph' was built under R version 4.3.3
alpha_sig<-0.05
JB<-salida_JB$statistic
gl<-salida_JB$parameter
VC<-qchisq(1-alpha_sig,gl,lower.tail = TRUE)
shadeDist(JB,ddist = "dchisq",
          parm1 = gl,
          lower.tail = FALSE,xmin = 0,
          sub=paste("VC:",round(VC,2)," ","JB:",round(JB,2)))

b) La prueba KS

library(dplyr)  # Carga la librería dplyr para manipulación de datos
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(gt)  # Carga la librería gt para crear tablas de datos
## Warning: package 'gt' was built under R version 4.3.3
library(gtExtras)  # Carga la librería gtExtras para agregar funcionalidades a las tablas creadas con gt
## Warning: package 'gtExtras' was built under R version 4.3.3
residuos<-modelo_estimado$residuals  # Crea un vector con los residuos del modelo estimado
residuos %>%  # Utiliza el operador %>% para encadenar las operaciones siguientes al vector residuos
  as_tibble() %>%  # Convierte el vector residuos en una tibble (tabla) de una columna
  mutate(posicion=row_number()) %>%  # Agrega una columna llamada "posicion" con el número de fila
  arrange(value) %>%  # Ordena la tabla por los valores de residuos en orden ascendente
  mutate(dist1=row_number()/n()) %>%  # Agrega una columna "dist1" con los percentiles según su posición en la tabla (usando la función row_number() y n() para obtener el número de filas)
  mutate(dist2=(row_number()-1)/n()) %>%  # Agrega una columna "dist2" con los percentiles según su posición en la tabla, pero ajustando en una unidad para evitar problemas con los extremos de la distribución
  mutate(zi=as.vector(scale(value,center=TRUE))) %>%  # Agrega una columna "zi" con los valores de residuos escalados para tener media cero y varianza uno
  mutate(pi=pnorm(zi,lower.tail = TRUE)) %>%  # Agrega una columna "pi" con los valores de la función de distribución acumulada (CDF) de una distribución normal estándar evaluada en los valores de zi
  mutate(dif1=abs(dist1-pi)) %>%  # Agrega una columna "dif1" con las diferencias absolutas entre los percentiles según la posición y los valores de pi
  mutate(dif2=abs(dist2-pi)) %>%  # Agrega una columna "dif2" con las diferencias absolutas entre los percentiles ajustados según la posición y los valores de pi
  rename(residuales=value) -> tabla_KS  # Renombra la columna "value" como "residuales" y asigna la tabla resultante a la variable tabla_KS


#Formato
 tabla_KS %>%  # Utiliza el operador %>% para encadenar las operaciones siguientes a la tabla tabla_KS
  gt() %>%  # Crea una tabla con la función gt()
  tab_header("Tabla para calcular el Estadistico KS") %>%  # Agrega un encabezado a la tabla
  tab_source_note(source_note = "Fuente: Elaboración propia") %>%  # Agrega una nota de fuente a la tabla
  tab_style(  # Cambia el estilo de algunas celdas de la tabla
    style = list(
      cell_fill(color = "#A569BD"),  # Cambia el color de fondo de las celdas a un tono de morado
      cell_text(style = "italic")  # Cambia el estilo de texto de las celdas a itálico
      ),
    locations = cells_body(  # Aplica el estilo a las celdas del cuerpo de la tabla que cumplan las siguientes condiciones:
      columns = dif1,  # Que pertenezcan a la columna "dif1"
      rows = dif1==max(dif1)  # Que pertenezcan a la fila donde el valor de "dif1" es máximo
    )) %>%
   tab_style(  # Cambia el estilo de algunas celdas de la tabla
    style = list(
      cell_fill(color = "#3498DB"),  # Cambia el color de fondo de las celdas a un tono de azul
      cell_text(style = "italic")  # Cambia el estilo de texto de las celdas a itálico
      ),
    locations = cells_body(  # Aplica el estilo a las celdas del cuerpo de la tabla que cumplan las siguientes condiciones:
      columns = dif2,  # Que pertenezcan a la columna "dif2"
      rows = dif2==max(dif2)  # Que pertenezcan a la fila donde el valor de "dif2" es máximo
    ))
Tabla para calcular el Estadistico KS
residuales posicion dist1 dist2 zi pi dif1 dif2
-41.2989150 68 0.01136364 0.00000000 -3.375648564 0.0003682096 1.099543e-02 0.0003682096
-23.3204472 53 0.02272727 0.01136364 -1.906142909 0.0283158335 5.588561e-03 0.0169521971
-22.5628916 69 0.03409091 0.02272727 -1.844222609 0.0325753524 1.515557e-03 0.0098480796
-20.9181052 37 0.04545455 0.03409091 -1.709782732 0.0436530287 1.801517e-03 0.0095621196
-20.1036293 12 0.05681818 0.04545455 -1.643209930 0.0501697531 6.648429e-03 0.0047152076
-19.6482343 48 0.06818182 0.05681818 -1.605987318 0.0541383482 1.404347e-02 0.0026798336
-18.9942513 31 0.07954545 0.06818182 -1.552532727 0.0602674041 1.927805e-02 0.0079144141
-18.3298397 44 0.09090909 0.07954545 -1.498225730 0.0670373064 2.387178e-02 0.0125081481
-16.4864218 33 0.10227273 0.09090909 -1.347550322 0.0889015289 1.337120e-02 0.0020075620
-12.8744141 66 0.11363636 0.10227273 -1.052315718 0.1463273614 3.269100e-02 0.0440546341
-11.0038306 16 0.12500000 0.11363636 -0.899419872 0.1842145291 5.921453e-02 0.0705781654
-10.0332997 36 0.13636364 0.12500000 -0.820091612 0.2060819418 6.971831e-02 0.0810819418
-9.6484892 63 0.14772727 0.13636364 -0.788638365 0.2151617004 6.743443e-02 0.0787980641
-8.6214495 25 0.15909091 0.14772727 -0.704691238 0.2405012026 8.141029e-02 0.0927739299
-8.6137642 32 0.17045455 0.15909091 -0.704063066 0.2406967499 7.024220e-02 0.0816058408
-7.5049668 57 0.18181818 0.17045455 -0.613433313 0.2697949324 8.797675e-02 0.0993403869
-6.7752121 46 0.19318182 0.18181818 -0.553785374 0.2898628694 9.668105e-02 0.1080446876
-6.7305352 82 0.20454545 0.19318182 -0.550133615 0.2911138660 8.656841e-02 0.0979320479
-6.5480845 88 0.21590909 0.20454545 -0.535220644 0.2962486463 8.033956e-02 0.0917031918
-6.3671194 34 0.22727273 0.21590909 -0.520429109 0.3013822628 7.410954e-02 0.0854731719
-4.7071332 75 0.23863636 0.22727273 -0.384746848 0.3502124911 1.115761e-01 0.1229397639
-4.1467978 77 0.25000000 0.23863636 -0.338946729 0.3673249306 1.173249e-01 0.1286885670
-4.1068770 13 0.26136364 0.25000000 -0.335683718 0.3685546927 1.071911e-01 0.1185546927
-3.9417052 29 0.27272727 0.26136364 -0.322183078 0.3736570015 1.009297e-01 0.1122933652
-3.5767192 3 0.28409091 0.27272727 -0.292350226 0.3850094303 1.009185e-01 0.1122821576
-3.3545986 65 0.29545455 0.28409091 -0.274194755 0.3919674794 9.651293e-02 0.1078765704
-3.0586260 72 0.30681818 0.29545455 -0.250002848 0.4012925732 9.447439e-02 0.1058380277
-2.8256330 1 0.31818182 0.30681818 -0.230958704 0.4086734420 9.049162e-02 0.1018552602
-2.5550806 49 0.32954545 0.31818182 -0.208844568 0.4172847890 8.773933e-02 0.0991029708
-2.5206267 87 0.34090909 0.32954545 -0.206028415 0.4183843579 7.747527e-02 0.0888389033
-2.4270263 9 0.35227273 0.34090909 -0.198377799 0.4213747431 6.910202e-02 0.0804656522
-2.2831744 10 0.36363636 0.35227273 -0.186619778 0.4259793795 6.234302e-02 0.0737066522
-2.1248700 80 0.37500000 0.36363636 -0.173680459 0.4310582977 5.605830e-02 0.0674219341
-1.8079549 79 0.38636364 0.37500000 -0.147776775 0.4412594694 5.489583e-02 0.0662594694
-1.7304233 11 0.39772727 0.38636364 -0.141439575 0.4437613463 4.603407e-02 0.0573977099
-1.3793116 43 0.40909091 0.39772727 -0.112740766 0.4551180405 4.602713e-02 0.0573907678
-1.3107578 15 0.42045455 0.40909091 -0.107137381 0.4573399961 3.688545e-02 0.0482490871
-0.9841003 85 0.43181818 0.42045455 -0.080437384 0.4679446975 3.612652e-02 0.0474901520
-0.8218197 55 0.44318182 0.43181818 -0.067173057 0.4732219670 3.004015e-02 0.0414037852
-0.7654623 58 0.45454545 0.44318182 -0.062566579 0.4750558216 2.051037e-02 0.0318740034
-0.1756014 67 0.46590909 0.45454545 -0.014353127 0.4942741275 2.836504e-02 0.0397286730
-0.1165840 56 0.47727273 0.46590909 -0.009529222 0.4961984478 1.892572e-02 0.0302893569
0.1503223 62 0.48863636 0.47727273 0.012286888 0.5049016357 1.626527e-02 0.0276289085
0.2850896 19 0.50000000 0.48863636 0.023302361 0.5092954558 9.295456e-03 0.0206590921
0.4808659 60 0.51136364 0.50000000 0.039304530 0.5156762025 4.312566e-03 0.0156762025
0.7404134 27 0.52272727 0.51136364 0.060519159 0.5241289212 1.401649e-03 0.0127652849
0.8431883 83 0.53409091 0.52272727 0.068919665 0.5274732175 6.617692e-03 0.0047459448
1.0116768 50 0.54545455 0.53409091 0.082691410 0.5329515422 1.250300e-02 0.0011393669
1.0651444 73 0.55681818 0.54545455 0.087061687 0.5346887605 2.212942e-02 0.0107657849
1.4331671 26 0.56818182 0.55681818 0.117142748 0.5466265325 2.155529e-02 0.0101916493
1.5478694 21 0.57954545 0.56818182 0.126518170 0.5503391163 2.920634e-02 0.0178427019
1.6330240 54 0.59090909 0.57954545 0.133478451 0.5530924971 3.781659e-02 0.0264529574
1.7791547 22 0.60227273 0.59090909 0.145422733 0.5578114415 4.446129e-02 0.0330976494
1.9280651 17 0.61363636 0.60227273 0.157594218 0.5626117200 5.102464e-02 0.0396610072
2.0434993 64 0.62500000 0.61363636 0.167029459 0.5663265653 5.867343e-02 0.0473097983
2.4686017 4 0.63636364 0.62500000 0.201776043 0.5799540943 5.640954e-02 0.0450459057
2.5455524 20 0.64772727 0.63636364 0.208065761 0.5824111895 6.531608e-02 0.0539524469
2.6803507 59 0.65909091 0.64772727 0.219083766 0.5867076018 7.238331e-02 0.0610196709
2.7600191 41 0.67045455 0.65909091 0.225595625 0.5892420282 8.121252e-02 0.0698488808
3.1473027 51 0.68181818 0.67045455 0.257251019 0.6015074992 8.031068e-02 0.0689470463
3.1719704 7 0.69318182 0.68181818 0.259267282 0.6022854892 9.089633e-02 0.0795326926
3.2162912 47 0.70454545 0.69318182 0.262889931 0.6036822914 1.008632e-01 0.0894995268
3.3807103 78 0.71590909 0.70454545 0.276329048 0.6088523263 1.070568e-01 0.0956931282
3.5031146 52 0.72727273 0.71590909 0.286334010 0.6126888439 1.145839e-01 0.1032202470
3.6694580 18 0.73863636 0.72727273 0.299930414 0.6178848825 1.207515e-01 0.1093878448
4.5321986 70 0.75000000 0.73863636 0.370448226 0.6444757267 1.055243e-01 0.0941606370
4.5920714 84 0.76136364 0.75000000 0.375342048 0.6462969509 1.150667e-01 0.1037030491
5.3185296 74 0.77272727 0.76136364 0.434720546 0.6681173584 1.046099e-01 0.0932462780
5.4787177 30 0.78409091 0.77272727 0.447813834 0.6728562208 1.112347e-01 0.0998710519
6.0680656 28 0.79545455 0.78409091 0.495985351 0.6900476267 1.054069e-01 0.0940432824
6.1464676 8 0.80681818 0.79545455 0.502393691 0.6923046921 1.145135e-01 0.1031498533
7.0166330 40 0.81818182 0.80681818 0.573518388 0.7168531237 1.013287e-01 0.0899650581
7.8700740 23 0.82954545 0.81818182 0.643276078 0.7399775122 8.956794e-02 0.0782043060
8.0367148 86 0.84090909 0.82954545 0.656896792 0.7443763594 9.653273e-02 0.0851690952
8.0592050 35 0.85227273 0.84090909 0.658735073 0.7449670468 1.073057e-01 0.0959420441
8.1208002 14 0.86363636 0.85227273 0.663769681 0.7465811333 1.170552e-01 0.1056915939
8.1761378 61 0.87500000 0.86363636 0.668292810 0.7480266491 1.269734e-01 0.1156097145
8.1833683 45 0.88636364 0.87500000 0.668883803 0.7482151985 1.381484e-01 0.1267848015
8.7462391 39 0.89772727 0.88636364 0.714891164 0.7626618512 1.350654e-01 0.1237017851
10.1459482 71 0.90909091 0.89772727 0.829299156 0.7965324259 1.125585e-01 0.1011948469
10.8897858 5 0.92045455 0.90909091 0.890098200 0.8132934202 1.071611e-01 0.0957974889
11.3520843 24 0.93181818 0.92045455 0.927885078 0.8232664073 1.085518e-01 0.0971881382
13.0234074 2 0.94318182 0.93181818 1.064493978 0.8564475096 8.673431e-02 0.0753706722
23.7752790 6 0.95454545 0.94318182 1.943319493 0.9740112161 1.946576e-02 0.0308293980
24.7262254 76 0.96590909 0.95454545 2.021046976 0.9783625488 1.245346e-02 0.0238170942
26.3001756 38 0.97727273 0.96590909 2.149696908 0.9842104014 6.937674e-03 0.0183013105
31.5993386 42 0.98863636 0.97727273 2.582834491 0.9951003840 6.464020e-03 0.0178276567
53.4624652 81 1.00000000 0.98863636 4.369860414 0.9999937837 6.216299e-06 0.0113574201
Fuente: Elaboración propia 
D<-max(max(tabla_KS$dif1),max(tabla_KS$dif2))
print(D)
## [1] 0.1381484

Conclusion:

En este caso dado que 0.1381484 < 0.875897 No se rechaza la Hipótesis Nula: ϵ∼N(0,σ2), por lo que los residuos siguen una distribución normal.

library(nortest)
prueba_KS<-lillie.test(modelo_estimado$residuals)
prueba_KS
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  modelo_estimado$residuals
## D = 0.13815, p-value = 0.0002732
p.value<-prueba_KS$p.value

c) La prueba SW

library(dplyr)
library(gt)
residuos<-modelo_estimado$residuals
residuos %>%  
  as_tibble() %>%
  rename(residuales=value) %>%
  arrange(residuales) %>%
  mutate(pi=(row_number()-0.375)/(n()+0.25)) %>%
  mutate(mi=qnorm(pi,lower.tail = TRUE)) %>% 
  mutate(ai=0)->tabla_SW

m<-sum(tabla_SW$mi^2)
n<-nrow(hprice1)
theta<-1/sqrt(n)
tabla_SW$ai[n]<- -2.706056*theta^5+4.434685*theta^4-2.071190*theta^3-0.147981*theta^2+0.2211570*theta+tabla_SW$mi[n]/sqrt(m)
tabla_SW$ai[n-1]<- -3.582633*theta^5+5.682633*theta^4-1.752461*theta^3-0.293762*theta^2+0.042981*theta+tabla_SW$mi[n-1]/sqrt(m)
tabla_SW$ai[1]<- -tabla_SW$ai[n]
tabla_SW$ai[2]<- -tabla_SW$ai[n-1]
omega<-(m-2*tabla_SW$mi[n]^2-2*tabla_SW$mi[n-1]^2)/(1-2*tabla_SW$ai[n]^2-2*tabla_SW$ai[n-1]^2)
tabla_SW$ai[3:(n-2)]<-tabla_SW$mi[3:(n-2)]/sqrt(omega)

tabla_SW %>% 
  mutate(ai_ui=ai*residuales,ui2=residuales^2) ->tabla_SW

tabla_SW %>%
  gt() %>% tab_header("Tabla para calcular el Estadistico W") %>%  # Agrega un encabezado a la tabla
  tab_source_note(source_note = "Fuente: Elaboración propia")
Tabla para calcular el Estadistico W
residuales pi mi ai ai_ui ui2
-41.2989150 0.007082153 -2.45306927 -0.286093929 11.8153688426 1.705600e+03
-23.3204472 0.018413598 -2.08767462 -0.226331231 5.2781455054 5.438433e+02
-22.5628916 0.029745042 -1.88455395 -0.201511408 4.5466800637 5.090841e+02
-20.9181052 0.041076487 -1.73832835 -0.185875811 3.8881697572 4.375671e+02
-20.1036293 0.052407932 -1.62194155 -0.173430814 3.4865887894 4.041559e+02
-19.6482343 0.063739377 -1.52411994 -0.162970954 3.2020914774 3.860531e+02
-18.9942513 0.075070822 -1.43903134 -0.153872609 2.9226949969 3.607816e+02
-18.3298397 0.086402266 -1.36324747 -0.145769197 2.6719260222 3.359830e+02
-16.4864218 0.097733711 -1.29457343 -0.138426027 2.2821498734 2.718021e+02
-12.8744141 0.109065156 -1.23151500 -0.131683320 1.6953455908 1.657505e+02
-11.0038306 0.120396601 -1.17300649 -0.125427129 1.3801788730 1.210843e+02
-10.0332997 0.131728045 -1.11825971 -0.119573169 1.1997134451 1.006671e+02
-9.6484892 0.143059490 -1.06667420 -0.114057239 1.1004800454 9.309334e+01
-8.6214495 0.154390935 -1.01778137 -0.108829231 0.9382657131 7.432939e+01
-8.6137642 0.165722380 -0.97120790 -0.103849228 0.8945327592 7.419693e+01
-7.5049668 0.177053824 -0.92665123 -0.099084876 0.7436286973 5.632453e+01
-6.7752121 0.188385269 -0.88386232 -0.094509548 0.6403222346 4.590350e+01
-6.7305352 0.199716714 -0.84263354 -0.090101040 0.6064282202 4.530010e+01
-6.5480845 0.211048159 -0.80278966 -0.085840618 0.5620916168 4.287741e+01
-6.3671194 0.222379603 -0.76418130 -0.081712307 0.5202720168 4.054021e+01
-4.7071332 0.233711048 -0.72667986 -0.077702356 0.3657553367 2.215710e+01
-4.1467978 0.245042493 -0.69017366 -0.073798824 0.3060288053 1.719593e+01
-4.1068770 0.256373938 -0.65456498 -0.069991263 0.2874455070 1.686644e+01
-3.9417052 0.267705382 -0.61976766 -0.066270458 0.2612186106 1.553704e+01
-3.5767192 0.279036827 -0.58570518 -0.062628228 0.2240035887 1.279292e+01
-3.3545986 0.290368272 -0.55230918 -0.059057264 0.1981134138 1.125333e+01
-3.0586260 0.301699717 -0.51951819 -0.055550992 0.1699097071 9.355193e+00
-2.8256330 0.313031161 -0.48727661 -0.052103467 0.1472252757 7.984202e+00
-2.5550806 0.324362606 -0.45553386 -0.048709282 0.1244561405 6.528437e+00
-2.5206267 0.335694051 -0.42424369 -0.045363489 0.1143444238 6.353559e+00
-2.4270263 0.347025496 -0.39336354 -0.042061540 0.1020844645 5.890457e+00
-2.2831744 0.358356941 -0.36285409 -0.038799229 0.0885854047 5.212885e+00
-2.1248700 0.369688385 -0.33267878 -0.035572645 0.0755872484 4.515073e+00
-1.8079549 0.381019830 -0.30280344 -0.032378138 0.0585382146 3.268701e+00
-1.7304233 0.392351275 -0.27319601 -0.029212277 0.0505496052 2.994365e+00
-1.3793116 0.403682720 -0.24382619 -0.026071824 0.0359611692 1.902501e+00
-1.3107578 0.415014164 -0.21466524 -0.022953704 0.0300867461 1.718086e+00
-0.9841003 0.426345609 -0.18568573 -0.019854987 0.0195392978 9.684534e-01
-0.8218197 0.437677054 -0.15686137 -0.016772858 0.0137842642 6.753876e-01
-0.7654623 0.449008499 -0.12816677 -0.013704604 0.0104903585 5.859326e-01
-0.1756014 0.460339943 -0.09957734 -0.010647596 0.0018697326 3.083585e-02
-0.1165840 0.471671388 -0.07106908 -0.007599268 0.0008859529 1.359182e-02
0.1503223 0.483002833 -0.04261848 -0.004557105 -0.0006850343 2.259678e-02
0.2850896 0.494334278 -0.01420234 -0.001518626 -0.0004329445 8.127607e-02
0.4808659 0.505665722 0.01420234 0.001518626 0.0007302556 2.312321e-01
0.7404134 0.516997167 0.04261848 0.004557105 0.0033741415 5.482121e-01
0.8431883 0.528328612 0.07106908 0.007599268 0.0064076139 7.109665e-01
1.0116768 0.539660057 0.09957734 0.010647596 0.0107719266 1.023490e+00
1.0651444 0.550991501 0.12816677 0.013704604 0.0145973828 1.134533e+00
1.4331671 0.562322946 0.15686137 0.016772858 0.0240383072 2.053968e+00
1.5478694 0.573654391 0.18568573 0.019854987 0.0307329262 2.395900e+00
1.6330240 0.584985836 0.21466524 0.022953704 0.0374839503 2.666767e+00
1.7791547 0.596317280 0.24382619 0.026071824 0.0463858081 3.165392e+00
1.9280651 0.607648725 0.27319601 0.029212277 0.0563231721 3.717435e+00
2.0434993 0.618980170 0.30280344 0.032378138 0.0661647023 4.175889e+00
2.4686017 0.630311615 0.33267878 0.035572645 0.0878146910 6.093994e+00
2.5455524 0.641643059 0.36285409 0.038799229 0.0987654678 6.479837e+00
2.6803507 0.652974504 0.39336354 0.042061540 0.1127396768 7.184280e+00
2.7600191 0.664305949 0.42424369 0.045363489 0.1252040980 7.617706e+00
3.1473027 0.675637394 0.45553386 0.048709282 0.1533028568 9.905514e+00
3.1719704 0.686968839 0.48727661 0.052103467 0.1652706584 1.006140e+01
3.2162912 0.698300283 0.51951819 0.055550992 0.1786681696 1.034453e+01
3.3807103 0.709631728 0.55230918 0.059057264 0.1996555004 1.142920e+01
3.5031146 0.720963173 0.58570518 0.062628228 0.2193938641 1.227181e+01
3.6694580 0.732294618 0.61976766 0.066270458 0.2431766631 1.346492e+01
4.5321986 0.743626062 0.65456498 0.069991263 0.3172143073 2.054082e+01
4.5920714 0.754957507 0.69017366 0.073798824 0.3388894739 2.108712e+01
5.3185296 0.766288952 0.72667986 0.077702356 0.4132622799 2.828676e+01
5.4787177 0.777620397 0.76418130 0.081712307 0.4476786605 3.001635e+01
6.0680656 0.788951841 0.80278966 0.085840618 0.5208864993 3.682142e+01
6.1464676 0.800283286 0.84263354 0.090101040 0.5538031197 3.777906e+01
7.0166330 0.811614731 0.88386232 0.094509548 0.6631388126 4.923314e+01
7.8700740 0.822946176 0.92665123 0.099084876 0.7798053058 6.193807e+01
8.0367148 0.834277620 0.97120790 0.103849228 0.8346066255 6.458878e+01
8.0592050 0.845609065 1.01778137 0.108829231 0.8770770798 6.495079e+01
8.1208002 0.856940510 1.06667420 0.114057239 0.9262360559 6.594740e+01
8.1761378 0.868271955 1.11825971 0.119573169 0.9776467141 6.684923e+01
8.1833683 0.879603399 1.17300649 0.125427129 1.0264163848 6.696752e+01
8.7462391 0.890934844 1.23151500 0.131683320 1.1517338019 7.649670e+01
10.1459482 0.902266289 1.29457343 0.138426027 1.4044632937 1.029403e+02
10.8897858 0.913597734 1.36324747 0.145769197 1.5873953403 1.185874e+02
11.3520843 0.924929178 1.43903134 0.153872609 1.7467748206 1.288698e+02
13.0234074 0.936260623 1.52411994 0.162970954 2.1224371189 1.696091e+02
23.7752790 0.947592068 1.62194155 0.173430814 4.1233660018 5.652639e+02
24.7262254 0.958923513 1.73832835 0.185875811 4.5960071921 6.113862e+02
26.3001756 0.970254958 1.88455395 0.201511408 5.2997854104 6.916992e+02
31.5993386 0.981586402 2.08767462 0.226331231 7.1519172024 9.985182e+02
53.4624652 0.992917847 2.45306927 0.286093929 15.2952866999 2.858235e+03
Fuente: Elaboración propia

Calculo del estadistico W

W<-(sum(tabla_SW$ai_ui)^2)/sum(tabla_SW$ui2)
print(W)
## [1] 0.8973197

Cálculo del Wn y su p value

mu<-0.0038915*log(n)^3-0.083751*log(n)^2-0.31082*log(n)-1.5861
sigma<-exp(0.0030302*log(n)^2-0.082676*log(n)-0.4803)
Wn<-(log(1-W)-mu)/sigma
print(Wn)
## [1] 4.474404
p.value<-pnorm(Wn,lower.tail = FALSE)
print(p.value)
## [1] 3.831244e-06
library(fastGraph)
shadeDist(Wn,ddist = "dnorm",lower.tail = FALSE)

Conclusion:

En este caso dado que 3.831244 > 0.05 No se rechaza la Hipótesis Nula: ϵ∼N(0,σ2), por lo que los residuos siguen una distribución normal.

salida_SW<-shapiro.test(modelo_estimado$residuals)
print(salida_SW)
## 
##  Shapiro-Wilk normality test
## 
## data:  modelo_estimado$residuals
## W = 0.89732, p-value = 3.831e-06